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Adult Literacy Fundamental Mathematics: Book 4 - 2nd Edition by Katherine Arendt; Mercedes de la Nuez; and Liz Girard is licensed under a Creative Commons Attribution 4.0 International License, except where otherwise noted.
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Content edits to the 2nd Edition were made by Katherine Arendt and Mercedes de la Nuez.
Originally prepared by Liz Girard. Revised and reduced in 2013 by Mercedes de la Nuez.
This book is based on the work of Leslie Tenta (1993), Marjorie E. Enns (1983), and Steve Ballantyne, Lynne Cannon, James Hooten, Kate Nonesuch (1994).
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1
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3
Adult Literacy Fundamental Mathematics: Book 4 – 2nd Edition by Katherine Arendt, Mercedes de la Nuez, and Liz Girard was funded by BCcampus Open Education.
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4
Welcome to Adult Literacy Fundamental Mathematics: Book 4.
You have the skills you need to be a strong student in this class. Your instructor knows this because you have passed the Adult Literacy Fundamental Mathematics Level 3 class, or you have been assessed into this level.
Adult math learners have many skills. They have a lot of life experience. They also use math in their everyday lives. This means that adult math learners may already know some of what is being taught in this book. Use what you already know with confidence!
This textbook has:
You have also been given a sheet to write down your grades. After each test, you can write in the mark. This way you can keep track of your grades as you go through the course. This is a good idea to use in all your courses.
Unit | Practice Test | Date of Test A | Test A | Date of Test B | Test B |
---|---|---|---|---|---|
Example | September 4, 2020 | 25/33 | September 7, 2020 | 25/33 | |
1 | |||||
2 | |||||
3 | |||||
4 | |||||
5 | |||||
6 | |||||
Final Test |
5
Emotions, or what we feel about something, play a big part in how we learn. If we are calm, we learn well. If we are afraid or stressed, we do not learn as well.
Many people are afraid of math. They fear making a mistake. “Math anxiety” is the fear of math. People who suffer from math anxiety may get headaches, sick stomachs, cold hands, or they may just sweat a lot or just feel scared. Math anxiety can happen for a few different reasons:
Math anxiety is a learned habit. If it is learned, it can be unlearned. Most math anxiety comes from bad memories while learning math. It may be from doing badly on a test or asking a question then being made fun of. These bad memories can make learning math hard.
Everyone can learn math. There is no special talent for math. There are some people who are better at math than others, but even these people had to learn to be good at math.
Read the list below and put a check mark beside the ones you feel when thinking about or doing math.
If you answered yes to two or more of these items, you may have math anxiety.
If you have math anxiety, a first step to understanding it is to look at where it all started.
Make a list of your experiences with learning math. Think back to the first math experiences you had and write about them. Think about learning math in school from the younger grades to the higher grades and write about your experiences and feelings. Include this class and how you are feeling right now about learning math.
Beside each experience, write if it was a positive or negative experience.
Look at the examples below to give you an idea:
Positive or negative? | Math experience |
---|---|
Negative | My teacher in elementary school lined the whole class up in a row and made us play a multiplication game. I could see which question was mine, and I didn’t know the answer so I had to figure it out on my fingers before my turn came up. I got the answer right, but I was so nervous that I would be teased because I didn’t know the answer off the top of my head. I still don’t know my times tables. |
Positive | In high school, I could use a calculator to figure out the simple multiplication problems, and then I could figure out the tougher problems without worrying about knowing my times tables. |
Negative | Now that I am upgrading my math, I feel nervous every time I even think about opening the book. I want to get all the answers right, and I know that I won’t be able to. I really need everything to be right so that I know that I am getting it. |
Once you have made a list of experiences, go over the stories with your instructor, or by yourself and try to find some common themes.
Hopefully by examining the beginnings of the anxiety, you can feel more in control of it.
Anyone can feel anxiety that will slow down learning. The key to learning is to be the “boss” of your anxiety. Here are an overview of some strategies that may help deal with your anxiety:
Remember, learning to deal with your math anxiety may take some time. It took you a long time to learn math anxiety, so it will take some time to overcome it.
One way to be the “boss” is to relax. Try this breathing exercise.
Breathing Exercise
Start by breathing slowly to the count of four. It may help to close your eyes and count.
Now hold your breath for four counts and then let your breath out slowly to the count of four.
The counting is silent and should follow this pattern: “Breath in, two, three, four. Hold, two, three, four. Breath out, two, three, four. Wait, two, three, four.”
With practice, the number of counts can be increased. This is an easy and good way to relax.
Now, try this exercise quietly and repeat it five times slowly.
Each time you feel anxious about learning, use the breathing exercise to help calm yourself. Ask yourself if what you tried worked. Do you feel calmer?
Another way to be the “boss” is to give yourself positive math messages.
Read and think about the positive math messages listed below. Do you say any of those things to yourself?
I like math.
I am good at math.
I understand math.
I can relax when I am studying math.
I am capable of learning math.
Math is my friend.
My math improves every day.
I am relaxed, calm and confident when I study math.
I understand math when I give myself a chance.
Math is creative.
Pick three statements that you like and say them to yourself as much as you can in each day. You can also write the statements out on paper and post them around your house so that you read them throughout the day.
Look at the Table of Contents in the front of your textbook. It tells you what you will be learning. You may see some things that you already know, some things that you may have forgotten, and some things that are new to you.
Flip the pages. You can see that the textbook is split into units. Each unit is something to learn.
Each unit has exercises to do. Notice the answers are at the end of the exercise. You can check your answers as soon as you are done. You can also check your answer before moving on if are not sure if you are doing the question right.
At the end of each unit is a self-test. It is a chance for you to see how well you have learned the skills in the unit. If you do well, you can move on. If you don’t do well, you can go back and practice those skills.
Knowing your textbook gives you a good skill. If you get frustrated, you can use the Table of Contents to go back and find some help.
There are four reasons people are anxious when writing tests. Any of the four reasons listed below might be the reason a person might feel anxious in a test-taking situation.
Here is an explanation of each reason and how to work your way out of the anxiety you may feel during tests.
Many students feel anxiety about taking math tests because they do not feel prepared for the test. To feel prepared, a student needs to have studied the work and know that they can do the problems they will be given. Get help from your classmates, friends, or your instructor to find out how you can improve your study habits.
Getting ready for a test starts on the first day of class. Everything you do in class and at home is part of that getting ready.
Here are some strategies students should know about how to write a test to do the best as possible on it:
There are many reasons why a student may feel mental pressure when writing a test. Listed below are a few main reasons:
When students feel this kind of pressure, it is very hard to feel calm and relaxed about a test. The key to success in a math test is to keep the anxiety at a manageable level. You can do this in two ways:
When your body and mind are healthy, you will have a better chance of doing well on a test. Eat well, drink plenty of water and get daily exercise. The better you feel, the better you can perform (and a test is a performance!).
I
1
This is the beginning of an adventure with numbers that represent part of the whole thing. These numbers can be shown in a few different ways:
Fraction name | Example |
---|---|
Decimal fraction | 0.50 |
Common fraction | or |
Percent fraction | 50% |
When we talk about fractions in any of the three ways listed above, we are talking about numbers in relation to the whole thing. What do we mean by “the whole thing”? We mean one complete thing.
An example would be one full jug of juice. That is 1 whole thing.
Once someone starts taking some juice, less than the whole thing remains. Now, half of the juice is gone.The remaining amount can be written as
Now almost all the juice has been taken.
The remaining amount can be written as
Now there are two full jugs of juice. This shows two whole things.
A fraction does not tell us much unless we know what the fraction is part of—we need to know exactly what the whole thing is! If someone says to you, “Sure, let’s go! I still have half!” you really need to know, “Half of what?”
The answer could be a tank of gas, or a paycheque, or a vacation, or an hour.
Decimal fractions are one way to consider parts of the whole thing. The whole thing = 1.
You use decimal fractions every time you think about money. The dollars are written as whole numbers and the cents are written as a decimal fraction of a dollar.
A decimal fraction has a decimal point that separates the whole number from the fraction. The decimal point looks like this:
A whole pizza might be divided into eight pieces, or ten pieces, or twelve pieces. However, for decimal fractions the whole is always divided into ten pieces, which are called tenths. This is because we use a decimal system based on the number ten (“deci” is the Latin word for ten). The tenths are also divided into ten pieces to make hundredths. And then the hundredths are divided by ten to make thousandths, and so on.
Decimal fractions are often used in our daily lives, especially for money and measurement. For example:
You will be working with decimal fractions in the first two units of this book.
Common fractions are a second way we will work with parts of the whole thing.
They are written with two numbers, one above the other, with a line in between. The line may be straight, or it may be on an angle.
or ¾
The numerator is the top number in a common fraction. The numerator tells how many parts. The denominator is the bottom number. The denominator tells how many equal parts there are in the whole thing.
Example A
The whole thing is 1 pizza. This pizza has been cut into 8 equal pieces. The denominator is 8.
As a fraction, the whole thing is (eight-eigths).
If I ate 3 pieces, that would be of the pizza.
Here are some things to keep in mind while you complete the following exercise:
Exercise 1
Look at the pictures and use a fraction to answer the questions.
Answers to Exercise 1
Answers may differ because the fraction is approximate. Ask your instructor to check any different answers.
A third and useful way to think about parts of the whole thing is as a percent.
Percent fractions are written with a number and a percent sign.
1% 12% 50% 99%
In percent fractions, there is always a denominator of 100. That makes the arithmetic much easier and helps us to understand the fraction.
For example, if you got on a test last week, and on a test this week, it is hard to get a sense of how you are doing. But if you know you got 70% last week and 76% this week, it is easier to see your improvement.
In percent fractions, the whole thing is 100% so 100% equals 1.
Statistics and general information are often reported in percent fractions.
As you know, fractions describe part of the whole thing—a fraction is smaller than 1. And as you also know, 1 (the whole thing) can be many things. For example, it can be:
A decimal might represent part of a year, part of the population of Canada, part of an hour, or part of anything.
Decimal fractions are different from common fractions in several ways:
We tell the size of the denominator by looking at how many numerals are placed after the decimal point.
Decimal fraction denominators are always ten or ten multiplied by tens. Decimal means “based on the number ten”.
A whole number and a decimal can be written together. This is called a mixed decimal.
4.35 100.47 $12.39
Every whole number has a decimal point after it, even though we usually do not bother to write the decimal point unless apart of the whole (fraction) follows the whole number.
We can also put zeros to the right of the decimal point of any whole number without changing its value. Get used to thinking of a decimal point after every whole number!
2
Remember the place value chart of whole numbers? Complete the following exercise for a refresher.
Exercise 1
352 is the number on the first line of the chart below. The 3 is in the hundreds spot, the 5 is in the tens spot, and the 2 is in the ones spot.
Place the following numbers on the place value chart:
Thousands | Ones | |||||
---|---|---|---|---|---|---|
Hundred thousands | Ten thousands | One thousand | Hundreds | Tens | Ones | . (decimal point) |
3 | 5 | 2 | . | |||
Answers to Exercise
Check with your instructor to see if you have placed the numbers in the chart correctly.
Have you ever wondered what goes to the right of the decimal in a place value chart? That is where the decimal numbers go! (The parts of the whole.)
Here is a place value chart for decimals:
Hundreds | Tens | Ones | Decimal | Tenths | Hundredths | Thousandths | Ten thousandths | Hundred thousandths |
---|---|---|---|---|---|---|---|---|
3 | . | 4 | 5 | 3 | ||||
0 | . | 9 | 6 |
See the words in to the right of the decimal point? They look different than the usual whole number words you are used to. These are all the names for the decimal places. You will see them in the next lesson.
The first number on the chart above is 3.453. We say “Three point four five three” or “Three and four hundred fifty-three thousandths.”
The second number is 0.96. We say “Zero point nine six” or “Zero and ninety six hundredths.”
Common fractions with a denominator of 10 are written as a decimal with one place to the right of the decimal point. This is the tenths place.
We often shorten “places to the right of the decimal point” to “decimal places.” We can say that tenths have one decimal place.
Exercise 2
Hundreds | Tens | Ones | Decimal | Tenths | Hundredths | Thousandths | Ten thousandths | Hundred thousandths |
---|---|---|---|---|---|---|---|---|
0 | . | 4 | ||||||
Answers to Exercise 2
Decimals with one digit to the right of the decimal point have an unwritten denominator of ten. This means that the whole thing is broken into 10 equal parts. Each part is called a tenth.
When we write decimals, we put a zero to the left of the decimal point to show there is no whole number. This zero keeps the decimal point from being “lost” or not noticed.
For example, .2 should be written as 0.2.
Exercise 3
Write each decimal as a common fraction and in words.
Answers to Exercise 3
Decimals with two digits to the right of the decimal point have an unwritten denominator of one hundred. This means that the whole thing is broken into 100 equal parts. Each part is called a hundredth.
Exercise 4
Write each decimal as a common fraction and in words.
Hundreds | Tens | Ones | Decimal | Tenths | Hundredths | Thousandths | Ten thousandths | Hundred thousandths |
---|---|---|---|---|---|---|---|---|
0 | . | 3 | 4 | |||||
0 | . | 7 | 1 | |||||
Answers to Exercise 4
Common fractions with a denominator of one hundred are written as decimals with two decimal places.
Look at that last example. The 0 must be used after the decimal point in 0.04 to hold the tenths place. This makes it clear that the denominator is one hundred. There are two zeros in the denominator, so there must be two decimal places taken up.
This is called prefixing zeros.
Exercise 5
Write these common fractions as decimals.
Answers to Exercise 5
Decimals with three digits to the right of the decimal point (three decimal places) have an unwritten denominator of one thousand. This means that the whole thing is broken into 1000 equal parts. Each part is one thousandth.
Look carefully at how thousandths are written. Watch for the prefixing zeros that may be needed to hold the tenth decimal place or the hundredth decimal place.
There are three zeros in the denominator, so there must be three decimal places taken up.
Exercise 6
Write each decimal as a common fraction and in words. Practice saying them out loud.
Answers to Exercise 6
Exercise 7
Write each common fraction as a decimal.
Hundreds | Tens | Ones | . | Tenths | Hundredths | Thousandths | Ten thousandths | Hundred thousandths |
---|---|---|---|---|---|---|---|---|
0 | . | 7 | 3 | 6 | ||||
0 | . | 1 | 4 | 2 | ||||
Answers to Exercise 7
Decimals with four decimal places have an unwritten denominator of ten-thousand. The whole thing is being thought of as having 10000 equal parts. Each part is one ten-thousandth.
Exercise 8
Write each decimal as a common fraction and in words. Practice saying these aloud to someone else; they can be real tongue-twisters!
Answers to Exercise 8
Exercise 9
Write these common fractions as decimals.
Now place the above decimal numbers in the place value chart below. The first two are done for you. Then ask your instructor to mark it.
Hundreds | Tens | Ones | . | Tenths | Hundredths | Thousandths | Ten thousandths | Hundred thousandths |
---|---|---|---|---|---|---|---|---|
0 | . | 1 | 4 | 8 | 9 | |||
0 | . | 0 | 0 | 0 | 2 | |||
Answers to Exercise 9
Mixed decimals are a whole number and a decimal written together.
4.3 = = four and three tenths
27.27 = = twenty-seven and twenty-seven hundredths
8.104 = = eight and one hundred four thousandths
Digits to the left of the decimal point are whole numbers.
Digits to the right of the decimal point are fractions.
We say “and” for the decimal point.
Look at the mixed decimals from the examples above in the place value chart below:
Hundreds | Tens | Ones | Decimal | Tenths | Hundredths | Thousandths | Ten thousandths | Hundred thousandths |
---|---|---|---|---|---|---|---|---|
4 | . | 3 | ||||||
2 | 7 | . | 2 | 7 | ||||
8 | . | 1 | 0 | 4 |
Example A
We write money with a dollar sign, a whole number, and a decimal with two decimal places.
$1.00 = 1 dollar
What do we call of a dollar? Right! One cent.
Exercise 10
Write the amount of money in words.
Write with numerals, using $.
Answers to Exercise 10
“Centum” is a Latin word that means hundred! Here are English words that start with “cent”:
When we read $12.25 as “twelve dollars and twenty-five cents” we are using the Latin word for “one hundredths.”
We could also write our money like this, as we do on cheques (although it looks funny!):
$14.75 =
$12.25 =
We have another way of writing money. We often write money that is less than one dollar using a cent sign which is a c for cent with a line through it ¢.
It is incorrect to use both a dollar sign and a cent sign. Instead of $4.53¢, do $4.53 or 453¢.
It is incorrect to use a cent sign with a decimal point. Instead of 4.53¢, do $4.53 or 453¢.
Important Information
We do not need to use a decimal point with the cent sign. A decimal point would indicate a fraction or part of one cent.
For example, If a sign said “Ice cream cones 0.50¢” those ice cream cones would only cost half a cent each!
Pay careful attention to the way amounts of money are written.
Exercise 11
Rewrite these using the other common way of writing money. Remember to use the ¢ or $ as needed.
Answers to Exercise 11
Exercise 12
Correct the following ways of writing money.
Answers to Exercise 12
Exercise 13: Review
Complete the chart so that each question has the amount written as a decimal, a common fraction, and in words. The first two are done.
# | Decimal | Fraction | In words |
---|---|---|---|
a | .048 | forty eight thousandths | |
b | 0.7 | seven tenths | |
c | four hundredths | ||
d | 0.006 | ||
e | |||
f | twelve and fifteen hundredths | ||
g | 463.03 | ||
h | |||
i | seventy-five and twenty-eight thousandths | ||
j | 1833.018 | ||
k | |||
l | nine tenths |
Answer to Exercise 13
# | Decimal | Fraction | In words |
---|---|---|---|
c | 0.04 | four hundredths | |
d | 0.006 | six thousandths | |
e | 16.002 | sixteen and two thousandths | |
f | 12.15 | twelve and fifteen hundredths | |
g | 463.03 | four hundred sixty-three and three hundredths | |
h | 213.025 | two hundred thirteen and twenty-five thousandths | |
i | 75.028 | seventy-five and twenty-eight thousandths | |
j | 1833.018 | one thousand eight hundred thirty-three and eighteen thousandths | |
k | 12.0418 | twelve and four hundred eighteen ten-thousandths | |
l | 0.9 | nine tenths |
Mark /41 Aim 36/41
3
A whole number can have a decimal point and many zeros after it without changing its value.
47 = 47.0 = 47.000 = 47.0000000000000000
Zeros are used to hold a place when we write whole numbers.
In decimals, any zero to the right of the decimal point and to the left of another digit is important because the zero is holding a place and giving the decimal the correct value.
A zero is usually placed to the left of the decimal point if there is no whole number.
0.5 0.937
Zeros on the outside edges of mixed decimals do not change the value of the number and are not necessary.
0028.9710 = 28.971
00100.003000 = 100.003
890.407 = 00890.4070000000
Exercise One
Cross out the zeros that are not needed.
Answers to Exercise One
Zeros at the end of a decimal do not change the value.
6. = 6.0 = 6.00
And zeros at the beginning of a whole number do not change the value.
8 = 08 = 00008
But zeros between a decimal point and a digit do change the value.
Example A
405 is very different than 45. And 0.05 (five hundredths) is very different than 0.5 (five tenths).
You have probably heard the old saying: “You cannot compare apples to oranges!” And it’s true, it is tough to compare things that do not have much in common. So before we compare decimals, we give the decimals something in common—the same number of decimal places which gives them a common understood denominator.
Before comparing decimals, put zeros at the end or cross out any unnecessary zeros so the decimals have a common (same) number of decimal places. If you write the decimals that you are comparing right underneath each other, your eye will often tell you which is the larger amount or if the amounts are equal.
Example B
Compare 0.43 and 0.4. Which is larger?
0.43 has two decimal places; it is forty-three hundredths = . 0.4 has one decimal place; it is four tenths = .
Give them a common number of decimal places.
Add a zero to 0.4 to make it 0.40; now we read it as forty hundredths = .
Now, which is larger? .
You can easily see that 0.43 is the larger amount.
An easy way to remember these signs is to think that the big (wide) end of the sign is closer to the bigger (greater) number, and the small end of the sign is closer to the smaller number.
0.43 is larger than 0.40, 0.43 > 0.40
0.52 is smaller than 0.60, 0.52 < 0.60
Exercise Two
Which is greater? Draw a box around the bigger decimal fraction in each pair and write a greater than > or a less than < sign to make a true statement.
Answers to Exercise Two
You can compare decimals using a number line. A number line organizes what you are thinking about on paper – or on a ruler. You can plot your decimals on the number line and then be able to see which number is larger. Take a look:
Example C
First try to put the following numbers in order without looking at the number line below:
2.347 2.3 2.37 2.33 2.39 2.341 2.41
Then, look at the number line and see if you ordered your numbers correctly. The number line has a jagged edge which means it does not start at zero. It starts in the middle of a ruler. Using a number line can help you see your work and think about it at the same time.
Exercises
Try plotting the following decimals on the number line below:
4.59 4.32 4.7 5.23 4.47 4.3 4.17
Exercises
And now, plot these numbers on an empty number line. (You need to fill in the numbers yourself. Plot 7.3 on the first large vertical line on the left)
7.35 7.3 8.2 7.53 7.98 8.34 7.9 7.5
This is one way to organize and order decimals, please use it if the system is helpful for you.
Exercise Three
Draw a circle around the smallest decimal fraction in each group.
Answers to Exercise Three
Exercise Four
Identify whether the pair of numbers is equal (=) or not equal (≠).
Answers to Exercise Four
Mark /14 Aim 12/14
4
If a pair of jeans cost $49.98, what amount would you say if someone asks what you paid for them? You would probably say, “They cost around $50.”
We often round cents to dollars as we go about our lives. You may already have an idea of how to do this. For example, answer these questions.
Look at your answers. The amount for groceries may be quite large. When you estimated your answer, how did you round the amount? For example, if your real monthly grocery bill was $481.73 you might have said $482 or perhaps $480. Perhaps you even have estimated to the nearest hundred dollars and said, “About $500 a month for groceries.” All those estimates would be correct.
The amount for a tank of gas is less than a month’s groceries. How did you estimate?
For example, a small car may take $54.72 of gas.
If you estimated to the nearest dollar, you would say, “About $55.”
If you estimated to the nearest ten dollars, you would say, “About $50.”
If you rounded to the nearest dollar you would say, “54 dollars.”
We round a number in different ways depending on several things:
Carefully review the place value for whole numbers.
Thousands | Ones | |||||
---|---|---|---|---|---|---|
Hundred thousands | Ten thousands | One thousand | Hundreds | Tens | Ones | Decimal |
We round down if the digit to the right is less than 5. We round up if the digit to the right is 5 or more.
Example A
23 is rounded down to 20. The tens digit stays the same.
23 ≈ 20
Here’s another example:
Example B
287 is rounded up to 290. Tthe tens digit increases by 1.
287 ≈ 290.
Exercise 1
Round each of the following to the nearest ten. Use the “approximate equality” sign ≈.
Answers to Exercise 1
Example C
473 is rounded up to 500.
473 ≈ 500
Round down if the tens digit is less than 5 and up if it is 5 or more:
Exercise 2
Round each of the following to the nearest HUNDRED. Use the “approximate equality” sign ≈.
Answers to Exercise 2
Example D
3485 is rounded down to 3000.
3485 ≈ 3000
Round down if the hundreds digit is less than 5 and round up if it is 5 or more:
Exercise 3
Round each of the following to the nearest thousand. Use the “approximate equality” sign ≈.
Answers to Exercise 3
Remember, decimals are part of the whole thing. We can round the decimal to the nearest whole number. Rounding to whole numbers means rounding off to the ones place.
When rounding to the whole number:
Example E
37.482 rounded to the nearest whole number is 37. (The tenths digit is 4, which is less than 5.)
37.482 ≈ 37
37.906 rounded to the nearest whole number is 38. (The tenths digit is 9, which is more than 5.)
37. 906 ≈ 38
Example F
Zeros again –
You know that zeros at the end of a decimal do not change the value of the amount. You can add as many as you like.
But when a decimal has been rounded, drop any zeros after the place where you have rounded.
Instead of 39.52 ≈ 40.0, do 39.52 ≈ 40
Instead of 960.802 ≈ 961.000, do 960.802 ≈ 961
Exercise 4
Round each of the following to the nearest whole number. Use the “approximate equality” sign ≈.
Answers to Exercise 4
Important Information
If these exercises on rounding are becoming tiresome, please do not despair—there is a purpose. When you do operations (+ − × ÷) with decimals, you will often end up with answers in the ten-thousandths place when you really only need the accuracy of a tenth or a hundredth place decimal. If you do decimal operations on a calculator, you may end up with 6 decimal places (millionths)—not too practical if you are working with money and only want two decimal places! You will know how to round the answer to the decimal place you need for that question or situation.
Example G
Round to the nearest tenth.
Exercise 5
Round each of the following to the nearest tenth.
Answers to Exercise 5
Rounding decimals to the nearest hundredth is similar to rounding to the nearest tenth.
Example H
Round to the nearest hundredth.
Exercise 6
Round to the nearest hundredth. Keep significant zeros!
Answers to Exercise 6
A cent is what fraction of a dollar?
Yes, a cent is of a dollar (one hundredth).
You may be asked to round amounts of money to the nearest cent. What you are actually doing is rounding to the nearest hundredth of a dollar.
one cent = one hundredth of a dollar
Exercise 7
Round to the nearest cent.
Answers to Exercise 7
Example I
Round to the nearest thousandth (1000th).
2.0486 ⇒ 2.0486 ≈ 2.049
Round to the nearest thousandth (1000th).
29.4324 ⇒ 29.4324 ≈ 29.432
Use rounded numbers to estimate answers in daily situations, in math problem solving, and to get an idea of the answer before you figure something out on a calculator. Numbers that are rounded off make calculations simpler.
Exercise 8
Round the following numbers as called for at the left of the chart.
Answers to Exercise 8
Exercise 9
Round the numbers to estimate the answer. Circle the estimate that is the best answer.
Answers to Exercise 9
Mark /10 Aim 8/10
5
This section is for extra practice and review. If you are unsure about how to do something, look back at the lesson on that skill.
# | Decimal | Fraction | In words |
---|---|---|---|
a. | 0.0005 | Five ten thousandths | |
b. | 0.07 | Seven hundredths | |
c. | |||
d. | |||
e. | Fourteen and seventeen thousndths | ||
f. | 647.8 | ||
g. | |||
h. | 75.13 | ||
i. | Forty-two and three tenths | ||
j. | 0.789 | ||
k. | Ten and five hundred sixty-seven thousandths |
# | Decimal | Fraction | In words |
---|---|---|---|
a. | 0.0005 | Five ten thousandths | |
b. | 0.07 | Seven hundredths | |
c. | 0.086 | Eighty six thousandths | |
d. | 7.11 | Seven and eleven hundredths | |
e. | 14.017 | Fourteen and seventeen thousandths | |
f. | 647.8 | Six hundred forty seven and eight tenths | |
g. | 103.062 | One hundred forty seven and eight tenths | |
h. | 75.13 | Seventy five and thirteen hundredths | |
i. | 42.3 | Forty-two and three tenths | |
j. | 0.789 | Seven hundred eighty nine thousandths | |
k. | 10.567 | Ten and five hundred sixty-seven thousandths |
Test time!
Please see your instructor to get your Practice Test.
When you are confident, you can write your Unit 1 Test or do the Unit 1 Assignment.
Congratulations!
II
6
Review place value in whole numbers and in decimal fractions.
Here is a place value chart for decimals:
Hundreds | Tens | Ones | . | Tenths | Hundredths | Thousandths | Ten thousandths | Hundred thousandths |
---|---|---|---|---|---|---|---|---|
3 | . | 4 | 5 | 3 | ||||
0 | . | 9 | 6 |
Vocabulary Review
Use the example below and the glossary to help you write the definitions.
Definition of Addends:
Definition of Sum:
When adding decimals, you must be very careful to add together the digits with the same place value.
The best way to do this is to line up your decimals.
Exercise 1
Rewrite each question in columns and add.
Answers to Exercise 1
Exercise 2
Rewrite in columns and add.
Answers to Exercise 2
Exercise 3
Find the perimeter of the squares described in each question. The measure of one side has been given. Draw a picture of each square to help visualize the question.
Answers to Exercise 3
Exercise 4
Find the perimeter of the rectangles described below. Draw your own rectangle if there is no picture.
Answers to Exercise 4
Exercise 5
Find the perimeter of the polygons described below. Be sure the measurements are in the same unit value. Use a formula for each calculation, the formula work is started in the first two for you.
Answers to Exercise 5
In math, word problems describe real-life situations that involve numbers.
Often the most difficult part of a word problem is knowing what we should do. Once we know what to do, it is much easier to figure out how to do it.
It is sort of like driving. You may be all ready to go, but before you get into the car, turn on the engine, or put your foot on the gas pedal, you need to know where you are going and figure out how to get there.
The first thing to do is decide on your destination.
Okay, how do you “decide on a destination” for a math problem?
Use these steps:
Step 1: Question |
|
---|---|
Step 2: Information |
|
Step 3: Operation |
|
Step 4: Estimate |
|
Step 5: Solve |
|
Unit | Abbreviations |
---|---|
kilometre | km |
metre | m |
centimetre | cm |
kilogram | kg |
gram | g |
litre | L |
Example A
The nutrition information on a box of cereal says that a regular serving contains 2.8 g of protein, 0.2 g of fat, 25 g of carbohydrate, and 1.9 g of “other nutrients.” Give the total number of grams in a regular serving.
Step 1: Question | How many grams in a regular serving? Draw a picture: |
---|---|
Step 2: Information | What information is necessary to solve the problem?
|
Step 3: Operation |
|
Step 4: Estimate |
|
Step 5: Solve | 2.8 g + 0.2 g + 25.0g + 1.9 g = 29.9 g Answer: A regular serving of cereal is 29.9 grams ← (include the units)
|
Some key words that point to addition include:
Exercise 6
Use your skills in adding decimal fractions to do the following problems. Underline key words in the problems that will help you to recognize addition problems. Remember to draw a picture first!
Answers to Exercise 6
Mark /6 Aim 5/6
7
To subtract decimals you must subtract each digit from the digit of the same place value.
The best way to do this is to line up your decimals.
The same techniques that you used in adding decimals are helpful when you subtract decimals.
Example A
Vocabulary Review.
Write the definition.
← Difference
Difference:
Exercise 1
Subtract to find the differences.
Answers to Exercise 1
Follow these steps to subtract a decimal from a whole number:
Example B
Example C
Exercise 2
Rewrite each question in columns and find the difference.
Answers to Exercise 2
If you had problems with this, go over your subtraction method with your instructor before you continue.
Exercise 3
Rewrite each question in columns and find the difference.
Answers to Exercise 3
Some key words that point to subtraction include:
A math question may ask you to compare or find the difference between two amounts. Look for such words as “how much more” (or larger, taller, greater) or “how much less” (or smaller, shorter). What are the savings?
Subtract to find the answer.
Exercise 4
Use your skills in subtracting decimal fractions to do the following problems. Underline key words in the problems that will help you to recognize subtraction problems. Remember to draw a picture first!
Answers to Exercise 4
/50 marks
Mark | Criteria |
---|---|
/2 | A ruler was used for drawing lines. |
/2 | The house has five rooms. |
/5 | All wall lengths (internal and external) are marked clearly on the sketch. |
/2 | Locations for doors and windows have been marked on the sketch. |
/2 | One door and one window have been drawn with measurements marked. |
/2 | The house has a yard and measurements have been clearly marked on the sketch. |
Mark | Criteria |
---|---|
/2 | The perimeter of the house has been calculated correctly. |
/10 | The perimeter of each room has been calculated correctly. |
/2 | Bedroom 1 |
/2 | Bedroom 2 |
/2 | Bathroom |
/2 | Kitchen |
/2 | Living room |
/2 | Window and door locations have been marked on the graph paper sketch. |
/2 | One window and one door has been sketched and measurements labelled. |
/5 | The amount of trim for the windows has been calculated correctly. |
/5 | The amount of trim for the doors has been calculated correctly. |
Mark /6 Aim 5/6
8
One everyday use of adding and subtracting decimals is the bookkeeping that we all must do with our money.
Here are some examples:
What are some other examples of bookkeeping that you do?
The bookkeeping that most of us do is straightforward:
The result of the addition or subtraction is the balance.
There are many different methods of paying for purchases. Some of the most common methods are:
There are benefits to each method of payment. Each person chooses to do what works best for them depending on the situation. Here is a list of some of the benefits and drawbacks of each method of payment.
No matter what method of payment you choose to use, it is very helpful to keep track of your money. You can use a record book to mark in when you spent money and when you were paid money. This will help with budgeting and planning.
Many people use online banking to keep track of their finances. When online banking, you will see a record of your transactions that looks something like this:
Date | Transactions | Debit | Credit | Running Balance |
---|---|---|---|---|
2023-01-29 | Electronic Funds Transfer PAYCHEQUE | 175.00 | 1439.66 | |
2023-02-23 | Internet Banking INTERNET BILL PAY TELUS COMMUNICATIONS | 65.49 | 1374.06 | |
2023-03-10 | Electronic Funds Transfer DEPOSIT CANADA | 125.00 | 1499.06 | |
2023-03-16 | Internet Banking E-TRANSFER Larissa | 100.00 | 1599.06 |
The transactions are usually recorded in chronological order, by the date and time.
Here is a description of each column:
Exercise 1
Look carefully at this sample online banking transaction record, and answer the questions that follow.
Date | Transactions | Debit | Credit | Running Balance |
---|---|---|---|---|
Balance Forward | 121.16 | |||
2022-03-29 | Electronic Funds Transfer PAYCHEQUE | 675.62 | 798.78 | |
2022-03-30 | Internet Banking INTERNET BILL PAY MCCARTHY GM | 175.40 | 621.38 | |
2022-03-30 | Internet Banking INTERNET BILL PAY BC HYDRO | 50.27 | 571.11 | |
2022-04-05 | CASH DEPOSIT | 25.00 | 596.11 | |
2022-04-08 | Internet Banking INTERNET BILL PAY CITYWEST | 19.80 | 576.31 | |
2022-04-09 | INTERAC PAYMENT MAVERICK FOODS | 128.54 | 447.77 | |
2022-04-09 | CASH WITHDRAWAL | 30.00 | 417.77 |
Answers to Exercise 1
Exercise 2
Complete the transaction record using the information below.
Continue to fill out the “Running Balance” column as you add each credit or debit.
Date | Transactions | Debit | Credit | Running Balance |
---|---|---|---|---|
Balance Forward | ||||
Date | Details | Transaction |
---|---|---|
April 23, 2022 | Balance forward | $210.83 |
April 25, 2022 | Cash withdrawal | $45.00 |
April 28, 2022 | Debit to Maverick Mart | $99.95 |
April 30, 2022 | Pay deposit | $843.29 |
May 1, 2022 | Online payment Mark Jones for rent | $420.00 |
May 3, 2022 | E-transfer to Kathy Smythe (for Facebook raffle) | $25.00 |
May 6, 2022 | Interac payment to Chevron gas | $18.27 |
May 8, 2022 | Cash withdrawal | $110.00 |
May 10, 2022 | Online bill payment for Mastercard | $150.00 |
May 12, 2022 | Deposit Child Care Tax Credit | $66.48 |
May 13, 2022 | Interac payment Maverick Mart | $183.00 |
May 15, 2022 | Pay deposit | $792.18 |
Answers to Exercise 2
Date | Transactions | Debit | Credit | Running Balance |
---|---|---|---|---|
2022-04-23 | Balance Forward | 210.83 | ||
2022-04-25 | Cash withdrawal | 45.00 | 165.83 | |
2022-04-28 | INTERAC PAYMENT MAVERICK FOODS | 99.95 | 65.88 | |
2022-04-30 | Electronic Funds Transfer PAYCHEQUE | 843.29 | 909.17 | |
2022-05-01 | Internet Banking INTERNET BILL PAY MARK JONES | 420.00 | 489.17 | |
2022-05-03 | Internet Banking E-TRANSFER KATHY SMYTHE | 25.00 | 464.17 | |
2022-05-06 | INTERAC PAYMENT CHEVRON GAS | 18.27 | 445.90 | |
2022-05-08 | Cash withdrawal | 100.00 | 335.90 | |
2022-05-10 | Internet Banking INTERNET BILL PAY MASTERCARD | 150.00 | 185.90 | |
2022-05-12 | DEPOSIT CANADA CHILD TAX CREDIT | 66.48 | 252.38 | |
2022-05–013 | INTERAC PAYMENT MAVERICK MART | 183.00 | 68.38 | |
2022-05-15 | Electronic Funds Transfer PAYCHEQUE | 792.18 | 861.56 |
As soon as you write a cheque, be sure to enter the details in your cheque book.
A cheque book is a simple accounts book or ledger. A ledger is a convenient way to record expenditures (money spent) and income.
Exercise 3
Use the information below to complete the chequing account ledger. Arrange the information in chronological order. That means put the information with the earliest date first, then the next date, and so on.
Date | Cheque # | Details | Debit |
---|---|---|---|
2022-05-01 | #122 | Mortgage payment | $375.00 |
2022-05-06 | #123 | Cable | $32.17 |
2022-04-23 | E-transfer Mike the Mechanic | $45.82 | |
2022-04-18 | #121 | B.C. Hydro (Feb & Mar) | $62.53 |
2022-03-02 | Cash withdrawal | $75:00 | |
2022-03-02 | Debit charge | $1.50 | |
2022-05-04 | Grocery Mart | $111.95 |
Date | Details | Credit |
---|---|---|
2022-04-30 | Pay | $596.27 |
2022-04-15 | Birthday money | $200.00 |
2022-04-20 | Child Care Tax Refund | $33.64 |
DATE | CHEQUE # | TRANSACTION | DEBIT OR CHEQUE AMOUNT | DEPOSIT AMOUNT | BALANCE |
---|---|---|---|---|---|
BALANCE FORWARD | |||||
Use the cheque blank to write out cheque # 121 from part A. Use any name and address you want. Ask your instructor to check your work.
Answers to Exercise 3
DATE | CHEQUE # | TRANSACTION | DEBIT OR CHEQUE AMOUNT | DEPOSIT AMOUNT | BALANCE |
---|---|---|---|---|---|
BALANCE FORWARD | 312.07 | ||||
2022-03-02 | Cash Withdrawal | 75.00 | 237.07 | ||
2022-03-02 | Debit charge | 1.50 | 235.57 | ||
2022-04-15 | Birthday money | 200.00 | 435.57 | ||
2022-04-18 | 121 | BC Hydro (Feb & Mar) | 62.52 | 373.04 | |
2022-04-20 | Child Care Tax Refund | 33.64 | 406.68 | ||
2022-04-23 | Mike the Mechanic (fix shocks) | 45.82 | 360.86 | ||
2022-04-30 | Pay | 596.27 | 957.13 | ||
2022-05-01 | 122 | Mortgage Payment | 375.00 | 582.13 | |
2022-05-04 | Grocery Mart | 111.95 | 470.18 | ||
2022-05-06 | 123 | Cable | 32.17 | 438.01 |
9
Date | Transactions | Debit | Credit | Running Balance |
---|---|---|---|---|
Balance Forward | 559.58 | |||
2022-04-20 | CASH DEPOSIT | 200.00 | ||
2022-04-21 | INTERAC PAYMENT Kaien Island Optometry | 74.53 | ||
2022-04-29 | DEPOSIT CANADA CHILD TAX CREDIT | 89.70 | ||
2022-05-01 | Electric Funds Transfer PAYCHEQUE | 609.74 | ||
2022-05-08 | Internet Banking INTERNET BILL PAY BC HYDRO | 52.46 | ||
2022-05-08 | INTERAC PAYMENT FEES | 1.75 | ||
2022-05-10 | INTERAC PAYMENT Safeway | 73.02 | ||
2022-05-10 | INTERAC PAYMENT FEES | 1.89 | ||
2022-05-12 | CASH WITHDRAWAL | 60.00 |
Date | Transactions | Debit | Credit | Running Balance |
---|---|---|---|---|
Balance Forward | 559.58 | |||
2022/04/20 | CASH DEPOSIT | 200.00 | 685.05 | |
2022/04/21 | INTERAC PAYMENT Kaien Island Optometry | 74.53 | 774.75 | |
2022/04/29 | DEPOSIT CANADA CHILD TAX CREDIT | 89.70 | 1384.49 | |
2022/05/01 | Electric Funds Transfer PAYCHEQUE | 609.74 | 734.49 | |
2022/05/08 | Internet Banking INTERNET BILL PAY BC HYDRO | 52.46 | 682.03 | |
2022/05/08 | INTERAC PAYMENT FEES | 1.75 | 680.28 | |
2022/05/10 | INTERAC PAYMENT Safeway | 73.02 | 607.26 | |
2022/05/10 | INTERAC PAYMENT FEES | 1.89 | 605.37 | |
2022/05/12 | CASH WITHDRAWAL | 60.00 | 545.37 |
Test time!
Please see your instructor to get your Practice Test.
When you are confident, you can write your Unit 2 Test and/or do the Unit 2 Assignment.
Congratulations!
III
10
Multiplying decimals uses the same method that you learned for multiplying whole numbers. Review multiplication of whole numbers.
Vocabulary Review
Review the diagram below and try to write in the explanations of the mathematical terms. You may refer to the glossary, if you wish. For right now, it is mostly important to remember what factor means.
Product:
Factors:
Multiplying decimals follows almost the same steps as multiplying whole numbers. On the next few pages, you will be shown two ways to multiply decimals.
One method is to estimate the product using whole numbers to determine where the decimal goes.
Example A
Estimate: 4.3 × 5.7 ≈ 4 × 6 = 24
This tells us that the correct answer will be around 24 (which is two whole number places). We know that the answer will not be around 2.4 and it will not be around 240.
If we take the decimals out and just multiply the digits, the answer is 2451.
The estimate shows that the decimal point will come after two whole number places, so 4.3 × 5.7 = 24.51
Example B
Estimate: 23.24 × 3.9 ≈ 23 × 4 = 92
The answer will be around 92. It will not be around 9.2 and it will not be around 920.
If we take the decimals out and just multiply the digits, the answer is 90636.
The estimate shows that the decimal point will come after two whole number places.
So
If the whole numbers in the question are large, you can round to the nearest ten or hundred to help you decide where to put the decimal point. This is a quick estimate.
Example C
383.298 × 213.87 ≈ 400 × 200 = 80000
The answer will be around 80000. It will not be around 8000 or 800000.
If we take the decimals out and just multiply the digits 383.298 by 213.87, the numerals in the product are 8197594326.
The estimate shows that the whole number will go up to the ten-thousands place, which is five whole number places, so
383.298 × 213.87 = 81975.94326 Whew!
Exercise 1
All the multiplying has been done already. Your task is to put the decimal point in the product by doing a whole number estimate of the question.
Example
Estimate:
Answers to Exercise 1
Another way of locating the decimal point in the product is to look at the number of decimal places in the decimals you are multiplying.
Example D
Then add the number of decimal places you counted above (2 + 1 = 3)
This is the number of decimal places you will have in your answer.
Example E
Example F
Exercise 2
Again, the multiplying has been done. Use the method of multiplying the understood denominators to put the decimal point in the product.
Answers to Exercise 2
Exercise 3
If you had trouble with the first two exercises, then get help from your instructor. Here is extra practice if you want or need it.
Answers to Exercise 3
Exercise 4
Multiply to find the product. Remember to put the decimal point in the correct place; you know two methods!
Answers to Exercise 4
Remember this skill?
– The 00 must be used after the decimal point in 0.0019 to hold the tenths and hundredths place. This makes it clear that the denominator is ten thousand.
When changing from a fraction to a decimal:
If there are not enough digits to fill all the decimal places, put zeros between the decimal point and the digits from the fraction—this is called prefixing zeros.
How does this apply to multiplying decimals? Look at the examples.
Example G
Uh oh! There are not enough spots in the answer to make the decimals fit in!
Add zeros before your product. It is completely within the rules of math to do that. Then put in the decimal in the place in the correct place.
Example H
Example I
Look carefully at this one – it is tricky!
Because the last digit, the zero, is the result of multiplying 8 × 5, you must count it when working out the decimal places to put in the decimal point.
The product is forty thousandths:
which can now also be written as four hundredths:
Note that if you had not counted that zero, you would have written 0.004 which is four thousandths and not correct.
Exercise 5
Find the products. Be certain to place all decimal points correctly.
Answers to Exercise 5
There is a pattern that you can see when we multiply by a decimal number by 10, 100, 1000, 10000, and so on. Look at the following example and try to find the pattern:
45.9264 × 10 = 459.264
45.9264 × 100 = 4592.64
45.9264 × 1000 = 45926.4
45.9264 × 10000 = 459264
Do you see a pattern?
When you multiply by ten, move the decimal point one place to the right. Remember that every whole number can have a decimal point at the right.
Example J
Exercise 6
Answers to Exercise 6
When you multiply by 100, move the decimal point two places to the right. Note that zeros may be needed at the end of the numeral.
Example K
Exercise 7
Answers:
To multiply by 1000, move the decimal point three places to the right.
Example L
4.2 × 1000 = 4200.
Exercise 7
Answers to Exercise 7
Exercise 8
Write the products using the short method you now know.
Answers to Exercise 8
The area of an object is: the measurement of the amount of space the object surface covers. Area is described in square units.
Exercise 9
Find the area of the rectangles described below. The measures of the length (l) and width (w) have been given. You should draw and label a sketch for each.
Answers to Exercise 9
Exercise 10
Find the area of each square described in the questions below. Even though this is a simple square, it is still good practice to draw the picture.
Remember, all four sides of a square are the same length.
Answers to Exercise 10
Multiplication problems usually give information about one thing and ask you to find a total amount for several of the same things. Look for this pattern in the following problems. Also look for key words.
Some key words which point to multiplication include:
Multiplication by a decimal or fraction often uses the word “of” in word problems.
“Of” usually means multiply one number by another number.
Example M
Kathy spends 0.25 of her salary on rent. Her salary is $1445 a month. How much is her rent?
0.25 × $1445 = $361.25
She spends $361.25 on rent every month.
Remember, it can be very useful to draw a picture to help yourself visualize the problem.
Exercise 11
Solve these problems. Do an estimation first.
Answers to Exercise 11
Mark: /16
Use the graph paper house sketch that you made in the Design Your Own House Project Part 1 in Unit 2 – Topic B: Subtracting Decimals to do this activity.
When you have finished this project, put your graph paper somewhere safe, because you will be using it again at the end of Unit 5 Topic A.
Calculations:
Mark /6 Aim 5/6
11
Test time!
Please see your instructor to get your Practice Test.
When you are confident, you can write your Unit 3 Test and/or do the Unit 3 Assignment.
Congratulations!
IV
12
Dividing decimals uses the same method that you learned for dividing whole numbers.
Vocabulary Review
dividend ÷ divisor = quotient
Using the above diagram, write the definitions.
Divisor:
Dividend:
Quotient:
Remember to use zeros to hold the places in the quotient if there is no other digit.
Dividing decimals follows almost the same steps as dividing whole numbers. Here you will be shown two ways to figure out where to place the decimal point.
One way is to estimate the quotient using rounded whole numbers.
Example A
Estimate: 17.7 ÷ 3 ≈ 18 ÷ 3 = 6
This tells us that the correct answer will be around 6 (which is one whole number place).
We know that the answer will not be around 0.6 and it will not be around 60.
If we take the decimals out and just divide the digits, the answer is 59.
The estimate shows that the the decimal point will come after one whole number.
17.7 ÷ 3 = 5.9
Example B
Estimate: 137.88 ÷ 18 ≈ 140 ÷ 20 = 7
The answer will be around 7. It will not be around 0.7 or 70 or 700.
If we take the decimals out and just divide the digits, the answer is 7.66.
The estimate shows that the the decimal point will come after one whole number.
137.88 ÷ 18 = 7.66
To check the accuracy of your division, multiply the quotient by the divisor.
dividend ÷ divisor = quotient
quotient × divisor = dividend
The product will equal the dividend if your arithmetic is correct.
23.72 ÷ 8 = 2.965
Exercise 1
The division has been done. Your task is to put the decimal point in the quotient by doing a whole number estimate of the question.
Answers to Exercise 1
Have you found the shortcut?
If the divisor is a whole number, put the decimal point in the quotient right above the decimal point in the dividend.
Then just go ahead and divide, ignoring the decimal point all together.
Example C
Example D
Exercise 2
Find the quotients. Check the answer by multiplying the quotient by the divisor.
Example
Check:
Answers to Exercise 2
The past section taught us that if the divisor is a whole number, we put the decimal point in the quotient right above the decimal point in the dividend. Then we just go ahead and divide.
But what if the divisor has a decimal in it? A decimal divisor must be changed to a whole number before we can divide.
Remember:
Your instructor will give you more information about why this method works if you wish to know.
Example E
If the divisor has a decimal, do this:
1.255 ÷ 0.05 = 25.1
Note: Zeros may have to be put at the end of the dividend when you move the decimal point.
Example F
48.6 ÷ 0.24 =
changes to
There is nothing here, so we must add a zero.
Remember that if the dividend is a whole number, put a decimal to the right of it first, and then move the decimal as needed to match what you did to the divisor. You will need to add zeros to hold the places.
Example G
Put a decimal to the right of the dividend.
Move the decimals for both numbers one place to the left. This is like multiplying both numbers by ten. Add a zero to the dividend to hold the tens place.
Put the decimal directly above the decimal in the dividend.
Exercise 3
Find the quotients.
Answers to Exercise 3
If you are having any difficulty with this exercise, ask your instructor for help before you go any further.
Exercise 4
Now try these:
Answers to Exercise 4
Exercise 5
Set the question up for long division and find the quotient. Check your answers by multiplying quotient divisor. The product should equal the dividend.
Example
0.2448 ÷ 0.008 =
Check:
Answers to Exercise 5
The questions that you have been practicing all work out evenly. But, as you know, the world is seldom perfect and division questions often have remainders! For everyday uses of mathematics, answers to the hundredths or thousandths decimal places are accurate enough.
This is what you do if the division problem does not work out evenly:
Example H
422 ÷ 1.7 =
The quotient 248.2352 will round this way:
Example I
12.5 ÷ 7 =
The quotient 1.7857 will round this way:
Always round money to the nearest cent.
Example J
$47.26 ÷ 3 =
$15.753 ≈ $15.75
Sometimes numbers repeat when you divide. This will go on forever — to infinity.
Example K
100 ÷ 3 =
To show that the 3 keeps repeating as a decimal fraction, put a · (dot) or a ¯ (bar) above the repeating decimal digit.
Sometimes a group of digits will repeat. Put a bar above the repeating decimal digits. For example 2.341341341341
Exercise 6
Use long division to find the quotient. Round the quotient to the nearest tenth.
Answers to Exercise 6
Exercise 7
Divide and round the quotient to the nearest hundredth.
Answers to Exercise 7
Multiplication and division are opposite operations. Multiplying by ten, hundred, etc. moves the decimal point the same number of decimal places to the right as there are zeros in the 10, 100, 1000, etc. Moving a decimal point to the right gives a larger number.
Therefore, dividing by ten, hundred, etc. must move the decimal point to the left. Remember that moving a decimal point to the left gives a smaller number. Study the examples.
You may need to prefix zeros. Look at these examples:
Exercise 8
Write the quotient. Use the short method you have just learned.
Answers to Exercise 8
Division problems usually give information about groups of things and ask you to find the information for one thing.
Some key words which point to division include:
Exercise 9
Solve these division problems. Look carefully for the pattern of the problems and underline any key words which point to division. Do an estimation before you find the actual solution.
Answers to Exercise 9
Mark /13 Aim 10/13
13
Cost | Detail |
---|---|
$395.36 | Adoption cost |
$159.30 | Vet care |
$67.49 | Immunizations |
$38.99 | First month of food |
$278.43 | Extra gear a dog needs (collars, leash, toys, crate, and a bed) |
$30.00 | Licence fee |
What will each child pay?
V
14
This next topic will help you practice some math skills you have already learned:
Have you ever stood in front of a grocery store shelf holding two different sizes of the same product in your hands trying to decide on the “best buy”? The different sized packages make it difficult to compare the prices. Many stores now help by putting the unit prices on the shelf below their products, but sometimes you need to figure the unit price out yourself.
The unit price is the price for one measure or one unit of a product.
To calculate the unit price, do this:
total price ÷ number of units = unit Price
To compare unit prices, you need to compare the same unit to the same unit.
Compare kilograms to kilograms
Compare litres to litres
Compare pairs of slippers to pairs of slippers
Compare grams to grams
…and so on!
Example A
A 210 gram bag of potato chips costs $4.20 while an 110 g bag sells for $3.30 Which is the better buy? We will compare the price per gram for the two bags.
Of course the item with the best unit price may not be the best buy for you. You may only have enough money to buy a small quantity, or you may not want to have a large quantity of something. This is a helpful skill to know for if you need to use it.
Exercise 1
Calculate the unit price of these items which are of equal quality and then put a checkmark beside the better buy. (Divide the price by number of units.)
Item | Unit to Compare | Total Price | Number of Units | Unit Price | |
---|---|---|---|---|---|
Socks – 4 pair $2.80 | pairs | $2.80 | 4 | $0.70/pr | |
Socks – 6 pairs $4.08 | pairs | $4.08 | 6 | $0.68/pr |
Item | Unit to Compare | Total Price | Number of Units | Unit Price | |
---|---|---|---|---|---|
Toilet paper – 6 rolls $1.86 | |||||
Toilet paper – 8 rolls $2.56 |
Item | Unit to Compare | Total Price | Number of Units | Unit Price | |
---|---|---|---|---|---|
Laundry Soap – 3 Litres $5.94 | |||||
Laundry Soap – 5 Litres $9.80 |
Item | Unit to Compare | Total Price | Number of Units | Unit Price | |
---|---|---|---|---|---|
A dozen eggs $2.79 | |||||
A dozen and a half eggs $4.09 |
Answers to Exercise 1
Item | Unit to Compare | Total Price | Number of Units | Unit Price | |
---|---|---|---|---|---|
Toilet paper – 6 rolls $1.86 | rolls | $1.86 | 6 | $0.31/roll | |
Toilet paper – 8 rolls $2.56 | rolls | $2.56 | 8 | $0.32/roll | |
Laundry Soap – 3 Litres $5.94 | litres | $5.94 | 3 | $1.98/L | |
Laundry Soap – 5 Litres $9.80 | litres | $9.80 | 5 | $1.96/L | |
A dozen eggs $2.79 | eggs | $2.79 | 12 | $0.2325/egg | |
A dozen and a half eggs $4.09 | eggs | $4.09 | 18 | $0.227/egg |
Now look at this example:
Examples
Shoppers Drug Mart is advertising one brand of toothpaste at $1.39 per 100 mL tube and another brand at 99¢ per 75 mL tube. Which is the better buy?
Step 1 – Check that the units are the same.
Step 2 – Work out the unit price for each tube by dividing total price by the contents (number of mL).
Step 3 – Decide which tube is cheaper per unit price.
Remember:
Unit | Abbreviations |
---|---|
kilogram | kg |
gram | g |
litre | L |
millilitre | mL |
package | pkg |
1 kilogram = 1000 grams
1 litre = 1000 millitres
This might be a good time to review Dollars and Cents and Rounding.
Exercise 2
Round to the nearest cent.
Answers to Exercise 2
Exercise 3
Decide which item in each group is the “best buy” by figuring out the unit price. Round the unit price to the nearest cent and put a checkmark next to the best buy.
Amount | Price | Unit price | Best buy |
---|---|---|---|
200 g | $4.99 | $0.024/g ≈ $0.02/g | |
1 kg (1000 g) | $11.99 | $0.011/g ≈ $0.01/g |
$4.99 ÷ 200 = $0.02495/g ≈ $0.02/g
$11.99 ÷1000 g = $0.0011/g ≈$0.01/g
Amount | Price | Unit Price | Best buy |
---|---|---|---|
5 kg | $9.99 | ||
8 kg | $16.99 |
Amount | Price | Unit Price | Best buy |
---|---|---|---|
170 g | $4.49 | ||
300 g | $3.98 |
Amount | Price | Unit Price | Best buy |
---|---|---|---|
20 bags | $2.29 | ||
45 bags | $3.89 |
Amount | Price | Unit Price | Best buy |
---|---|---|---|
1.4 kg | $3.69 | ||
2 kg | $5.39 |
Amount | Price | Unit Price | Best buy |
---|---|---|---|
2 pairs | 99¢ | ||
5 pairs | $2.58 |
Answers to Exercise 3
Amount | Price | Unit Price | Best buy |
---|---|---|---|
5 kg | $9.99 | $2.00/kg | |
8 kg | $16.99 | $2.12/kg |
Amount | Price | Unit Price | Best buy |
---|---|---|---|
170 g | $4.49 | $0.03/g | |
300 g | $3.98 | $0.01/g |
Amount | Price | Unit Price | Best buy |
---|---|---|---|
20 bags | $2.29 | $0.11/bag | |
45 bags | $3.89 | $0.09/bag |
Amount | Price | Unit Price | Best buy |
---|---|---|---|
1.4 kg | $3.69 | $2.64/kg | |
2 kg | $5.39 | $2.70/kg |
Amount | Price | Unit Price | Best buy |
---|---|---|---|
2 pairs | 99¢ | $0.50/pr | |
5 pairs | $2.58 | $0.52/pr |
We do not have a coin that equals one tenth of one cent ($0.001), but this amount of money is often used to calculate prices and can be significant for large amounts.
The unit price information on store shelves also may include tenths of a cent.
One other place where you see tenths of a cent is at the gas station.
Gasoline is priced at cents per litre and is usually written like this, without the $ or ¢:
156.9 L (156.9¢/L) or 0.999 L ($0.999/L)
Gas Pricing in the Past, Present, and Future
Gas prices have risen and fallen thousands of times over the years.
On the gas station signs, the cost is listed as cents per litre (¢/L).
Before 2010, it was unthinkable that gas would ever go over a dollar per litre. However, in the next ten years it came close to two dollars per litre in some parts of Canada.
Here are a few pump prices from the past for comparison:
Year | Average cost of gas in BC in ¢/L |
---|---|
1980 | 23.6 |
1990 | 58.5 |
2000 | 69.4 |
2010 | 114.3 |
2015 | 123.5 |
2019 | 149.1 |
April 2020 in some parts of BC | 63.9 |
As you can see, gas prices rose steadily over the decades. In 2019, gas was as high as 169 cents per litre.
In early 2020, the COVID-19 pandemic led to a crash of the oil market, leading to extraordinarily low gas prices. By mid-April, gas in some parts of BC had dropped to below 65 cents per litre, which was the lowest it had been in over 20 years.
Exercise 4
Answers to Exercise 4
Answers will vary. Show your work to your instructor
Goal: Good Shopping!
Think about your grocery needs for this week while you do this activity.
Item | Amount | Price | Unit price | Best buy |
---|---|---|---|---|
Safeway Compliments dry spaghetti | 900 g | $2.43 | $0.0027 | |
Extra Foods Western Family dry spaghetti | 500 g | $1.29 | $0.0025 | |
Mark: /20
Use the graph paper house sketch that you made in the Design Your Own House Project Part 1 in Unit 2 – Topic B: Subtracting Decimals to do this activity. Clearly label and organize/show your work!
Picture | Flooring material | Covers | Price | Cost per metre squared |
---|---|---|---|---|
Box of 20 peel and stick floor tiles | 6.2 m² | 47.99 | ||
Vinyl floor tiles | 7.3 m² | 94.80 | ||
Vinyl plank flooring | 6.1 m² | 72.86 | ||
Hardwood flooring | 7.2 m² | 148.61 | ||
Ceramic tile | 6.9 m² | 202.05 | ||
Carpet | 1 m² | 8.89 |
When you have finished this project, put your graph paper somewhere safe, because you will be using it again at the end of Unit 5 Topic B.
Calculations:
15
Spend a few minutes reviewing the key words that will help you identify addition, subtraction, multiplication and division word problems.
Some key words that point to addition include:
Some key words that point to subtraction include:
Some key words which point to multiplication include:
Some key words which point to division include:
Read over some of the problems that you have done in each unit to remind yourself of the patterns to expect for different operations.
Carefully review the five steps to use when solving problems:
Exercise 1
Answers to Exercise 1
Mark /6 Aim 5 / 6
Use the graph paper house sketch that you made in Unit 2, Topic B: Subtracting Decimals in the Design Your Own House Project Part 1 do this activity.
Give your house a yard.
Material | Quantity | Cost (Include units if applicable. e.g. per metre) | Total price of material |
---|---|---|---|
Examples: Fence posts, cedar, 2m | 24 | $15.26 each | $366.24 |
Fence rails, cedar, 4m, pack of 4 | 10 | $45.36 each | $453.60 |
Total cost of fencing materials: |
Sketch:
Calculations:
16
Use the skills you learned in this unit to figure out the best buy:
Amount | Price | Unit Price | Best Buy |
---|---|---|---|
740 mL | $3.40 | ||
4.3 L | $16.10 |
Amount | Price | Unit Price | Best Buy |
---|---|---|---|
Bag of 7 | $4.99 | ||
1 | $0.75 |
Amount | Price | Unit Price | Best Buy |
---|---|---|---|
1 can | $2.59 | ||
12 pack | $27.97 |
Amount | Price | Unit Price | Best Buy |
---|---|---|---|
3 pack | $8.99 | ||
1 loaf | $2.49 |
Amount | Price | Unit Price | Best Buy |
---|---|---|---|
Pack of 4 | $1.89 | ||
Econo pack of 12 | $5.97 |
Amount | Price | Unit Price | Best Buy |
---|---|---|---|
740 mL | $3.40 | $4.59/L | |
4.3 L | $16.10 | $3.74/L |
Amount | Price | Unit Price | Best Buy |
---|---|---|---|
Bag of 7 | $4.99 | $0.71 each | |
1 | $0.75 | $0.75 each |
Amount | Price | Unit Price | Best Buy |
---|---|---|---|
1 can | $2.59 | $2.59/can | |
12 pack | $27.97 | $2.33/can |
Amount | Price | Unit Price | Best Buy |
---|---|---|---|
3 pack | $8.99 | $3.00/loaf | |
1 loaf | $2.49 | $2.49/loaf |
Amount | Price | Unit Price | Best Buy |
---|---|---|---|
Pack of 4 | $1.89 | $0.47/bulb | |
Econo pack of 12 | $5.97 | &0.50/bulb |
Test time!
Please see your instructor to get your Practice Test.
When you are confident, you can write your Unit 5 Test and/or complete Part 3 Flooring & 4 Fencing and Decorating of the ongoing Project.
Congratulations!
VI
17
This unit will help you explore the system of metric measurement.
First, why metric?
The end of this unit will look at how metric measurement (metres, litres, grams, etc.) and imperial measurement (inches, feet, cups, ounces, pounds, etc) compare to each other.
The metre is the base unit used to measure length, height, and distance.
Here are some ways we use length, height, and distance measurement in our everyday lives:
The gram is the unit for measuring mass. (We use the words mass and weight in the same way.)
Here are some ways we use the measurement of mass in our everyday lives:
Litres are the everyday unit that we use to measure volume or capacity.
Volume or capacity tells how much a container can hold. For example, the volume of the classroom would be represented by the amount of air in the room. The capacity of a container would be the amount of liquid it could hold.
We use litres to measure liquids and gases such as air.
Here are some ways we use volume measurement in our everyday lives:
Degrees Celsius is the common unit for measuring temperature. The symbol is °C.
The Celsius temperature scale was determined this way:
(The name Celsius comes from the 18th century Swedish scientist, Anders Celsius.)
We say that temperatures colder than the freezing point of water are “below zero” or “below freezing” and we put a minus sign in front of the number.
Exercise 1
What are the temperatures on the thermometers pictured on the page?
Answers to Exercise 1
Temperature | Details |
---|---|
37°C | normal |
38°C | slightly feverish |
39°C | very feverish |
40°C | dangerously high body temperature (equal to 104°F) |
Temperature | Details |
---|---|
40°C | too hot – sit down in the shade and relax! |
30°C | very warm summer’s day |
20°C | pleasant temperature for outdoor activities |
10°C | quite cool, you need a coat |
0°C | water is freezing |
−10°C | brisk winter‘s day |
−20°C | cold, watch for frostbite |
−30°C | very cold |
−40°C | extremely cold!!! |
Exercise 2
Keep track of the morning temperatures each day for a week. Put a thermometer outside your window and fill in the following chart. This is a great activity to do with your kids. The purpose of this activity is to get familiar with reading a thermometer, which is practicing a scientific measurement.
Day of week | Sunday | Monday | Tuesday | Wednesday | Thursday | Friday | Saturday |
---|---|---|---|---|---|---|---|
Temperature in °C |
The name of a unit starts with a lower case (small) letter except at the beginning of a sentence and except for degrees Celsius.
gram metre litre second
Use only one prefix at a time with a base unit. Do not use a hyphen (-) between the prefix and the base unit.
kilogram centimetre millilitre
18
The metric system uses the base units gram, metre, and litre. It would not be practical to use only the base units because sometimes the unit would be far too large and other times it would be too small.
These measures would all be correct but inconvenient to use. They would be easier to understand as:
The metric prefixes are similar to the place values in our number system. The prefix in front of a base unit tells how many of the base unit. Each prefix can be combined with almost any unit.
You will need to memorize the most common prefixes, their symbols, and their meaning.
In our everyday life and studies, we use only a few of these prefixes. However, it is interesting to look at the pattern of the prefixes and compare their pattern to the place value that you know so well.
The ones to memorize are marked with an *.
Prefix | Symbol | Number of Base Units |
---|---|---|
terra | T | 1000000000000 |
giga | G | 1000000000 |
mega | M | 1000000 |
kilo* | k | 1000 |
hecto* | h | 100 |
deca* | da | 10 |
no prefix | base | 1 |
deci* | d | 0.1 |
centi* | c | 0.01 |
milli* | m | 0.001 |
micro | μ | 0.000001 |
nano | n | 0.000000001 |
pico | o | 0.000000000001 |
Exercise 1
Use the Prefix Chart to answer these questions.
As a memory helper, notice that these three units which give a fraction of the base unit, all end with the letter i. You already know that centi is the Latin word for one-hundredth, and that one cent is one hundredth of a dollar.
Answers to Exercise 1
Exercise 2
Symbol | Word Name | Meaning | Measures |
---|---|---|---|
kL | kilo Litre | one thousand litres | capacity |
hm | hectometre | one hundred metres | distance |
dg | decigram | one tenth of a gram | mass |
mm | |||
daL | |||
kg | |||
m | |||
mL | |||
dag | |||
cL | |||
cm | |||
hL | |||
hg |
Answers to Exercise 2
Symbol | Word Name | Meaning | Measures |
---|---|---|---|
kL | kilo Litre | one thousand litres | capacity |
hm | hectometre | one hundred metres | distance |
dg | decigram | one tenth of a gram | mass |
mm | millimetre | one-thousandth of a metre | distance |
daL | decalitre | ten litres | capacity or volume |
kg | kilogram | thousand grams | mass |
m | metre | one metre | distance |
mL | millilitre | one-thousandth of a litre | capacity |
dag | decagram | ten grams | mass |
cL | centilitre | one-hundredth of a litre | capacity |
cm | centimetre | on hundredth of a metre | distance |
hL | hectolitre | hundred litres | capacity |
hg | hectogram | hundred grams | mass |
19
The metre is the base unit for this purpose. In Topic C, all the prefixes were combined with the base unit metre. But for everyday purposes, we use only kilo, centi, and milli with metre.
Use… | To Measure… |
---|---|
kilometres | long distances, such as road distances, length of rivers, to measure car speed per hour, highway signs. |
metres | medium lengths, such as room size, track and field events, size of building lots, rope, extension cords, fabric, carpeting. |
centimetres | common, smaller things such as a person’s height, waist measurement, size of furniture, length of pants, width of wax paper, shoelaces, skis. |
millimetres | very small things such as postage stamps, size of precise tools, length of screws and nails, fine sewing measurements, thickness of plywood and glass. |
Exercise 1
Get a metre stick or tape measure. If you have problems, your instructor will assist you in reading the measuring tool that you use and will check your work.
Your hand span is a handy measurement to know because you can use it as a measuring tool to make quick measurements of smaller objects. Knowing the length of your pace is also useful for quick measurements of room size, etc.
Exercise 2
The answers to questions a are listed below. Your instructor will check your other measurements and assist you as needed.
Answers to Exercise 2
Exercise 3
Make the following measurements. Choose the most convenient unit (metres, centimetres, or millimetres) for each question. Draw a sketch of the shapes. Record your results carefully because you will use them at the end of the Unit Two.
Mass measures the weight of something. The unit for mass to which prefixes are attached is the gram – a very small mass. We use the kilogram (1000 g) for many everyday purposes. In fact, SI uses the kilogram as the official base unit because it is the most used, most practical amount.
Let’s look at the use of the common measurements for mass.
Use… | To Measure |
---|---|
tonne (t) | Very large amounts such as trucks and farm crops; loads on trucks, trains, and ships; coal; factory production. |
kilogram | Common amounts such as our body mass, meat and vegetables, packaged foods, packaged household. |
gram | Small amounts of mass such as breakfast cereals, light packaged food, newborn babies, ingredients in some recipes. The amount of certain nutrients that we should eat. Bulk and delicatessen foods may be priced per 100 g. |
milligram | Extremely small amounts of mass such as in medicines (3 mg of pain-reliever in every tablet!); the vitamins and minerals in foods (check the nutrient information on a package); the recommended dose of daily vitamins. |
The tonne, symbol t, has not been mentioned before. Notice that the name does not use a prefix or a base unit.
Exercise 4
Use a scale marked in kilograms at a supermarket, at home, or in class for b. to e.
The base unit for capacity is the litre. Capacity measures how much fluid a container will hold. The fluid might be liquids such as milk, water, and blood or it might be a gas such as air or oxygen. The litre and the millilitre are the everyday measurements for capacity.
Use… | To Measure |
---|---|
litre | Common large amounts of liquids such as milk, gasoline, paint, household cleaners, bottled drinks (pop, juice, etc.), large cans of food; car engines may be described by the litres of air displaced in the cylinders (for example, a 1.5 L engine in a small car). The capacities of buckets, cookware and ice cream are given in litres. |
millilitre | Liquids in smaller containers less than one litre such as food, soft drinks, and wine. Spices and flavouring for cooking (one teaspoon 5 mL). Measuring cups are often 250 mL or 500 mL. |
Look at your home and around the grocery store to find items measured in litres and items measured in millilitres.
Look at measuring spoons to help you get a feeling for small amounts measured in millilitres.
Exercise 5
Write the measurement (prefix and unit) which would be most practical to measure these objects in real life. Answer every part of each question.
Answers to Exercise 5
20
In this topic, you will learn a quick method to change (convert) between different units with the same base. In the conversion, the number and the prefix both change; the length or mass or volume of the object is not changed – only the way we express the measurement changes.
Are you a visual learner? If you are, then ask your instructor to show you the next skill. It will save you a lot of frustration. You may learn this skill much faster with a real life example.
Metric Prefixes | kilo | hecto | deca | BASE UNIT | deci | centi | milli |
---|---|---|---|---|---|---|---|
Mass | kg | hg | dag | g | dg | cg | mg |
Volume | kL | hL | daL | L | dL | cL | mL |
Length | km | hm | dam | m | dm | cm | mm |
Place Value | 1000 | 100 | 10 | 1 | 0.1 | 0.01 | 0.001 |
Example A
A book weighs 12 g. Convert this amount to mg.
On the chart, every time you cross over a bar ( | ), the factor is 10.
Review Multiplying by 10, 100, 1000 in Unit 3, Topic A.
Example B
A room measures 450 cm long. Convert this measurement to m.
Example C
The container holds 45.5 dL. Write this amount in daL.
Exercise 1
Complete the metric conversions. Some units are not common, but the practice in conversion is useful.
Answers to Exercise 1
kilo | hecto | deca | base unit | deci | centi | milli |
The skill of converting within the metric system is very useful.
Example D
50 g − 275 mg = ?
Convert 50 g to mg: 50 g = 50000 mg
Subtract
OR
Convert 275 mg to g: 275 mg = 0.275 g
Subtract (add a decimal and zeros to make subtraction easier)
Subtract
Example E
Jill wants to put lace around her tablecloth. The bottom of the table cloth measures 2.6 m around. The lace trim is packaged in 75 cm lengths. How many packages of lace will Jill need to buy so she can trim the tablecloth?
First, convert the measurements to the same values. 2.6 m = 260 cm
This is a division problem. How many groups of 75 cm are in 260 cm? 260 cm ÷ 75 cm = 3.47
Jill will need to buy 4 packages. (She needs more than 3 packages and cannot buy a part of a package.)
Exercise 2
Convert as needed to solve these word problems.
Answers to Exercise 2
kilo | hecto | deca | deci | centi | milli |
Only use one unit for a measurement.
For example, use
When there is a mixed measurement such as shown in the examples, do this:
Example F
16 cm + 4 mm
4 mm = 0.4 cm
16 cm + 0.4 cm = 16.4 cm
Example G
1 km + 350 m
350 m = 0.350 km
1 km + 0.35 km = 1.35 km
Exercise 3
Write these measurements using only one unit.
Answers to Exercise 3
Exercise 4
Here is more conversion practice.
Watch for different units! Use the simplest form for the answer.
Answers to Exercise 4
kilo | hecto | deca | deci | centi | milli |
Heads up – a new important twist for you!
When you are dividing two items of the same units, the units cancel themselves out. This means that your answer will not have a unit.
Follow this example:
Exercise 5
Answers to Exercise 5
Mark /16 Aim 13/16
Originally, people would measure things compared to their body parts.
But the imperial system has problems. Measuring things with your own body is not practical because we are all different shapes. And if you have ever tried to divide a foot into 5 equal parts, you will know that it is not easily done. (A foot is 12 inches, which is not easily divided into 5 equal parts). This problem is found with almost all measurements in the imperial system.
Then, the International System (also known as Metric) was created to make it even easier for people to work with measurements. It is made on a Base Ten System. The Base Ten System is another name for the decimal number system that we use every day. Because we already use the Base Ten System as our decimal system, which many cultures around the world use, it is easy to measure things and divide them up or add them together.
Here are some of the measurements that you may see in the Imperial System and the Metric System:
Measurement | Imperial System | International System (Metric) |
---|---|---|
Length | Inch, foot, yard, mile | Millimetre, centimetre, metre, kilometre |
Mass | Ounce, pound, ton | Milligram, gram, kilogram |
Volume | Fluid ounce, cup, pint, quart, gallon | Millilitre, litre, kilolitre |
Here are some conversions between the two systems:
Imperial System | International System (Metric) |
---|---|
1 inch | 2.54 cm |
1 foot | 0.30 m |
1 mile | 1.61 km |
1.09 yards or 3.28 feet | 1 m |
0.62 miles | 1 km |
Imperial System | International System (Metric) |
---|---|
1 ounce | 28.35 g |
1 pound | 0.45 kg |
0.04 ounces | 1 g |
2.20 pounds | 1 kg |
Imperial System | International System (Metric) |
---|---|
1 fluid ounce | 29.57 mL |
1 quart | 0.95 L |
1 gallon | 3.79 L |
0.03 fluid ounces | 1 mL |
1.06 quarts | 1 L |
You may find this is useful information. It is not necessary to learn or memorize any of the above numbers.
21
Test time!
Please see your instructor to get your Practice Test.
When you are confident, you can write your Unit 6 Test.
Congratulations!
1
You will now practice all the skills you learned in Book 4. You can use this as a review for your final test.
If you can’t remember how to do a question, go back to the lesson on this topic to refresh your memory.
The unit and topic for where each question came from is listed in the heading preceding the question. Example: 1B means Unit 1, Topic B.
Date | Cheque number | Details | Transaction |
---|---|---|---|
2022/09/03 | n/a | INTERAC PAYMENT Pharmacy | $28.81 |
2022/09/04 | #207 | Terrace Aquatic Centre | $101.00 |
2022/09/16 | n/a | AUTOMATIC PAYMENT Car Payment | $291.00 |
2022/09/02 | n/a | INTERAC PAYMENT Sally‘s Clothing Store | $132.55 |
2022/09/23 | #208 | Citywest Cable | $74.32 |
2022/09/08 | n/a | WITHDRAWAL Cash | $150.00 |
Date | Cheque number | Details | Transaction |
---|---|---|---|
2022/09/30 | n/a | ELECTRONIC FUNDS TRANSFER Paycheque | $997.26 |
2022/09/15 | n/a | ELECTRONIC FUNDS TRANSFER Paycheque | $948.74 |
DATE | CHEQUE NO. | TRANSACTION | DEBIT | CREDIT | BALANCE |
---|---|---|---|---|---|
BALANCE FORWARD | |||||
Date | Amount of rain in mm |
---|---|
January 10 | 15.5 mm |
January 14 | 2.4 mm |
January 19 | 10.73 mm |
January 24 | 1.9 mm |
January 29 | 13.05 mm |
Unit | Symbol | Measures | Examples |
---|---|---|---|
Metres | |||
Grams | |||
Seconds |
base unit |
DATE | CHEQUE NO. | TRANSACTION | DEBIT | CREDIT | BALANCE |
---|---|---|---|---|---|
BALANCE FORWARD | $621.95 | ||||
2022/09/02 | INTERAC PAYMENT Sally‘s Clothing Store | 132.55 | 489.40 | ||
2022/09/03 | INTERAC PAYMENT Pharmacy | 28.81 | 460.59 | ||
2022/09/04 | 207 | Terrace Aquatic Centre | 101.00 | 359.59 | |
2022/09/08 | WITHDRAWAL Cash | 150.00 | 209.59 | ||
2022/09/15 | ELECTRONIC FUNDS TRANSFER Pay | 948.74 | 1158.33 | ||
2022/09/16 | AUTOMATIC PAYMENT Car Payment | 291.00 | 867.33 | ||
2022/09/23 | 208 | Citywest‘s Cable | 74.32 | 793.01 | |
2022/09/30 | ELECTRONIC FUNDS TRANSFER Pay | 997.26 | 1790.27 |
Unit | Symbol | Measures | Examples |
---|---|---|---|
Metres | m | Length | Running race, height |
Grams | g | Weight/mass | Medication, baby’s weight |
Seconds | s | Time | Time left on a test |
kilo | hecto | deca | base unit | deci | centi | milli |
Final Test Time!
This is the review unit of your course, so, now is the time to write the final test!
See your instructor for the Practice Final Test, and when you are confident, write the Final Test A or B.
Congratulations!
2
3
The numbers to be added together in an addition question. In 3 + 5 = 8, the addends are 3 and 5.
Any straight line used for measuring or as a reference.
Balance has many meanings. In money matters, the balance is the amount left. It might be the amount left in a bank account (bank balance) or it might be the amount you still must pay on a bill (balance owing).
A cheque that has been cashed. The cheque is stamped, or cancelled, so it is no longer negotiable.
The distance around a circle; the perimeter of a circle.
Salespeople may be paid a percentage of the money made in sales. The commission is part or all of their earnings.
e.g., ⅔, ³⁄₇ , ⁴⁹⁄₅₀
In a proportion, multiply the numerator of the first fraction times the denominator of the second fraction. Then multiply the denominator of the first fraction times the numerator of the second fraction. In a true proportion, the products of the cross multiplication are equal.
The bottom number in a common fraction; tells into how many equal parts the whole thing has been divided.
The distance across a circle through its centre.
The result of a subtraction question, the answer. Subtraction gives the difference between two numbers.
Any of the ten numerals (0 to 9) are digits. This term comes from our ten fingers which are called digits. The numerals came to be called "digits" from the practice of counting on the fingers!
An amount taken off the regular cost. If something is bought "at a discount" it is bought at less than the regular price.
To separate into equal parts.
The number or quantity to be divided; what you start with before you divide.
The number of groups or the quantity into which a number (the dividend) is to be separated.
The same as
A mathematical statement that two quantities are equal. An equation may use numerals with a letter to stand for an unknown quantity. 6 + Y = 9
Equal in value; equivalent numbers (whole or fractions) can be used interchangeably; that is, they can be used instead of each other.
Make an approximate answer. Use the sign ≈ to mean approximately equal.
The numbers or quantities that are multiplied together to form a given product. 5 × 2 = 10, so 5 and 2 are factors of 10.
Part of the whole; a quantity less than one unit.
In a flat position, e.g. we are horizontal when we lie in a bed. A horizontal line goes across the page.
A common fraction with a value equal to or more than one.
Without end, without limit.
To turn upside down.
With the same denominators.
When the terms of a common fraction or ratio do not have a common factor (except 1), the fraction or ratio is in lowest terms (also called simplest form).
The first number in a subtraction question.
A whole number and a decimal fraction. 1.75
A whole number and a common fraction. 1 ¾
If a certain number is multiplied by another number, the product is a multiple of the numbers. Think of the multiplication tables. For example, 2, 4, 6, 8, 10, 12, 14... are multiples of 2.
The number to be multiplied.
The number you multiply by.
Something which can be cashed, that is, exchanged or traded as money.
Numbers represent the amount, the place in a sequence; number is the idea of quantity or order.
The digits 1, 2, 3, 4, 5, 6, 7, 8, 9, 0 are also called numerals. These ten digits are combined to make infinite numerals. Digits are like letters, numerals are like words, and numbers are the meaning.
The top number in a common fraction; the numerator tells how many parts of the whole thing are being considered.
If the value of the cheques or money taken from a bank account is higher than the amount of money in the account, then the account is overdrawn. The account is "in the hole" or "in the red" are expressions sometimes used.
Two objects or lines side by side, never crossing and always the same distance from each other. Railway tracks are parallel, the lines on writing paper are parallel.
For every one hundred.
The distance around the outside of a shape.
We understand numbers by the way the digits (numerals) are arranged in relationship to each other and to the decimal point. Each position has a certain value. Our number system is a decimal system. The place value is based on ten.
A number that can only be divided evenly by itself and 1.
The result of a multiplying question, the answer.
A common fraction with a value less than one.
Generally, proportion is a way of comparing a part of something to the whole thing. E.g., his feet are small in proportion to his height. In mathematics, proportion is used to describe two or more ratios that are equivalent to each other.
The result of a division question; the quotient tells how many times one number is contained in the other.
The distance from the centre of a circle to the outside of the circle.
The relationship between two or more quantities. E.g., the ratio of men to women in the armed forces is 10 to 3 (10:3)
A number, when multiplied by its reciprocal, equals 1. To find the reciprocal of a common fraction, invert it. ⅗ × ⁵⁄₃ = 1
Write a common fraction in lowest terms. Divide both terms by same factor.
The amount left when a divisor does not divide evenly into the dividend. The remainder must be less than the divisor.
In mathematics, a symbol that tells what operation is to be performed or what the relationship is between the numbers.
+ plus, means to add
− minus, means to subtract
× multiplied by, "times"
÷ divided by, division
= equal, the same quantity as
≠ not equal
≈ approximately equal
< less than
> greater than
≤ less than or equal to
≥ greater than or equal to
See reduce.
The amount that is taken away in a subtraction question.
The result of an addition question, the answer to an addition question.
A written or printed mark, letter, abbreviation etc. that stands for something else.
a) A definite period of time, such as a school term or the term of a loan.
b) Conditions of a contract; the terms of the agreement.
c) In mathematics, the quantities in a fraction and in a ratio are called the terms of the fraction or the terms of the ratio. In an algebra equation, the quantities connected by a + or − sign are also called terms.
The amount altogether.
One piece of business. A transaction often involves money. When you pay a bill, take money from the bank or write a cheque, you have made a transaction.
Any fixed quantity, amount, distance or measure that is used as a standard. In mathematics, always identify the unit with which you are working. E.g., 3 km, 4 cups, 12 people, $76, 70 books, 545 g.
The price for a set amount. E.g., price per litre, price per gram.
Fractions which have different denominators.
In an up and down position, e.g., we are vertical when we are standing up. On a page, a vertical line is shown from the top to the bottom of the page.
4
This page provides a record of edits and changes made to this book since its initial publication. Whenever edits or updates are made in the text, we provide a record and description of those changes here. If the change is minor, the version number increases by 0.01. If the edits involve substantial updates, the version number increases to the next full number.
The files posted by this book always reflect the most recent version. If you find an error in this book, please fill out the Report an Error form.
Version | Date | Change | Details |
---|---|---|---|
1.00 | October 3, 2014 | Book initially published in the BC Open Collection. | |
2.00 | March 23, 2023 | Book updated and republished in Pressbooks as the second edition. |