• Scores in games are ratios. For example, the Penguins won 4 to 3 or the Canucks lost 1 to 5.
• Directions for mixing can be ratios. For example, use 1 egg to each cup of milk or mix 25 parts gas to 1 part oil for the motorcycle.
• Betting odds are given as ratios. For example, Black Jade is a 3 to 1 favourite or the heavyweight contender is only given a 2 to 5 chance to win.
• The scale at the bottom of maps is a ratio. For example, 1 centimetre represents 10 kilometres.
• Prices are often given as ratios. For example, 100 grams for $0.79 or 2 cans for $1.85.

1. It rained four days and was sunny for three days last week. The ratio of rainy days to sunny days was [latex]4:3[/latex]. ([latex]4:3[/latex] is properly read "4 is compared to 3" but is often read "4 to 3").
2. The class has 12 men and 15 women registered. The ratio of men to women in the class is [latex]12:15[/latex].
3. At the barbeque, 36 hot dogs and 18 hamburgers were eaten. The ratio of hot dogs eaten to hamburgers eaten is [latex]36:18[/latex].
4. The class spends 3 hours on English and 2 hours on math each day. The ratio of time spent on English compared to math is [latex]3:2[/latex].

Ratios can be written 3 different ways:

1. Using the [latex]:[/latex] symbol — [latex]2:5[/latex]
2. As a common fraction — [latex]\frac{2}{5}[/latex]
   • The first number in the ratio is the numerator; the second number is the denominator.
   • Ratios written as a common fraction are read as a ratio, not as a fraction. Say "2 to 5," not "two-fifths."
3. Using the word "to" — 2 to 5

Exercise 3

Use the diagram to write a ratio comparing the quantity of each shape, as asked.

1. 
2. 
3. 

Answers to Exercise 3

1. [latex]9:6[/latex] or [latex]\frac{9}{6}[/latex] or 9 to 6
2. [latex]7:9[/latex] or [latex]\frac{7}{9}[/latex] or 7 to 9
3. [latex]6:9[/latex] or [latex]\frac{6}{9}[/latex] or 6 to 9

Equivalent Ratios

• Find equivalent ratios in higher terms
• Find equivalent ratios in lower terms
• Find a missing term

Topic A: Self-Test

1. Write the definitions. (3 marks)
   1. Ratio
   2. Terms of the ratio
   3. Equivalent ratios
2. Write the ratios asked for in lowest terms. Use the colon style like this: [latex]2:1[/latex]. Then write the ratio as it is read, like this: two to one. (4 marks)
   1. The campground had three vacant campsites and 47 occupied sites. Write the ratio of occupied sites to vacant sites. Ratio:                       Read:                                                            
   2. For every ten dogs in the city, only 2 have current dog licences. Write the ratio of licensed dogs to unlicensed dogs. (Find the number of unlicensed dogs first). Ratio:                       Read:                                                            
3. Simplify these ratios. (5 marks)
   1. [latex]9:12[/latex]
   2. [latex]6:4[/latex]
   3. [latex]500:1000[/latex]
   4. [latex]2:9[/latex]
   5. [latex]35:15[/latex]

Topic B: Self-Test

1. Write the definition. (1 mark)
   1. Rate
2. Write the following ratios as rates. Round people to the nearest person. (6 marks)
   1. 12 cups water, 3 cups sugar
   2. 72 metres, 24 seconds
   3. 1,365,000 people, 4,000 km²
   4. 5,000 cars on the road, 250 bikes on the road
   5. 12 cups of flour, 12 tsp. of baking powder
   6. 8 litres of gas, 2 litres of oil

Problems often give incomplete information; that is, one of the terms is missing. To solve such problems, you first find the comparison or ratio that is given. It may be:

• A quantity of one thing that is mixed with a larger quantity of something else
• A scale of measurement given on a map such as 1 cm on the map represents 100 km distance on land
• Cost for a certain number of items
• Time to travel a certain distance

[latex]\begin{equation*}\begin{split} \dfrac{\text{number of heads of lettuce}}{\text{cost}} &= \dfrac{\text{number of heads of lettuce}}{\text{cost}} \\ \\ \dfrac{3}{$1.49} &= \dfrac{7}{?} \\ \\ 3:$1.49 &= 7: ? \end{split}\end{equation*}[/latex]

[latex]\dfrac{\text{time}}{\text{distance}}=\dfrac{\text{time}}{\text{distance}}[/latex]

[latex]\dfrac{\text{distance}}{\text{time}}=\dfrac{\text{distance}}{\text{time}}[/latex]

• You can use your skills with equivalent ratios (finding higher and lower terms)
• You can use your fraction skills of cross-multiplying and then dividing to find the missing term

Using Equivalent Ratios to Solve Proportions

Using Cross-Multiplication to Solve a Proportion

[latex]\dfrac{2}{5}\rlap{\nearrow}{\searrow}\dfrac{4}{10}[/latex]

[latex] \begin{equation*} \begin{split} 2\times10 & =5\times4 \\ 20 & =20 \end{split} \end{equation*} [/latex]

[latex]2\times10=20[/latex] and [latex]5\times4=20[/latex]

[latex]\dfrac{6\textit{P}}{6}=\dfrac{1\textit{P}}{1}=\textit{P}[/latex]

The numbers in a ratio often are common fractions, decimals or mixed numbers. Follow exactly the same steps that you have been using to solve whole number proportions. The calculations will use your skills with fractions.

Topic C: Self-Test

1. Solve these proportions. (6 marks)
   1. [latex]\textit{N}:14=28:56[/latex]
   2. [latex]3:11=\textit{N}:22[/latex]
   3. [latex]50:45=10:\textit{N}[/latex]
   4. [latex]4\frac{1}{5}:\textit{Y}=3:2[/latex]
2. (14 marks)
   1. Get a map of BC, a map of Canada, and a map of your city or town.
   2. Find the scale on each map (usually at the bottom) and write down the ratio of map distance to the actual distance.
   3. With another student or an instructor, calculate actual distances between places by measuring the distance on the map and working out the proportion according to the scale given. Do at least three distance calculations on each map.
   Ask your instructor to mark your work.

1. Write the ratios asked for in the questions. Reduce when able.
   1. It snowed for two days and was sunny for five days last week. Write a ratio to compare snowy days to sunny days.
   2. The class spends 6 hours a week on math and 8 hours on English. Write the ratio of hours spent on math to English.
   3. One kilogram of pork will make enough sausages for 7 people. Write a ratio to express the amount of pork for sausages to the number of people.
   4. A jam recipe calls for 8 cups of blue berries to 3 cups of sugar. Write a ratio to express the amount of berries to sugar.
2. Write the ratios in lowest terms.
   1. [latex]14:21[/latex]
   2. [latex]8:24[/latex]
   3. [latex]15:150[/latex]
   4. [latex]9:54[/latex]
3. Write the following ratios as rates.
   1. 16 cups of water to 4 cups of sugar
   2. 150 kilometres to 1.25 hours
   3. 465,000 people to 3,000 square kilometres
   4. $3.99 to 10 pounds of apples
4. Use cross-multiplication to solve the proportions. Round to 2 decimal places, if needed.
   1. [latex]\dfrac{5}{8}=\dfrac{\textit{P}}{24}[/latex]
   2. [latex]\dfrac{\textit{S}}{100}=\dfrac{8}{25}[/latex]
   3. [latex]\dfrac{4}{\textit{N}}=\dfrac{8}{40}[/latex]
   4. [latex]\dfrac{4}{14}=\dfrac{\textit{F}}{68}[/latex]
5. Use cross-multiplication to solve the proportions.
   1. [latex]\dfrac{2\frac{1}{4}}{5}=\dfrac{\textit{A}}{30}[/latex]
   2. [latex]\dfrac{11}{8}=\dfrac{4\frac{1}{8}}{\textit{P}}[/latex]
   3. [latex]\dfrac{3\frac{3}{4}}{5}=\dfrac{8}{\textit{X}}[/latex]
   4. [latex]\dfrac{2\frac{2}{3}}{3}=\dfrac{\textit{A}}{16}[/latex]

Unit 1

1-A

1. Write the ratios asked for.
   1. Lillian biked for 6 hours, and covered a total of 45 km. What is the ratio of kilometers to hours?
   2. Nine hundred cars were lined up at the ferry terminal. 300 hundred cars got on the next sailing. Write a ratio of how many cars were left behind to how many cars got on the first sailing.

1-B

2. Simplify these ratios.
   1. [latex]9:12[/latex]
   2. [latex]50:5[/latex]
   3. [latex]56:7[/latex]
   4. [latex]100:120[/latex]
3. Write the following ratios as rates.
   1. 110 kilometres to 2 hours
   2. 9 cups of flour to 3 tablespoons of yeast
   3. 240,000 people to 300 square kilometers

1-C

4. Solve these proportions.
   1. [latex]1:3 = \textit{N}:12[/latex]
   2. [latex]25:\textit{N} = 20:4[/latex]
   3. [latex]\textit{N}:49 = 14:98[/latex]
   4. [latex]4\tfrac{1}{2}:6 = \textit{N}:3.6[/latex]
   5. The dose for cough syrup is 20 millilitres for each 100 pounds of body weight. How much should be given to a 34 pound child? Round to the nearest millilitre.

Unit 2

2-A

5. Write these percents using numerals and the percent sign.
   1. seventy-two percent
   2. three-fourths percent
   3. one hundred two percent
6. Write these percents in words.
   1. [latex]12\%[/latex]
   2. [latex]\tfrac{1}{5}\%[/latex]
7. Change the percents to equivalent decimals.
   1. [latex]17\%[/latex]
   2. [latex]98\tfrac{1}{2}\%[/latex]
   3. [latex]\tfrac{1}{3}\%[/latex]
8. Write the decimals as percents.
   1. [latex]0.45[/latex]
   2. [latex]4.75[/latex]
   3. [latex]0.099[/latex]
9. Change each percent to an equivalent common fraction. Put the fraction in lowest terms.
   1. [latex]33\tfrac{1}{3}\%[/latex]
   2. [latex]14\%[/latex]
   3. [latex]250\%[/latex]
10. Write the percent equivalent
    1. [latex]\tfrac{1}{5}[/latex]
    2. [latex]\tfrac{2}{3}[/latex]
    3. [latex]\tfrac{1}{4}[/latex]

Unit 3

3-A

11. Find the answers.(Express percents rounded to the nearest tenth, money to the nearest cent and decimals to the nearest thousandth. Please show all your work. Use proportion.)
    1. [latex]13\%\text{ of }52 =[/latex]
    2. [latex]\tfrac{9}{10}\%\text{ of }2,400[/latex] is                    .
    3. What is [latex]135\%\text{ of }1,080[/latex]?
12. Solve these problems. Be sure to show all your work.
    1. Marianne is renovating her kitchen, and she is ordering everything from her local hardware store. She is getting a sink for $204.79, a dishwasher for $524.95, a counter for $949.99, flooring for $719.95, and a fridge for $579.49.
       1. Calculate the HST (12%).
       2. Calculate the total cost, including the taxes.
    2. Shane sold a home for $340,500.00 for a client. He earned 6% commission. How much money did Shane make?
    3. A love seat is originally priced at $904.00, it is offered at 45% off. What is the discount price?
    4. Calculate the total cost in Canadian dollars of this purchase made in the United States. Assume $1.00 Canadian = $0.92 U.S. [latex]\text{Clothes} – \text{Total price in }$\text{US} = $317.98[/latex].
       1. Price in Canadian dollars
       2. Duty at 13.5%
       3. Total of Canadian value + duty
       4. HST (12%) on Canadian value + duty
       5. Total cost in Canadian dollars

Unit 4

4-A

13. Find the answers.
    1. 34 is what percent of 85?
    2. What % of 150 is 114?
    3. 33⅓% of what number is 60?
    4. 32 is 20% of what number?
    5. 75% of what number is 675?
    6. 3.75 is 1¼% of?
14. Solve these problems. Be sure to show all your work.
    1. A printer is priced at $399. It is marked 30% off.
       1. What is the sale price of the printer?
       2. What is the cost of this printer with HST (12%)?
    2. The Vancouver Fire and Rescue Service has 797 uniformed personnel, about 0.8% are women. About how many women are in uniform in the Vancouver Fire and Rescue Service? Answer to the nearest whole number (since you cannot have a fraction of a person).
    3. Jake is a computer salesperson. He receives a monthly salary of $1,055 plus 15% on all his sales over $5,500. What was his total monthly earnings if his sales were $12,400 in one month?
    4. The local ski hill sold 3,800 season’s passes in 2009. The 2010 sales are down 10.5%. Find the number of season’s passes sold in 2010.

Unit 5

5-A

15. Line graph.

    

    1. Which month has the highest temperature in Smithers?
    2. Which month has the lowest temperature in Smithers?
    3. Between the months of January to July, is there an increase or decrease in temperature?
    4. What is the difference between the monthly temperature for August and the monthly temperature for October?
    5. What is the trend of the temperature in Smithers?

5-B

16. Bar graph.

    

    1. What is the height of the tallest mountain in BC?
    2. How many mountains are over 4,000 metres and under 5,000 metres in height?
    3. Which two mountains in this chart are very similar in height?
    4. What is the difference (approximately) in height between Fairweather Mountain and Asperity Mountain?

5-C

17. Picture graph.

    

    1. How many students in grade 2 ride bikes to school?
    2. Which classes have the most bikers?
    3. Which class has the least bikers?
    4. How many more bikers are in grade 7 than kindergarten?
    5. How many students bike in total?
    6. What percent of the school bikes each day?

5-D

18. Circle graph.

    

    1. Which is the most favourite ice cream flavour?
    2. Which is the least liked ice cream flavour?
    3. How many people (out of 1,000) like fruit-flavoured ice cream?
    4. What percentage of people like vanilla over chocolate?

Image Descriptions

Graph 1 (Line Graph)

• The horizontal axis lists each month of the calendar year.
• The vertical axis is temperature in degrees Celsius, and contains the numbers -15 to 20 in increments of 5.

Graph 2 (Bar Graph)

• The horizontal axis lists the following mountains: Fairweather Mountain, Mount Quincy Adams, Mount Waddington, Mount Robson, Mount Root, Mount Tiedemann, Combatant Mountain, Mount Columbia, and Asperity Mountain.
• The vertical axis is height in metres, and contains the numbers 5,000 in increments of 100.

Graph 3 (Picture Graph)

• The vertical axis lists the following grades at Marmot Elementary School: Grade 7, Grade 6, Grade 5, Grade 3, Grade 2, Grade 1, and Kindergarten.
• The horizontal axis contains pictures of bicycles, with each bicycle representing 5 bikers according to the legend.
• The total school population is 563 students.

Graph 4 (Circle Graph)

• The entire graph represents all 1,000 people surveyed for their favourite ice cream flavour.
• Each part represents an ice cream flavour and its popularity as a percent of the whole. The flavours are (clockwise from top): Vanilla, Fruit, Nut, Candy, Chocolate, and Cake and Cookie.

• Liz Girard, North Island College
• Wendy Tagami, Selkirk College

Advisory Committee Members

• Jill Auchinachie, Camosun College
• Leanne Caillier-Smith, College of the Rockies
• Mercedes de la Nuez, Coast Mountain College
• Barbara Stirsky, University of the Fraser Valley
• Jan Weiten, Vancouver Community College

The Deans and Directors of Developmental Education

• Stephanie Jewell, Vancouver Community
• College Vivian Hermansen, North Island College
• Lyle Olsen, Selkirk College
• Allison Alder, Selkirk College

Also

• The Adult Literacy Fundamental Working Group
• Cheryl Porter, North Island College
• Stephen & Jennifer Marks, Layout editors

• Easy navigation. This text has a linked table of contents and uses headings in each chapter to make navigation easy.
• Accessible math equations. Many of the equations in this text have been written in LaTeX and rendered with MathJax, which makes them accessible to people using screen readers that are set up to read MathML. The rest of the equations are rendered as images with appropriate alternative text.
• Accessible images. All images in this text that convey information have alternative text. Images that are decorative have empty alternative text.
• Accessible links. All links use descriptive link text.

Known Accessibility Issues and Areas for Improvement

Let Us Know if You are Having Problems Accessing This Book

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How to Use This Book

• A Table of Contents listing the units, the major topics, and the subtopics.
• A Grades Record to keep track of your marks.
• Many Exercises to practice what you learned. Some are quite short, but others have a great number of questions. You do not have to do every single question!
  • Do as many questions as you feel are necessary for you to be confident in your skill. It is best to do all the word problems.
  • If you leave out some questions, try doing every second or every third question. Always do some questions from the end of each exercise because the questions usually get harder at the end. You might use the skipped questions for review before a test.
  • If you are working on a difficult skill or concept, do half the exercise one day and finish the exercise the next day. That is a much better way to learn.
• Self-tests at the end of most topics have an "Aim" at the top. If you do not meet the aim, talk to your instructor, find what is causing the trouble, and do some more review before you go on.
• A Review and Extra Practice section is at the end of each unit. If there is an area of the unit that you need extra practice in, you can use this. Or, if you want, you can use the section for more review.
• A Practice Test is available for each unit. You may:
  • Write the practice test after you have studied the unit as a practice for the end-of-chapter test, OR
  • You might want to write it before you start the unit to find what you already know and which areas you need to work on.
• Unit Tests are written after each unit. Again, you must reach the Aim before you begin the next unit. If you do not reach the aim, the instructor will assist you in finding and practising the difficult areas. When you are ready, you can write a B test to show that you have mastered the skills.
• A Final Test is to be written when you have finished the book. This final test will assess your skills from the whole book. You have mastered the skills in each unit and then kept using many of them throughout the course. The test reviews all those skills.

Grades Record

Grade Record - Book 2

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
Final Test

• Write the number in the usual way
• Place the percent sign after the numerals
  • [latex]50\%[/latex]
  • [latex]5\frac{1}{2}\%[/latex] or [latex]5.5\%[/latex]
  • [latex]\frac{3}{4}\%[/latex] or [latex]0.75\%[/latex]

• Read the numbers in the usual way
• Say “percent" after the number
  • [latex]16\%[/latex]: say “sixteen percent"
  • [latex]4\frac{1}{2}\%[/latex]: say "four and one-half percent"
  • [latex]0.25\%[/latex]: say "twenty-five hundredths percent," or “one-quarter percent," or “point two five percent"

Changing Decimals to Percents

[latex]4.27\times100=427[/latex] [latex]0.287\times100=28.7[/latex] [latex]53\times100=5300[/latex]

[latex] \begin{equation*}\begin{split} &\curvearrowright \\ 0.24=0&.24=\cancel{0.}24\%=24\% \end{split}\end{equation*}[/latex]

[latex] \begin{equation*}\begin{split} &\curvearrowright \\ 0.05=0&.05=\cancel{0.0}5\%=5\% \end{split}\end{equation*}[/latex]

[latex] \begin{equation*}\begin{split} &\curvearrowright \\ 0.4=0&.40=40\% \end{split}\end{equation*}[/latex]

[latex] \begin{equation*}\begin{split} &\curvearrowright \\ 1.7=1&.70=170\% \end{split}\end{equation*}[/latex]

[latex] \begin{equation*}\begin{split} &\curvearrowright \\ 2=2&.00=200\% \end{split}\end{equation*}[/latex]

Changing Percents to Decimals

• If there is no decimal point in the percent, place the decimal point after the last numeral and then divide by 100. \[24\%=24.0\%=0.24\]
• It may be necessary to prefix zeros. (This means adding zeros in front of the number, if needed). \[6\%=6.0\%=0.06\]
• A zero at the right of a decimal is not needed and may be left off. \[40\%=40.0\%=0.40=0.4\]

• Change the common fraction in the percent to a decimal in the percent.
• Divide by 100 (move the decimal 2 places to the left).

Changing Common Fractions to Percents

Method One

Method Two

Convert [latex]\dfrac{3}{8}[/latex] to a percentage

	[latex]\dfrac{3}{8} = \,?\,\%[/latex]
Use long division to write fraction as a decimal.
	[latex]\dfrac{3}{8} = 0.375[/latex]
Move the decimal point two places to the right and add the percent sign.	[latex]0.375 = 37.5\%[/latex]

Convert [latex]\dfrac{1}{3}[/latex] to a percentage

	[latex]\dfrac{1}{3} = \,?\,\%[/latex]
Use long division to write fraction as a decimal.
	[latex]\dfrac{1}{3} = 0.33\overline{3}[/latex]
Move the decimal point two places to the right and add the percent sign.	[latex]0.33\overline{3}=33.\overline{3}\% \text{ also written as } 33\dfrac{1}{3}\%[/latex]

Convert [latex]\dfrac{11}{12}[/latex] to a percentage

	[latex]\dfrac{11}{12} = \,?\,\%[/latex]
Use long division to write fraction as a decimal.
	[latex]\dfrac{11}{12} = 0.91\overline{6}[/latex]
Move the decimal point two places to the right and add the percent sign.	[latex]0.916\overline{6} = 91.\overline{6}\%[/latex]

• [latex]\dfrac{1}{3}=33\frac{1}{3}\%[/latex]
• [latex]\dfrac{2}{3}=66\frac{2}{3}\%[/latex]

Changing Percents to Common Fractions

• Write the numerals in the percent as the numerator.
• Write 100 as the denominator. (Remember that the line in a fraction can be a "divided by" sign, so [latex]58\%=\dfrac{58}{100}[/latex] is the same as [latex]58\div100[/latex].)
• Remove the % sign.
• Simplify the fraction: [latex]\dfrac{58}{100}=\dfrac{29}{50}[/latex]

[latex]110\%=\dfrac{110}{100}=1\dfrac{10}{100}=1\dfrac{1}{10}[/latex]

[latex]\begin{array}{r}1\\ 100\enclose{longdiv}{110}\\\underline{100}\\ 10\end{array}[/latex]

[latex]120\%=\dfrac{120}{100}=1\dfrac{20}{100}=1\dfrac{1}{5}[/latex]

[latex]\begin{array}{r}1\\ 100\enclose{longdiv}{120}\\ \underline{100}\\ 20\end{array}[/latex]

Percents Less Than 1%

[latex]\dfrac{1}{4}\%\text { is }\dfrac{1}{4}\text{ of }1\%[/latex]

[latex]1\%=\dfrac{1}{100}\text{, so }\dfrac{1}{4}\text{ of }1\%=\dfrac{1}{4}\times\dfrac{1}{100}=\dfrac{1}{400}[/latex]

[latex]\dfrac{1}{4}\%=0.25\%=0.0025[/latex]

What is [latex]\dfrac{1}{2}\%[/latex]?

[latex]\dfrac{1}{2}\%=\dfrac{1}{2}\text{ of }1\%=\dfrac{1}{2}\times\dfrac{1}{100}=\dfrac{1}{200}[/latex]

[latex]\dfrac{1}{2}\%=0.5\%=0.005[/latex]

[latex]0.2\%=0.002[/latex]

[latex]0.75\%=0.0075[/latex]

16⅔%, 33⅓%, 66⅔%, 83⅓% ...

Review of Equivalent Common Fractions, Decimals, and Percents

Topic A: Self-Test

1. Write these percents in numeral form. (2 marks)
   1. sixty-two and one-half percent
   2. one hundred six and one-fifth percent
2. Write these percents in words. (2 marks)
   1. [latex]72\%[/latex]
   2. [latex]\dfrac{3}{4}\%[/latex]
3. Change the percents to decimals. (5 marks)
   1. [latex]32\%[/latex]
   2. [latex]18.5\%[/latex]
   3. [latex]125\%[/latex]
   4. [latex]\dfrac{4}{5}\%[/latex]
   5. [latex]\dfrac{2}{3}\%[/latex]
4. Change these percents to common fractions in lowest terms. (4 marks)
   1. [latex]16\%[/latex]
   2. [latex]20\%[/latex]
   3. [latex]106\%[/latex]
   4. [latex]75\%[/latex]
5. Change these common fractions to equivalent percents. (2 marks)
   1. [latex]\dfrac{4}{5}[/latex]
   2. [latex]\dfrac{3}{8}[/latex]

1. Change these decimals to percents.
   1. [latex]0.75[/latex]
   2. [latex]0.156[/latex]
   3. [latex]0.03[/latex]
   4. [latex]0.0035[/latex]
   5. [latex]0.625[/latex]
   6. [latex]0.048[/latex]
   7. [latex]3.45[/latex]
2. Change each percent to a decimal.
   1. [latex]59\%[/latex]
   2. [latex]39.5\%[/latex]
   3. [latex]1\%[/latex]
   4. [latex]3\tfrac{1}{2}\%[/latex]
   5. [latex]1\tfrac{4}{5}\%[/latex]
   6. [latex]4\tfrac{3}{5}\%[/latex]
3. Change each fraction to an equivalent percent.
   1. [latex]1\tfrac{3}{4}[/latex]
   2. [latex]\tfrac{1}{5}[/latex]
   3. [latex]4\tfrac{3}{20}[/latex]
   4. [latex]\tfrac{9}{20}[/latex]
   5. [latex]2\tfrac{1}{3}[/latex]
4. Change each percent to a common fraction. Simplify your answer.
   1. [latex]16\%[/latex]
   2. [latex]25\%[/latex]
   3. [latex]110\%[/latex]
   4. [latex]95\%[/latex]
   5. [latex]650\%[/latex]
   6. [latex]284\%[/latex]
   7. [latex]\tfrac{1}{4}\%[/latex]
   8. [latex]\tfrac{1}{8}\%[/latex]
   9. [latex]0.125\%[/latex]
   10. [latex]\tfrac{5}{8}\%[/latex]
   11. [latex]\tfrac{3}{4}\%[/latex]
5. Change each percent to a common fraction. These few should be memorized.
   1. [latex]33\tfrac{1}{3}\%[/latex]
   2. [latex]66\tfrac{2}{3}\%[/latex]
   3. [latex]16\tfrac{2}{3}\%[/latex]
   4. [latex]83\tfrac{1}{3}\%[/latex]

• What is 14% of 60?
  • [latex]\dfrac{\text{is}}{\text{of}}=\dfrac{\%}{100}\longrightarrow\dfrac{\textit{N}}{60}=\dfrac{14}{100}[/latex]
• Find 10% of 27.
  • [latex]\dfrac{\text{is}}{\text{of}}=\dfrac{\%}{100}\longrightarrow\dfrac{\textit{P}}{27}=\dfrac{10}{100}[/latex]
• 5% of 15 is fill-in-the-blank.
  • [latex]\dfrac{\%}{100}=\dfrac{\text{is}}{\text{of}}\longrightarrow\dfrac{5}{100}=\dfrac{\textit{X}}{15}[/latex]
• 75% of 12 = fill-in-the-blank.
  • [latex]\dfrac{\%}{100}=\dfrac{\text{is}}{\text{of}}\longrightarrow\dfrac{75}{100}=\dfrac{\textit{K}}{12}[/latex]

Percents Greater Than or Equal to 100%

Taxes

Cross-Border Shopping

[latex]\dfrac{$1\text{ CAN}}{$0.92\text{ US}}=\dfrac{\textit{N}\text{ CAN}}{$1\text{ US}}[/latex]

• Change the US cost to the Canadian equivalent (multiply by 109%).
• If you have more than the purchases allowed (contact the Canada Border Services Agency for information), Canadian customs will charge duty on the Canadian value of your purchases. The percent of the duty (the rate) varies according to what the item is, where it was made, and the duty rates of the day. For example, at the time of writing, the duty on poultry is 12.5%, on non-U.S. cotton is 25%, and on liquor is 110%![footnote]As of January 2026, Canada, the United States, and Mexico have a free trade agreement that eliminates duty on many goods sold by one country and imported to another.[/footnote]
• HST (12%) is charged on the duty and on the Canadian value of the purchases (which includes any US sales taxes).

Increases and Decreases, Discounts and Markups

• The Insurance Corporation of B.C. increased car insurance rates by 3.3% in March 2007.
• The number of acute care beds at the local hospital has decreased by 28% in the last year.
• The new work contract provides a 4% wage increase in the first year and a 2½% increase in the second year.

[latex]\dfrac{\text{amount of increase or decrease}}{\text{whole amount}}=\dfrac{\text{increase or decrease }\%}{100}[/latex]

• "All items 20% off."
• "Everything in stock reduced by 25% to 50%."
• "33⅓% savings!"
• "2% discount for cash."

• the amount of the decrease (may be called the "saving") (1 step).
• the amount left after the decrease (2 steps).

• all costs of operating a business
• the profit wanted
• the community the business is in
• the competition the business has

Commission and Tips

• Real estate agents are paid by commission on their sales.
• Car and truck salespeople may be paid a small salary per month, but their main income is the commission on the vehicles they sell.

• add together several items to find the total of sales
• subtract a base amount for which salespeople do not receive a commission
• add the amount of commission to the basic wage to find out how much the person earned

Topic A: Self-Test

1. Answer the following. (4 marks)
   1. [latex]6\%\text{ of }30 =[/latex]
   2. [latex]\tfrac{1}{4}\%\text{ of }48[/latex] is?
   3. Find [latex]131\%\text{ of }400[/latex].
   4. Write the general proportion that can be used to solve percent problems.
2. Solve the problems. (2 marks each, except iii) (7 marks)
   1. The $125,000 house is insured for 85% of its value against fire damage. How much money should the owner receive if the house is destroyed by fire?
   2. Charlotte sells leisure clothes in her small town for a large national company. She receives $500 a month, and a 20% commission on all monthly sales over $1 000. What are her monthly earnings if her total sales are $2,300?
   3. The barbeque was originally priced at $599 but Jack bought it during a 35% off, end-of-season sale.
      1. What was the sale price? (1 mark)
      2. Calculate the harmonized sales tax (12%). (1 mark)
      3. Give the total cost of Jack's barbeque. (1 mark)

1. Solve each problem by setting up a proportion.
   1. [latex]150\%\text{ of }7[/latex]
   2. [latex]12.5\%\text{ of }48[/latex]
   3. [latex]20\%\text{ of }16[/latex]
   4. [latex]18\%\text{ of }40[/latex]
   5. [latex]\tfrac{1}{4}\%\text{ of }20[/latex]
   6. [latex]0.5\%\text{ of }122[/latex]
2. Use the proportion method to solve these questions. Round to 2 decimal places, if needed.
   1. [latex]75\%\text{ of }12[/latex]
   2. [latex]3\tfrac{1}{4}\%\text{ of }200[/latex] is?
   3. What is [latex]16\%\text{ of }34[/latex]?
   4. [latex]90\%\text{ of }75[/latex] is
   5. Find [latex]10\%\text{ of }27[/latex]
   6. [latex]16\tfrac{2}{3}\%\text{ of }163[/latex]
3. Find the total cost of each item, using 12% HST.

   	Item	Cost	HST (12%)	Total Cost
   A	T-shirt	$14.99	\[\begin{align*} \dfrac{X}{\$14.99}&=\dfrac{12}{100} \\ \\ X&= \$1.80 \end{align*}\]	[latex]$1.80 + $14.99 = $16.79[/latex]
   B	40" flat screen TV	$699.00
   C	tent	$168.79
   D	drill and bit set	$248.99
   E	shoes	$79.98

4. Solve these percent problems.
   1. All pants are 25% off said the sign in the window. What will be the sale price of a pair of pants originally priced at $59.78?
   2. 30% of the forest will be cut down in the next three years. The forest is 150 acres large. How many acres will be left after the cut?
   3. All winter clothes are on sale for 15% off. A set of gloves cost $18.00. How much will you save?
   4. Rent will increase 10% on Oliver’s apartment on January 1. His rent was $460.00 per month. What will his new rent be?
   5. The French Bread Bakery staff will get a one-time 15% pay increase on their Christmas pay check. If Manon works 63 hours at $12.78/hour for that pay check, how much will she get paid? (Figure out the regular pay first and then add on the 15% increase.)
   6. The bill at the restaurant was $38.00. Add a 20% tip. What did the customer pay in total?
   7. The mark up on a pair of fancy running shoes is 45%. The shoes cost the buyer $38.00. How much will they be sold for after mark-up?

[latex]\dfrac{\text{is}}{\text{of}}[/latex] will help to find [latex]\dfrac{\text{part}}{\text{whole}}[/latex].

[latex]\dfrac{12\text{ (is)}}{15\text{ (of)}}=\dfrac{\textit{N}}{100}[/latex]

Finding the Percent of an Increase or Decrease

1. Find the amount of change (either increase or decrease) by finding the difference between the two amounts given. Subtract to find the difference.
2. Find the percentage of increase/decrease. Always compare the change (amount of increase or decrease) to the amount before the change (the original amount) using the following proportion:

Other Problems

• 24 out of 25 on the test
• 6 out of 10 people are overweight
• The government spends 27¢ of every federal tax dollar on the national debt

School Grades

Topic A: Self-Test

1. Solve to find the missing percents. (4 marks)
   1. 12 is blank% of 60.
   2. 15 is blank% of 75.
   3. 8.2 = blank% of 32.8.
   4. What percent of 64 is 48?
2. Solve the following word problems: (4 marks)
   1. A $140 jacket was on sale for $126. What percent is the savings?
   2. The rent on an apartment went from $320 a month to $400 a month. What percent is this rent increase?
3. Find the percents for the following grades on tests. Round your answer to the nearest whole percent. (4 marks)
   1. [latex]\dfrac{12}{15}[/latex]
   2. [latex]\dfrac{10}{19}[/latex]
   3. [latex]\dfrac{71}{92}[/latex]
   4. [latex]\dfrac{132}{140}[/latex]

Solving Problems when the Percent of a Number is Given

Topic B: Self-Test

1. Solve these questions. (4 marks)
   1. 2.5% of what number is 160?
   2. 5 is [latex]\frac{4}{5}\%[/latex] of fill-in-the-blank.
   3. 180 is 90% of what number?
   4. 28 is 35% of what number?
2. Solve these problems. (4 marks)
   1. If a bank insists that new home buyers need a cash down payment of 12%, what house price can a couple afford if they have saved a $15,000 down payment?
   2. Jim has really cut down on his smoking. He now smokes 7 cigarettes a day, which he says is only 20% of what he used to smoke. How many cigarettes a day did Jim smoke before he started cutting down?

1. Finding a percent of a number
   • You are given the percent and the whole.
   • The missing term is the part (call it N). \[\dfrac{N}{\text{whole}}=\dfrac{\%}{100}\]
2. Finding what percent one number is of another
   • You are told the part and the whole.
   • The missing term is the percent (call it P). \[\dfrac{\text{part}}{\text{whole}}=\dfrac{P}{100}\]
3. Finding a number when a percent of it is given
   • You are given the part and the percent.
   • The missing term is the whole (call it W). \[\dfrac{\text{part}}{W}=\dfrac{\%}{100}\]

Questions

• Percents to the nearest tenth of a percent
• Money to the nearest cent
• Decimal fractions to the nearest thousandth

1. You need a minimum of 80% on the test, which means you must get at least 36 marks. What are the total possible marks on the test?
2. Ann and Joe bought their home twelve years ago and have paid 45% of the principal amount of their mortgage. They have paid $18,000 towards the principal of the mortgage. What was the principal amount of the mortgage to start with?
3. The waiters at the restaurant must contribute money to be shared among the cocktail servers and kitchen staff. Each waiter contributes 4% of their total food and drink sales. Craig's total sales were $645 in his 5-hour shift.
   1. How much money must he contribute to the kitchen and cocktail servers?
   2. Craig made 12% in tips on his sales tonight. How much money did he earn in tips?
4. The cost of hydroelectric power for our home last year was 210% of what it was six years ago. Last year, our power bill totalled $960. How much was it six years ago?
5. 16⅔% of the tickets for the rock concert were sold in the first hour that tickets were available for sale. In that hour, 2,500 tickets were sold. What was the total number of tickets available for the concert?
6. The total student enrolment in the school district has increased from 18,506 students to 19,724 students in the last year. What is the percent of this increase in student enrolment?
7. Al bought his secondhand off-road motorcycle for $1,500 and sold it three years later for $1,175. By what percent did his motorcycle depreciate (decrease in value)?
8. Pat operates a street-vendor's cart selling hot dogs, sausages on a bun, and soft drinks. The basic pay is $100 per week and 28% commission on all sales over $450 in a week. Pat sold $1,244 of food and soft drinks last week. Calculate Pat's earnings from the street-vending cart for the week.
9. The 1,500 blouses purchased by the large retail chain of ladies' clothing stores cost the company a total of $24,000. The blouses were then priced to sell at $45 each. What is the percent of the mark-up on these blouses? (Hint: First calculate the company's initial purchase price per blouse.)
10. Maureen was happy to see that she got 27 out of 30 on her English essay. What percent did she get?
11. The ski jackets were on the summer clearance rack, marked "45% off."
    1. What is the sale price of a jacket priced regularly at $229.95?
    2. What is the total cost of this jacket with HST (12% tax)?
12. Tuition fees at the university have increased from $49 per credit hour to $62 per credit hour in the last three years. What is the percent of the tuition increase?
13. Jill bought 3 bottles of liquor in the U.S. The bill, including U.S. sales tax, was $28.50. Assume the American dollar was $1.08 Canadian. Calculate:
    1. The value of the liquor in Canadian funds.
    2. Duty at 110%.
    3. HST at 12% (on Canadian value + duty).
    4. Total cost in Canadian funds.
14. The consignment store will sell your lightly used women's clothing for you. The store owners take a percentage of the selling price as their fee for service. The consignment charges (the % the store owners keep) are as follows:

    [latex]\begin{equation*}\begin{split} &\text{Coats} &\hspace{3cm} &45\% \\ &\text{Dresses and skirts} &\hspace{3cm} &33\tfrac{1}{3}\% \\ &\text{Bridal and evening gowns} &\hspace{3cm} &50\% \\ &\text{Blouses, jeans, and slacks} &\hspace{3cm} &25\% \end{split}\end{equation*}[/latex]

    Lisa and her daughters did a huge closet cleanout and had the following items sold at the consignment store. For each category, calculate the amount for the store fee and the amount Lisa and the girls received.

    	Item	Selling Price	Store Fee	Amount for Lisa and Her Daughters
    a	Wedding dress	$275
    b	3 dresses at $40 each	3 @ $40 = $120
    c	Lisa's winter coat at $120	$120
    d	4 pairs of outgrown jeans at $10 each	4 @ $10 = $40

15. You have just completed four units of the five units in this book. What percent of the book have you completed?!?!?

Graph 1

Leah has taken up cycling and jogging to improve her cardiovascular fitness and for weight control. She takes her pulse every Monday morning before she gets out of bed; that is her basal heart rate. Graph 1 records Leah’s heart rate for the first 12 weeks of her exercise program.

1. What is the title of the graph?
2. What is being measured on the vertical axis?

On this particular graph, the vertical scale is one heartbeat per line. The scale on the horizontal axis is one week per line.

3. What was Leah’s basal heart rate on the fourth week of her exercise program?
   • Find Week 4 on the horizontal (\(x\)) axis.
   • Look straight up from Week 4 until you come to the point in the graphed line.
   • Now look at the scale on the vertical (\(y\)) axis. Lay a ruler or straight piece of paper across the graph to help you read the scale at the point for Week 4.
   Leah’s basal heart rate was 74 beats/min in Week 4.
4. Find her basal heart rate in Week 7.
5. What does the graph show us happened between Week 9 and Week 10?
6. What trend does this graph show? The graph shows Leah’s basal heart rate is “going down” or decreasing.

Often, you need to estimate the value of the point in the graphed line. Look at Graph 2, which has Leah’s same heart rates recorded. Answers to Graph 1

1. Leah’s Weekly Basal Heart Rate
2. Heartbeats per minute
3. Given: 74 beats/min
4. 71 beats/min
5. Leah’s heart rate went up from 68 to 69 beats/min
6. Given: Leah's basal heart rate is "going down" or decreasing

Graph 2

Now the scale on the vertical axis is five heartbeats per line. Use a straightedge (ruler or paper) across the graph to help you read the vertical scale.

1. Give Leah’s heart rate in Week 5.
2. Give Leah’s heart rate in Week 10.
3. What was Leah’s heart rate in Week 12?
4. Using the information on the graphs, state how much Leah’s basal heart rate decreased (in beats per minute) from Week 1 to Week 12.

Answers to Graph 2

1. 75 beats/min
2. 69 beats/min
3. 67 beats/min
4. Decreased 11 beats/min (78 − 67 = 11)

Graph 3

Leah’s husband, John, decided to exercise as well. He had a rapid heart rate at the beginning of the exercise program. Since his heart rate is higher than 85, we must increase the numbers on the vertical scale so we can graph John’s heart rate on the same graph as Leah’s.

1. What was John’s heart rate in Week 6?
2. What was John’s heart rate in Week 10?
3. How much lower was Leah’s heart rate than John’s in Week 8?
4. How much did John’s heart rate drop in the 12-week exercise program?
5. What was the amount of change in John’s heart rate between Week 3 and Week 7? Was it an increase (+) or decrease (−)?
6. Compare the two graphed lines.
   1. How is the slant of the lines different?
   2. How are the lines the same?
   3. You can tell from looking at this graph that John and Leah had a similar trend in the change in their basal heart rates. Did their heart rates increase or decrease?

Answers to Graph 3

1. 88 beats/min
2. 83 beats/min
3. 17 beats/min
4. 12 beats/min
5. Decrease 4 beats/min
6. Answers:
   1. John’s goes up at Week 8, Leah’s goes up at Week 10, Leah stays the same from Week 11 to 12 while John’s goes down.
   2. Similar, because both decrease at a similar slant and both show an increase in two separate weeks.
   3. Both heart rates decreased.

Graph 4

1. What is the general trend in the Crosses' average monthly cost for electricity?
2. What was the average monthly cost of electricity in 1998?
3. How much more did they pay per month in 2003 than in 2000?
4. What happened to the average cost between 2005 and 2006?
5. By how much did the Crosses' average monthly electricity cost increase between 1998 and 2010?

Answers to Graph 4

1. Increased
2. $40
3. Approximately $23 ($77 – 54)
4. Decreased
5. $58

When we graph different types of information:

• A subtitle (written in smaller print under the title) usually explains the two types of information.
• The horizontal axis is the same.
• The vertical axis on the right side of the graph has the scale for the second set of information. For example, on the graph for Leah and John, the right vertical axis would be marked in kilograms for weight changes.

Graph 5

1. What is the title of this graph?
2. What is the subtitle?
3. Look at the legend. What does the graphed line for “Kilowatt Hours Used” look like?
4. Where is the scale for kilowatt hours?
5. How is the scale for kilowatt hours labelled?
   in thousands means that each figure in the scale is to be multiplied by 1,000. For example, "32" represents "32,000."
6. In which two years was the use of kWh the greatest?
7. In which year was the least kWh used?
8. Look at 1999 and 2000.
   1. Find the amount of kWh used (in thousands) in 1999 and the cost of electricity in 1999.
   2. Compare to the amount of kWh used in 2000 and the cost of electricity in 2000.
   3. What can you conclude by comparing the cost and the kWh used in 1999 and 2000?
9. Now look at 2001 and 2002.
   1. Compare the use of kWh.
   2. Compare the cost.
   3. What can you conclude?
10. Between 2009 and 2010, the use of kWh went up or down? by fill-in-the-blank kWh.The cost of electricity went up or down? by $fill-in-the-blank.

Answers to Graph 5

1. Cross Family’s Electricity Costs
2. Average Cost/month and Annual Kilowatt Hours Used
3. Dotted line
4. Right side of graph
5. kWh used in thousands
6. 1998 + 2000
7. 2002
8. Answers:
   1. ~36,000 kWh and $41.
   2. ~40,000 kWh and $54.
   3. The price per kWh increased.
9. Answers:
   1. 2001: ~34,500 kWh; 2002: ~33,500 kWh
   2. 2001: $69; 2002: $69
   3. You can conclude the price/kWh increased.
10. The use of kWh went up by ~500 kWh. Cost went up by $3.

Image Descriptions

Graph 1 (Line Graph)

• The vertical axis is heartbeats per minute and has the numbers 65 to 80 in increments of 1.
• The horizontal axis is weeks of exercise and has the numbers 1 to 12 in increments of 1.

Graph 2 (Line Graph)

• The vertical axis is heartbeats per minute and has the numbers 60 to 80 in increments of 5.
• The horizontal axis is weeks of exercise and has the numbers 1 to 12 in increments of 1.

Graph 3 (Line Graph)

• The vertical axis is heartbeats per minute and has the numbers 60 to 95 in increments of 5.
• The horizontal axis is weeks of exercise and has the numbers 1 to 12 in increments of 1.
• The legend refers to two different graphed lines on the line graph. One refers to Leah's heartbeats per minute, and the other refers to John's heartbeats per minute.

Graph 4 (Line Graph)

• The vertical axis is the average monthly cost in dollars, and contains the numbers 0 to 120 in increments of 20.
• The horizontal axis is years and contains the years 1998 to 2010 in increments of one year.

Graph 5 (Line Graph)

• The left vertical axis is the monthly cost in dollars and contains the numbers 35 to 99 in increments of 2.
• The right vertical axis is the kWh used in the thousands and contains the numbers 30 to 42 in increments of 2.
• The horizontal axis is years and contains the years 1998 to 2010 in increments of one year.
• The legend refers to two different graphed lines on the line graph. One refers to the monthly cost, and the other refers to the kWh used.

Graph 1

1. How many rivers are shown on this graph?
2. What is the title of the graph?
3. What is the unit of measure?
4. Look at the scale for kilometres. How many kilometres are represented by each division on the page?
5. Which river is the longest? What is its length?
6. Which river is the shortest? What is its length?
7. Name two rivers which are approximately the same length.
8. Compare the Columbia River and the Fraser River.
   1. Which is the longer?
   2. Give the approximate difference in their lengths.
9. Give the approximate length of the North Thompson, South Thompson, and Thompson Rivers combined.

Answers to Graph 1

1. 12 rivers
2. Lengths of some British Columbia Rivers
3. Kilometres
4. 250 km
5. Columbia; ~1,950 km
6. Quesnel; ~100 km
7. North Thompson & South Thompson
   1. Columbia
   2. ~600 km (1,950 – 1,350)
8. ~750 km

Graph 2

1. Give the source of the information for this graph.
2. What is the unit of measure for the population scale?
3. What number of people is represented by each section on the scale?
   1. Which country had the largest population?
   2. What was the approximate population of this country?
4. Name the two countries which were the closest in population size.
5. What was the approximate population of Bangladesh?
6. What was the approximate population of India?

Answers for Graph 2

1. United Nations
2. In the Millions
3. 50 million
   1. China
   2. 1,354,000,000
4. Nigeria and Bangladesh
5. 164,000,000
6. 1,214,000,000

Graph 3

1. What is the subtitle?
2. Look at the legend.
   1. For which year do the solid blue bars represent each country's population?
   2. For which year do the grey patterned bars represent each country's population?
3. What trend does the graph show?
4. Consider these questions:
   1. Which country had the largest increase in population? (In other words: which country’s population went up by the highest number?)
   2. About how much was that increase?
5. Consider these questions:
   1. Which country had the least change in population?
   2. About how much was that change?

Answers for Graph 3

1. Year 2010 and Year 1950
2. Answers:
   1. 2010
   2. 1950
3. That countries around the world are growing in population
4. Answers:
   1. India
   2. The increase was 843 million
5. Answers:
   1. Pakistan
   2. The increase was 108 million

Image Descriptions

Graph 1.1 (Bar Graph)

• The vertical axis is kilometres and has the numbers 0 to 2,000 in increments of 250.
• The horizontal axis is the names of the following British Columbia rivers: Fraser, North Thompson, South Thompson, Thompson, Quesnel, Nechako, Chilcotin, Lillooet, Kootenay, Columbia, Peace, and Laird.

Graph 1.2 (Bar Graph)

• The vertical axis is the names of the following British Columbia rivers: Fraser, North Thompson, South Thompson, Thompson, Quesnel, Nechako, Chilcotin, Lillooet, Kootenay, Columbia, Peace, and Laird.
• The horizontal axis is kilometres and has the numbers 0 to 2,000 in increments of 250.

Graph 2 (Bar Graph)

• The vertical axis is population in millions, and has the numbers 0 to 1,400 in increments of 50.
• The horizontal axis is countries, and contains the following: China, India, United States, Indonesia, Brazil, Bangladesh, Nigeria, and Pakistan.

Graph 3 (Bar Graph)

• The vertical axis is population in millions, and has the numbers 0 to 1,400 in increments of 50.
• The horizontal axis is countries, and contains the following: China, India, United States, Indonesia, Brazil, Bangladesh, Nigeria, and Pakistan.
• The legend denotes that each country is associated with two different bars - one referring to its population in 2010, and the other referring to its population in 1950.

Graph 1

1. As a quick first impression when you look at this graph, which type of vehicle is most in use?
2. What does each picture represent according to the legend?
3. Out of every 1,000 vehicles, how many are:
   1. cars?
   2. bikes and motorcycles?
   3. large trucks?
   4. RVs and small trucks?
4. Look for other examples of picture graphs in the newspaper and in magazines. Television programs often display picture graphs to illustrate statistics.

Answers for Graph 1

1. car
2. 100 vehicles
3. 1. 600
   2. 100
   3. 100
   4. 200

Image Descriptions

Graph 1 (Picture Graph)

• The vertical axis is vehicles, and contains the following types of vehicles: cars, bikes & motorcycles, large trucks, and RVs & small trucks.
• The horizontal axis is pictures of vehicles, each of which stands for 100 vehicles of the corresponding type according to the legend.

Graph 1

The circle represents each dollar the government spends. The information for the graph was sourced from the Department of Finance, April 2010, at Where Your Tax Dollar Goes - 2007–2008 (Department of Finance Canada). The parts are shown as cents of the dollar.

1. What is the biggest expense of the federal government?
2. How much of each federal dollar is spent in actually operating the government business?
3. What part of the federal dollar is spent on defence?
4. How much of each dollar is spent on Provincial Payments? Write this amount as a percent.
5. What is the smallest expenditure of the federal government? Write this amount as a percent.

Answers to Graph 1

1. Payments to Persons
2. 20¢
3. 7¢
4. 20¢; 20%
5. Budgetary Surplus; 4%

Graph 2

2004 Nanaimo Regional Landfill Solid Waste Composition

1. What makes up the largest part of the waste in the landfill site?
2. What four categories contribute equal weight to the landfill site?
3. In a municipality of 139,000 people, the amount of waste going to a landfill site in one day is 150 tonnes.
   1. What is the mass of plastics?
   2. What is the mass of yard waste?
   3. What is the mass of construction/demo waste?
   4. If all the food waste was composted, how many tonnes of waste would not end up in the landfill each day?
4. The plastics category can be separated into these categories:
   • 6% Non-recyclable mixed plastics
   • 4% film plastic
   • 3% recyclable rigid food containers
   If all the 3% recyclable rigid food containers were actually recycled, how many tonnes of waste would not end up in the landfill?

Answers to Graph 2

1. Food waste
2. • Diapers, Personal Hygiene
   • Glass
   • Bulky Goods
   • HHW (Household Hazardous Waste
3. 1. 19.5 tonnes
   2. 10.5 tonnes
   3. 24 tonnes
   4. 34.5 tonnes
4. 4.5 tonnes

Image Descriptions

Graph 1 (Circle Graph)

• The whole circle represents one dollar of the Canadian budgetary expenditure.
• Each part reflects one of the specific expenses, reflected in cents to the dollar, ¢. The included parts are (clockwise from top): Public Debt, Provincial Payments, Grants and Contributions, Payments to Persons, National Defense, Operating Costs, and Budgetary Surplus.

Graph 2 (Circle Graph)

• The whole circle represents the total composition of solid waste in the Nanaimo Regional Landfill in 2004.
• Each part reflects one element of the total composition. The included elements are (clockwise from top): Food Waste, Yard Waste, Compostable Paper, Construction/Demo Waste, Plastic, Mixed Paper, Metal, Textiles & Carpet & Tires, Diapers & Personal Hygiene, Glass, Bulky Goods, HHW, and Other.

• between 0°C and −5°C (1 day)
• between −6°C and −10°C (6 days)
• between −11°C and −15°C (8 days)
• between −16°C and −20°C (5 days)
• between −21°C and −25°C (9 days)
• between −26°C and −30°C (2 days)

Graph 1

1. How many degrees in temperature change is in each bar?
2. What is the source of the information?
3. Which temperature was the most common in the month of January?
4. Which community does this graph represent?
5. Which temperature was felt the least in Atlin in January, 2010?

Answers to Graph 1

1. Five degrees
2. Environment Canada
3. −21°C to −25°C
4. Atlin, BC
5. −1°C to −5°C

Graph 2

In this Fundamentals Math course, students’ marks were collected from the final test. The graph shows the results.

1. How many students took the test?
2. How many students scored 80% to 89% on the test?
3. In order to pass, students must get 80% or over on the test. How many students will have to re-write the test?
4. How many more students got 80% to 89% than 90% to 100%?

Answers to Graph 2

1. 25
2. 12
3. 3
4. 2

Image Descriptions

Graph 1 (Histogram)

• The horizontal axis contains the following temperature ranges, in degrees Celsius: −1°C to −5°C, −6°C to −10°C, −11°C to −15°C, −16°C to −20°C, −21°C to −25°C, and −26°C to −30°C.
• The vertical axis is numbers of days, and has the numbers 0 through 10.

Graph 2 (Histogram)

• The horizontal axis contains the following ranges of test scores, in percentages: 60%–69%. 70%–79%, 80%–89%, and 90%–99%.
• The vertical axis is numbers of students, and has the numbers 0 through 14 in increments of 2.

• Feeling anxious when writing tests
• Negative experiences in a past math class
• Embarrassment in a past math class
• Social pressures and expectations to not like math or not do well in math
• The want to get everything right
• Negative self-message (“I don’t know how to do it,” or “I hate math”)

Do You Suffer from Math Anxiety?

• Are your palms moist?
• Is your stomach fluttering?
• Do you feel like you can’t think clearly?
• Do you feel like you would rather do anything else than learn math?
• Are you breathing faster than normal?
• Is your heart pounding?
• Do you feel cold?
• Do you feel sweaty?

• Can you see when you felt anxiety?
• Can you see why you are now anxious about math?
• Is there any experience you could use now to help you feel calmer about math?

How to Deal with Math Anxiety