• half of one whole thing
• 0.5
• ½
• 50%

• 0.25
• ¼
• 25%

Decimal Fractions

• The total was $12.24.
• It is 3.5 kilometres from my house to the store.
• It costs $1.99 per kilogram for apples.
• She caught a 4.8 kilogram salmon.

Common Fractions

[latex]\frac{3}{4}[/latex] or ¾

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 [latex]\tfrac{8}{8}[/latex] (eight-eigths). If I ate 3 pieces, that would be [latex]\tfrac{3}{8}[/latex] of the pizza.

Fractions as a Percent

1%         12%        50%         99%

What is a Decimal Fraction?

• 1 dollar
• 1 city
• 1 school
• 1 pay cheque
• 1 year
• 1 second
• 1 loaf of bread
• 1 ferry ride

• A decimal point separates whole numbers from the fraction. [latex]\dfrac{1}{10} = 0.1 [/latex]                   [latex]\dfrac{34}{100} = 0.34[/latex]                     [latex]\dfrac{5}{10} = 0.5[/latex]
• In a decimal fraction, there is no denominator.

4.35        100.47          $12.39

Turning a Decimal into Words

• 3 is in the ones spot
• 4 is in the tenths spot
• 5 is in the hundredths spot
• 3 is in the thousandths spot

• 0 is in the ones spot
• 9 is in the tenths spot
• 6 is in the hundredths spot

Tenths Place

• [latex]\frac{6}{10}[/latex] = 0.6 = six tenths
• [latex]\frac{3}{10}[/latex] = 0.3 three tenths

For example, .2 should be written as 0.2.

Hudredths Place

• [latex]\frac{23}{100}[/latex] = 0.23
• [latex]\frac{99}{100}[/latex] = 0.99
• [latex]\frac{4}{100}[/latex] = 0.04

Thousandths Place

• 0.472 = four hundred seventy-two thousandths  = [latex]\tfrac{472}{1000}[/latex]
• 0.085 = eighty-five thousandths   = [latex]\tfrac{85}{1000}[/latex]
• 0.003 = three thousandths = [latex]\tfrac{3}{1000}[/latex]

Ten-thousandths Place

• 0.1458 = [latex]\frac{1458}{10000}[/latex] = one thousand four hundred fifty-eight ten-thousandths
• 0.0581 = [latex]\frac{581}{10000}[/latex] = five hundred eighty-one ten-thousandths

Mixed Decimals

4.3 = [latex]4\frac{3}{10}[/latex] = four and three tenths

27.27 = [latex]27\frac{27}{100}[/latex] = twenty-seven and twenty-seven hundredths

8.104 = [latex]8\frac{104}{1000}[/latex] = eight and one hundred four thousandths

Turning Words into a Decimal

1. Read the number. Does the word "and" show that this is a mixed decimal?
   1. If it does, the whole number is before the word "and." Write the whole number with the decimal point after it.
   2. If there is no whole number, write a 0 with the decimal point after it.
2. Decide how many decimal places you need. Look and listen for the "ths" ending. The word with "ths" is the understood denominator. It may help if you draw a little line for each decimal place that you need.
   • Tenths need one decimal place.
   • Hundredths need two decimal places.
   • Thousandths need three decimal places.
   • Ten-thousandths need four decimal places.
3. Write the decimal so the last digit is on the last little line and fill any remaining lines with zeros.

Reading and Writing Money

Dollars

$1.00 = 1 dollar

• $2.33 = two dollars and thirty-three cents
• $427.05 = four hundred twenty-seven dollars and five cents
• $0.62 = sixty-two cents
• $0.03 = three cents

• centurion - commander of a hundred soldiers
• century - a hundred years
• centennial - a hundredth anniversary
• centigrade - having a hundred degrees
• cent - one hundredth of a dollar
• centimetre - one hundredth of a metre
• centipede - wormlike creatures with a hundred legs

Cents

• $0.05 = 5¢
• $0.33 = 33¢
• $0.10 = 10¢
• $0.25 = 25¢
• $0.99 = 99¢
• $1.08 = 108¢

Topic B: Self-Test

1. Write as decimals. (10 marks)
   1. [latex]\dfrac{3}{10}[/latex]
   2. [latex]\dfrac{24}{1000}[/latex]
   3. [latex]\dfrac{36}{1000}[/latex]
   4. [latex]\dfrac{206}{10000}[/latex]
   5. [latex]3\dfrac{123}{1000}[/latex]
   6. [latex]\dfrac{2}{100}[/latex]
   7. [latex]6\dfrac{3}{10}[/latex]
   8. [latex]4\dfrac{11}{1000}[/latex]
   9. [latex]6\dfrac{250}{1000}[/latex]
   10. [latex]9\dfrac{47}{10000}[/latex]
2. Change these decimals to common fractions.  (8 marks)
   1. 0.5
   2. 0.04
   3. 0.37
   4. 0.010
   5. 3.0918
   6. 3.025
   7. 0.164
   8. 2.1498
3. Write as common fractions and as decimals. (20 marks)
   1. one hundredth
   2. forty-seven hundredths
   3. two hundred seventy-one thousandths
   4. forty-one thousandths
   5. one hundred twenty ten-thousandths
   6. four and four tenths
   7. two hundred sixty and fourteen ten-thousandths
   8. seven and two hundred eleven thousandths
   9. forty and six hundredths
   10. five dollars and sixty-three cents
4. Write the amount of money with numerals, using a $ sign. (3 marks)
   1. Five dollars and sixty cents
   2. Seventy-two cents
   3. Fifty-six cents
   4. Six cents
   5. One hundred twenty-four cents

Answers to Topic B Self-Test

1. Write as decimals.
   1. 0.3
   2. 0.024
   3. 0.036
   4. 0.0206
   5. 3.123
   6. 0.02
   7. 6.3
   8. 4.011
   9. 6.250
   10. 9.0047
2. Change these decimals to common fractions.
   1. [latex]\dfrac{5}{10}[/latex]
   2. [latex]\dfrac{4}{100}[/latex]
   3. [latex]\dfrac{37}{100}[/latex]
   4. [latex]\dfrac{10}{1000}[/latex]
   5. [latex]3\dfrac{918}{10000}[/latex]
   6. [latex]3\dfrac{25}{1000}[/latex]
   7. [latex]\dfrac{164}{1000}[/latex]
   8. [latex]2\dfrac{1498}{10000}[/latex]
3. Write as common fractions and as decimals.
   1. [latex]\dfrac{1}{100}\text{ and }0.01[/latex]
   2. [latex]\dfrac{47}{100}\text{ and }0.47[/latex]
   3. [latex]\dfrac{271}{1000}\text{ and }0.271[/latex]
   4. [latex]\dfrac{41}{1000}\text{ and }0.041[/latex]
   5. [latex]\dfrac{120}{10000}\text{ and }0.0120[/latex]
   6. [latex]4\dfrac{4}{10}\text{ and }4.4[/latex]
   7. [latex]260\dfrac{14}{10000}\text{ and }260.0014[/latex]
   8. [latex]7\dfrac{211}{1000}\text{ and }7.211[/latex]
   9. [latex]40\dfrac{6}{100}\text{ and }40.06[/latex]
   10. [latex]\$5\dfrac{63}{100}\text{ and }\$5.63[/latex]
4. Write the amount of money with numerals, using a $ sign.
   1. $5.60
   2. $0.72
   3. $0.56
   4. $0.06
   5. $1.24

47 = 47.0 = 47.000 = 47.0000000000000000

• in 100, the 0s hold the tens place and the ones place
• in 1206, the 0 holds the tens place

• in 4.306, the 0 holds the hundredths place
• in 17.0002, the 0's hold the tenth, hundredth and thousandth places.

0.5       0.937

Which Zeros are not Needed?

• Zeros at the beginning, or far left, of whole numbers are not needed.
  • 00004 = 4
  • 00100 = 100
• Zeros at the end, or far right, of decimal are not needed.
  • 3.210 = 3.21
  • 34.062000 = 34.062

6. = 6.0 = 6.00

8 = 08 = 00008

Comparing Decimals

Review of Greater Than > and Less Than <

0.43 is larger than 0.40, 0.43 > 0.40

0.52 is smaller than 0.60, 0.52 < 0.60

Comparing Decimals Using a Number Line

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

Topic C: Self-Test

1. Cross out the unnecessary zeros. (4 marks)
   1. 0401.02
   2. 1 000.001
   3. 68.3020
   4. 050.200
2. Draw a box around the larger amount in each pair. (4 marks)
   1. 0.8 or  0.08
   2. 0.004 or  0.04
   3. 0.006 or  0.6
   4. 33.006 or  33.06
3. Put the correct sign between the decimals.  Choose  =  or >  or <. (6 marks)
   1. 2.3          23
   2. 0.2          0.003
   3. 4.7          4.700
   4. 0.25          0.250
   5. 042.9002          042.9
   6. 0.4092          0.411

Answers to Topic C Self-Test

1. Cross out the unnecessary zeros.
   1. 401.02
   2. 1 000.001
   3. 68.302
   4. 50.2
2. Draw a box around the larger amount in each pair.
   1. 0.8
   2. 0.04
   3.  0.6
   4. 33.06
3. Put the correct sign between the decimals.  Choose  =  or >  or <.
   1. <
   2. >
   3. =
   4. =
   5. >
   6. <

• the size of the number we are rounding
• what we are going to do with the number after we have rounded it off
• our own convenience

Rounding Whole Numbers

• Rounding numbers gives an approximate amount; it is not an accurate figure.
• Use a different form of the equal sign (≈) which means “approximate equality.”

Review: Rounding to the Nearest Ten

• Underline the tens digit
• Look at the digit in the ones place (to the right). You can put an arrow above it to help you find it later.
  • If the ones digit is 5 or more, round up. Write the ones digit as zero and increase the tens digit by one.
  • If the ones digit is less than 5, round down. The tens digit does not change and the ones digit is written as a zero.

Review: Rounding to the Nearest Hundred

• Underline the hundreds digit.
• Look at the digit in the tens place (to the right). You can put an arrow above it to help you find it later.
  • If the tens digit is 5 or more, round up. Write the tens and ones digit as zero and increase the hundreds digit by one.
  • If the tens digit is less than 5, round down. The hundreds digit does not change and the tens and ones digit is written as a zero.

• 728 rounded to the nearest hundred is 700. (The tens digit is 2, which is less than 5, so the hundreds digit stays the same.)
• 758 rounded to the nearest hundred is 800. (The tens digit is 5, which is five or more, so the hundreds digit increases by 1.)

Review: Rounding to the Nearest Thousand

• Underline the thousands digit
• Look at the digit in the hundreds place (to the right). You can put an arrow above it to help you find it later.
  • If the hundreds digit is 5 or more, round up. Write the hundreds, tens and ones digit as zero and increase the thousands digit by one.
  • If the hundreds digit is less than 5, round down. The thousands digit does not change and the hundreds, tens and ones digit is written as a zero.

• 2109 rounded to the nearest thousand is 2000. (The hundreds digit is 1, which is less than 5.)
• 2643 rounded to the nearest thousand is 3000. (The hundreds digit is 6, which is more than 5.)
• 0940 rounded to the nearest thousand is 1000. (The hundreds digit is 9, which is more than 5, so the thousands digit increases from 0 to 1.)
• 0465 rounded to the nearest thousand is 0. (The hundreds digit is 4, which is less than 5, so the thousands digit stays at 0.)

Rounding Decimals to Whole Numbers

• Underline the ones digit.
• Look at the digit in the tenths place (to the right). You can put an arrow above it to help you find it later.
  • If the tenths digit is 5 or more, round up. Increase the ones digit by one. Do not write a decimal or any decimal digits.
  • If the tenths digit is less than 5, round down. The ones digit does not change. Do not write a decimal or any decimal digits.

Rounding Decimals to the Nearest Tenth

• Underline the tenths place digit.
• Look at the digit (to the right) in the hundredths place. You can put an arrow above it to help you find it later.
  • If the hundredths digit is less than 5, the tenths digit does not change and the hundredths digit (and all other decimals numbers after the hundredths) are not written at all.
  • If the hundredths digit is 5 or more, increase the tenths digit by one and write no more decimals in the hundredths spot or after.

Rounding Decimals to the Nearest Hundredth

• Underline the hundredths place digit.
• Look at the digit (to the right) in the thousandths place. You can put an arrow above it to help you find it later.
  • If the thousandths digit is less than 5, the hundredths digit does not change and the thousandths digit (and all other decimals numbers after the hundredths) are not written at all.
  • If the thousandths digit is 5 or more, increase the hundredths digit by one and write no more decimals in the thousandths spot or after.

More Dollars and Cents

• [latex]\begin{array}{l}\hspace{2.3em}\downarrow\\\$3.2\underline{8}6\approx\$3.29\end{array}[/latex]
• [latex]\begin{array}{l}\hspace{2.7em}\downarrow\\\$14.9\underline{2}3\approx\$14.92\end{array}[/latex]

Rounding Decimals to the Nearest Thousandth

Topic D: Self-Test

1. Round to the nearest hundred. (2 marks)
   1. 749
   2. 691
2. Round to the nearest whole number. (2 marks)
   1. 0.831
   2. 6.24
3. Round to the nearest tenth. (2 marks)
   1. 8.29
   2. 6.533
4. Round to the nearest hundredth. (2 marks)
   1. 34.792
   2. 6.459
5. Round to the nearest thousandth. (2 marks)
   1. 5.4392
   2. 0.8208
6. Estimate the answer. (2 marks)
   1. Mary baby-sat for her twin nephews for 6.75 hours on Saturday. She is paid $8.40 an hour. Estimate her earnings by rounding the numbers in the problem to whole numbers. Show how you worked out the estimate.

Answers to Topic D Self-Test

1. Round to the nearest hundred. (2 marks)
   1. 700
   2. 700
2. Round to the nearest whole number. (2 marks)
   1. 1
   2. 6
3. Round to the nearest tenth. (2 marks)
   1. 8.3
   2. 6.5
4. Round to the nearest hundredth. (2 marks)
   1. 34.79
   2. 6.46
5. Round to the nearest thousandth. (2 marks)
   1. 5.439
   2. 0.821
6. Estimate the answer. (2 marks)
   1. Estimation: 7 hours × $8 ≈ $56

1. Write as decimals:
   1. [latex]\dfrac{4}{10}[/latex]
   2. [latex]\dfrac{25}{100}[/latex]
   3. [latex]\dfrac{37}{100}[/latex]
   4. [latex]\dfrac{3}{100}[/latex]
   5. [latex]\dfrac{207}{10000}[/latex]
   6. [latex]3\dfrac{787}{1000}[/latex]
   7. [latex]\dfrac{11}{100}[/latex]
   8. [latex]5\dfrac{12}{10000}[/latex]
   9. [latex]38\dfrac{12}{100}[/latex]
   10. [latex]78\dfrac{43}{10000}[/latex]
2. Write these decimals as common fractions:
   1. 0.7
   2. 0.06
   3. 0.49
   4. 3.078
   5. 47.397
   6. 2.173
3. Write as common fractions and as decimals:
   1. three tenths
   2. fifty-one hundredths
   3. three hundred and sixty-one thousandths
   4. fifty one thousandths
   5. four hundred thirty-one ten-thousandths
   6. seven and seven tenths
   7. nine hundred seventy and eighty-nine hundredths
   8. nine and four hundred twelve thousandths
   9. six hundredths
4. Write the amount of money with numerals, using a $ sign:
   1. seven dollars and seventy-eight cents
   2. eighty-eight cents
   3. five hundred dollars and five cents
   4. ninety-nine dollars and ninety cents
   5. five thousand three hundred twenty-two dollars eighty-nine cents
5. Complete the chart. The first two are done for you as examples.

   #	Decimal	Fraction	In words
   a.	0.0005	[latex]\dfrac{5}{10000}[/latex]	five ten-thousandths
   b.	0.07	[latex]\dfrac{7}{100}[/latex]	seven hundredths
   c.		[latex]\dfrac{86}{1000}[/latex]
   d.		[latex]7\dfrac{11}{100}[/latex]
   e.			fourteen and seventeen thousandths
   f.	647.8
   g.		[latex]103\dfrac{62}{1000}[/latex]
   h.	75.13
   i.			forty-two and three tenths
   j.	0.789
   k.			ten and five hundred sixty-seven thousandths

Comparing Decimals

6. Cross out the zeros that are not needed:
   1. 0.5060
   2. 07.0307
   3. 900.380
   4. 05.200
7. Compare the decimals and then put the correct sign between the decimals (<, >, =):
   1. 4.3                  43
   2. 78.9                  7.89
   3. 3.5                  3.05
   4. 042.9003                  042.9
   5. 17.34                  13.34
   6. 4.01                  5.01

Rounding Decimals

8. Round the following decimals:
   1.  To the nearest tenth:
      1. 3.84
      2. 0.09
      3. 3.97
   2. To the nearest hundredth:
      1. 2.754
      2. 4.3856
      3. 5.9754
      4. 1.8032
      5. 37.439
   3. To the nearest thousandth:
      1. 0.1376
      2. 2.7499
      3. 0.00057
   4. To the nearest whole number:
      1. 0.39
      2. 78.78
      3. 4.44
      4. 80.745
      5. 901.399

Answers to Review

1. Write as decimals.
   1. 0.4
   2. 0.25
   3. 0.37
   4. 0.03
   5. 0.0207
   6. 3.787
   7. 0.11
   8. 5.0012
   9. 38.12
   10. 78.0043
2. Write these decimals as common fractions.
   1. [latex]\dfrac{7}{10}[/latex]
   2. [latex]\dfrac{6}{100}[/latex]
   3. [latex]\dfrac{49}{100}[/latex]
   4. [latex]3\dfrac{78}{1000}[/latex]
   5. [latex]47\dfrac{397}{1000}[/latex]
   6. [latex]2\dfrac{173}{1000}[/latex]
3. Write as common fractions and as decimals.
   1. [latex]\dfrac{3}{10}[/latex], 0.3
   2. [latex]\dfrac{51}{100}[/latex], 0.51
   3. [latex]300\dfrac{61}{1000}[/latex], 300.061
   4. [latex]\dfrac{51}{1000}[/latex], 0.051
   5. [latex]\dfrac{431}{10000}[/latex], 0.0431
   6. [latex]7\dfrac{7}{10}[/latex], 7.7
   7. [latex]970\dfrac{89}{100}[/latex], 970.89
   8. [latex]9\dfrac{412}{1000}[/latex]. 9.412
   9. [latex]\dfrac{6}{100}[/latex],  0.06
4. Write the amount of money with numerals, using a $ sign.
   1. $7.78
   2. $0.88
   3. $500.05
   4. $99.90
   5. $5 322.89
5. Complete the chart.

   #	Decimal	Fraction	In words
   a.	0.0005	[latex]\dfrac{5}{10000}[/latex]	five ten-thousandths
   b.	0.07	[latex]\dfrac{7}{100}[/latex]	seven hundredths
   c.	0.086	[latex]\dfrac{86}{1000}[/latex]	eighty-six thousandths
   d.	7.11	[latex]7\dfrac{11}{100}[/latex]	seven and eleven hundredths
   e.	14.017	[latex]14\dfrac{17}{1000}[/latex]	fourteen and seventeen thousandths
   f.	647.8	[latex]647\dfrac{8}{10}[/latex]	six hundred forty-seven and eight tenths
   g.	103.062	[latex]103\dfrac{62}{1000}[/latex]	one hundred three and sixty-two thousandths
   h.	75.13	[latex]75\dfrac{13}{100}[/latex]	seventy-five and thirteen hundredths
   i.	42.3	[latex]42\dfrac{3}{10}[/latex]	forty-two and three tenths
   j.	0.789	[latex]\dfrac{789}{1000}[/latex]	seven hundred eighty-nine thousandths
   k.	10.567	[latex]10\dfrac{567}{1000}[/latex]	ten and five hundred sixty-seven thousandths

6. Cross out the zeros that are not needed.
   1. 0.506
   2. 7.0307
   3. 900.38
   4. 5.2
7. Compare the decimals and then put the correct sign between the decimals (<, >, =).
   1. <
   2. >
   3. >
   4. >
   5. >
   6. <
8. Round the following decimals:
   1.  To the nearest tenth:
      1. 3.8
      2. 0.1
      3. 4.0
   2. To the nearest hundredth:
      1. 2.75
      2. 4.39
      3. 5.98
      4. 1.80
      5. 37.44
   3. To the nearest thousandth:
      1. 0.138
      2. 2.750
      3. 0.001
   4. To the nearest whole number:
      1. 0
      2. 79
      3. 4
      4. 81
      5. 901

Vocabulary Review Use the example below and the glossary to help you write the definitions. Definition of Addends: Definition of Sum:

• Add thousandths to thousandths.
• Add hundredths to hundredths.
• Add tenths to tenths.

How to Add Decimals

1. Write the [pb_glossary id="609"]addends[/pb_glossary] underneath each other so the decimal points are in a straight column. Notice how lining up the decimals also lines up the place values. [latex]0.43+0.2+0.804+0.1=[/latex] Rewrite as: [latex]\begin{array}{ll}&0.43\\&0.2\\&0.804\\+&0.1\\ \hline\end{array}[/latex]
2. Put zeros at the end of the decimal fractions so that all fractions have the same number of decimal places. [latex]\begin{array}{ll}&0.430\\&0.200\\&0.804\\+&0.100\\ \hline\end{array}[/latex]
3. It may help you to put the decimal point in the answer line before you do the addition. [latex]\begin{array}{ll}&0.430\\&0.200\\&0.804\\+&0.100\\ \hline &\phantom{0}\mathbf{.}\end{array}[/latex]
4. When adding [pb_glossary id="669"]mixed decimals[/pb_glossary], be sure to keep the whole number places lined up as well. As you know, ones add to ones, tens to tens, hundreds to hundreds and so on. Put a decimal point after any whole numbers. [latex]62.1 + 14.58 + 6. + 7.311 + 6.23 =\\ \begin{array}{lr}&62.100\\&14.580\\&6.000\\&7.311\\+&6.230 \\ \hline\end{array}[/latex]
5. Add each column, starting with the decimal place farthest to the right. If the total of a column is ten or more, carry the ten number to the next column as you are used to doing with whole numbers. [latex]\begin{array}{ll}&\small{1\; 1}\\&0.470\\&0.298\\&0.100\\+&5.600\\ \hline &6.468\end{array}[/latex]

How to Solve Word Problems

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? A regular serving contains 2.8 g protein, 0.2 g fat, 25 carbohydrate, and 1.9 g "other nutrients." Add the information to your Picture.
Step 3: Operation	The problem lists four different amounts and asks you to find one total. "Total" is a key word that points to addition. Add the operation you need to your picture: Next, write an equation: 2.8 + 0.2 + 25 + 1.9 = total number of grams
Step 4: Estimate	Round off each amount and add them together to get an estimated answer. 2.8 g ≈ 3 g, 0.2 g ≈ 0 g, 25 g ≈ 25 g, 1.9 g ≈ 2g 3 g + 0 g + 25 g + 2 g = 30 g Does this answer make sense? A slice of bread is about 35 grams. A serving of cereal would probably weigh a similar amount. Yes, this makes sense.
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) Check arithmetic Compare answer to estimate  (estimate = 30   answer =29.9) Does the answer make sense? Did I include the units in my answer?

• [pb_glossary id="721"]sum[/pb_glossary]
• plus
• [pb_glossary id="727"]total[/pb_glossary]
• total amount
• altogether
• combined
• complete
• entire
• in all
• added to
• increased by

Word Problems Using Addition of Decimals

Topic A: Self-Test

1. Find the sum. (4 marks)
   1. [latex]\begin{array}{rr}&3.67\\&12.55\\&8.19\\+&5.67\\ \hline\\ \end{array}[/latex]
   2. [latex]5.27 + 2.4 + 8 + 6.93 + 10.27 =[/latex]
   3. [latex]\begin{array}{rr}&4.648\\&1.92\phantom{0}\\&1.275\\+&86.9\phantom{00}\\ \hline\\ \end{array}[/latex]
   4. [latex]2.72 + 0.6 + 110 + 17.223 =[/latex]
2. Word Problem. (2 marks) Gwen mailed Christmas presents to her family. She sent a 3.7 kg box to her daughter in Vancouver, a 2.145 kg package to her sister's family in Campbell River, a box to Prince George that was 1.06 kg, and a parcel to Kitwanga that was 4 kg. What was the combined weight of Gwen's parcels?
   1. Estimate:
   2. Actual Solution:
   3. Answer:

Answers to Topic A Self-Test

1. Find the sum.
   1. 30.08
   2. 32.87
   3. 94.743
   4. 130.543
2. Word problem.
   1. Estimation: 4 kg + 2 kg +1 kg + 4 kg = 11 kg
   2. Actual Solution: 3.7 kg + 2.145 kg + 1.06 kg + 4 kg = 10.905 kg
   3. Answer: The combined weight of the parcels was 10.905 kg.

• Subtract thousandths from thousandths.
• Subtract hundredths from hundredths.
• Subtract tenths from tenths.

How to Subtract Decimals

1. Rewrite the problem. Write the first number. Put the amount you are subtracting underneath so the decimal points are in a straight column. [latex]\begin{array}{rrl}0.468&-&0.3=\\ \uparrow &&\uparrow \\ \text{starting number}&&\text{subtracting this much}\end{array}[/latex] [latex]\begin{array}{ll}&0.468\\-&0.3\\ \hline\end{array}[/latex]
2. Put zeros at the end of the decimals so that all the decimals in the question have the same number of decimal places. [latex]0.468-0.3=\begin{array}[t]{ll}&0.468\\-&0.3\mathbf{00}\\ \hline\end{array}[/latex]
3. Subtract the numbers, keeping the decimal point in the answer directly beneath the other decimal points. [latex]\begin{array}{ll}&0.468\\-&0.300\\ \hline &\phantom{0}\mathbf{.}\end{array}[/latex]

Subtracting a Decimal from a Whole Number

1. Put a decimal point after the whole number. 16. − 0.4 =
2. Rewrite the problem. Write the first number. Put the amount you are subtracting underneath so the decimal points are in a straight column. [latex]\begin{array}[t]{rr}&16.\hspace{0.5em}\\-&0.4\\ \hline\end{array}[/latex]
3. Put zeros after the decimal point as needed. [latex]\begin{array}[t]{rr}&16.\mathbf{0}\\-&0.4\\ \hline\end{array}[/latex]
4. Do the subtraction as usual. See that you will need to borrow right away.

Word Problems Using Subtraction of Decimals

• [pb_glossary id="629"]difference[/pb_glossary]
• [pb_glossary id="613"]balance[/pb_glossary]
• minus
• amount left
• subtracted from
• decreased by
• reduced by
• taken away
• less
• compare

Design Your Own House Part 1: Drawing and Measuring

1. On a sheet of graph paper, use a ruler to draw a one-story house (bird’s-eye-view). Use the scale of 1 cm² = 1m².
2. You may make your house any shape you choose (square, rectangle, L-shaped, etc.) but one wall must measure 15.5 metres (it will be 15.5 cm on your graph paper).
3. Clearly label the length of each wall and show your calculations! Be precise and careful with your sketching. Feel free to add colour or get creative.
4. Be sure to organize and label all your work!
   1. What is the perimeter of the entire house? (perimeter = side + side + side + side)
5. Give your house two bedrooms. Clearly label the length of each wall.
6. Include a bathroom, a living room, and a kitchen. Label the length of each wall.
   2. What is the perimeter of each room?
      • Bedroom 1:
      • Bedroom 2:
      • Bathroom:
      • Kitchen:
      • Living room:
7. On your sketch, give your house two exterior doors and four exterior windows, each 1m wide. Because it is two-dimensional bird’s eye view, you can’t see the height of your doors and windows, but imagine that each door would be 2.3 m tall and each window would be 1.1 m tall. Sketch one window and one door here, and label the measurements.
   3. Each window needs external trim and internal trim. How much trim would you need to buy to have enough to go around all of the windows?
   4. Each door would also need external and internal trim. How much trim would you need to go around both doors? Keep in mind that the bottom of the door will not need trim.

Marking Checklist of House Project Part 1

Topic B: Self-Test

1. Subtract. (4 marks)
   1. [latex]\begin{array}[t]{rr}&72.04\\-&13.98\\ \hline\\ \end{array}[/latex]
   2. [latex]19.6-6.254 =[/latex]
   3. [latex]\begin{array}[t]{rr}&11.21\\-&3.875\\ \hline\\ \end{array}[/latex]
   4. [latex]\$140-\$102.73 =[/latex]
2. Problems (2 marks)
   1. Gail spent $273.24 on her groceries. She had $300 with her. How much of her money is left?
      • Estimation:
      • Actual Solution:

Answers to Topic B Self-Test

1. Subtract.
   1. 58.06
   2. 13.346
   3. 7.335
   4. $37.27
2.  Problems.
   1. Estimation: $300 − $275 ≈ $25
   2. Actual Solution: $300 − $273.24 = $26.76. Gail had $26.76 left after buying groceries.

• Add money received or deposited to our accounts.
• Subtract money spent or paid out.

Methods of Payment

• Cash
• Debit card
• Credit card
• Cheque
• Online payment (i.e., PayPal, e-transfer)

Cash

Advantages:

• It is quick and easy to pull money out of your wallet.
• You can see how much money you have left.
• It is impossible to overspend.
• It is a great method to use if you do not have a bank account.

Disadvantages:

• It is easier to loose.
• You may need to continue to visit the bank to get money out.
• You might run out of cash while trying to pay at the till.

Debit Card

Advantages:

• It is quick at the till.
• You cannot spend more than you have in your bank account.
• It is safe.

Disadvantages:

• There is often a service fee when using the card to pay for shopping.
• You cannot always use it for online shopping.

Credit Card

Advantages:

• You only have to pay the company money once a month.
• It is quick at the till.
• It is easy to keep track of what you have spent because the credit card company sends you a monthly statement.
• You can use a credit card for online shopping.

Disadvantages:

• It is really easy to overspend your budget because you do not have to pay any money up front.
• There are often service charges once a year that are expensive.
• You can get into debt with a credit card and it may be really hard to get out of that debt.

Cheque

Advantages:

• It can be convenient when you want to mail someone money.
• It is safe.
• The cheque book helps you keep a written record of your bank balance.

Disadvantages:

• Some stores do not accept cheques or require several pieces of identification, usually a driver's licence and a credit card.
• Most banks and credit unions have a small service charge for each cheque that you write.
• If your account is [pb_glossary id="685"]overdrawn[/pb_glossary], your cheque will be N.S.F. (Not Sufficient Funds) for which you are charged extra by the store and the bank. To avoid this, keep careful, up-to-date records so you always know your balance.

Online Payment

Advantages:

• It allows you to shop online securely.
• You can pay directly online with money from your bank account or your credit card.
• You can easily send money to friends or family.

Disadvantages:

• You may not have rights that regular banks give you when you use an online payment company.
• The company is not local, and so any problems may be hard to resolve.
• There are fees charged to have an online payment account.

Online Banking

• Date – The date of the transaction. The examples given use this method: 2023-01-29. January 29 is the 29th day of the 1st month.
• Debit – This is money that is deposited into the account, either through a cash deposit, a paycheque, or a transfer in.
• Credit – This is money that has gone out of the account, either through a withdrawal, a bill payment, or a transfer out.
• Running Balance – The amount in the bank account after each transaction.

Cheque Writing

1. When you have a chequing account, you sometimes have cheques printed with your name, address and phone number, usually in the top left corner.
2. The cheques are numbered in sequence (in order) to help you keep track of your cheques.
3. This line is for the name of the person or institution that will be receiving the money.
4. This line is for the amount of the cheque in numbers: $22.98.
5. This spot is for you to write, in words, the dollars to be paid. Write the cents as a fraction over 100. If you do not use the whole line, fill unused parts of the space with a straight line so that nothing can be added. $22.98 becomes twenty-two and 98⁄100 dollars.
6. The Memo spot is a place for details. It is useful if you want to use the cheque as a receipt, too. You might list the invoice number for the bill you are paying, for example.
7. When you open a bank account, the bank will ask you for a sample signature for their files. Sign exactly as you plan to sign your cheques.
8. Your bank account number and codes used at the bank will be printed on your cheques.