Comparing and Ordering Fractions Worksheet

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In this pdf, we will learn how to compare and order fractions. A fraction represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, a fraction describes how many parts of a certain size there are, for example, one-half, eight-fifths, three-quarters.

1. 12-NEM6 WBAns 8/8/05 3:07 PM Page 104
CHAPTER 12
1 Comparing and Ordering Fractions
Goal Compare and order fractions on number lines.
1. Compare. Write >, <, or . At-Home Help
1 To compare fractions, use a
0 1 11 2 21 3
2 2 2 number line to mark the positions
of the fractions.
The order of the fractions can
be read from the number line.
4
a) >
2
d) 1
1
< 1
4 For example, to order 34, 38,
3 3 3 6
and 23, use a number line.
2 4 3 1
b) = e) 1 < 2 3 2 3
5 10 4 2 8 3 4
7 3 1 1 0 1
c) > f) 2 > 2
4 8 5 10
2. Order each set of numbers from least to greatest. The order from least to greatest
is 38, 23, and 34.
Use a number line.
3 1 3 5
a) , 1, ,
8 4 4 8
3 5 3 11
0 1 2 3 5 3 1
8 8 4 4 , , , 1
8 8 4 4
1 2 8 3
b) 2, 1, , 1
3 3 3 6
13 12 21 8
3 2 1 8
1 6 3 2 3 3 3 1, 1, 2,
6 3 3 3
4 1 2 7 5
c) , 1, , , 1
4 8 4 4 8
2 11 15 7
0 1 8 2 2 4 1 5 7
4 8 4 , , 1, 1,
4 4 8 8 4
4
4
5 2 1 1 6
d) , , , 1,
6 3 6 3 3
1 2 5 11
0 1 2 1 2 5 1 6
6 3 6 3 , , , 1 ,
6 3 6 3 3
6
3
104 Answers Chapter 12: Fractions, Decimals, Ratios, and Percents Copyright © 2006 Nelson

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CHAPTER 12
Comparing Fractions with
2 Unlike Denominators
Goal Compare fractions when the denominators are different.
1. Compare. Write >, <, or . At-Home Help
1 4 3 2 To compare fractions with unlike
a) < d) >
3 5 4 3 denominators, draw a number line
2 1 6 on grid paper.
b) < e) = 3
5 2 10 5
Choose a whole that you can easily
3 1 1
c) > f) 1 > 5 divide by each denominator.
8 3 2 8
For example, to compare 34, 23,
2. Which amount is greater? Tell how you know. and 32, choose a whole with
1 3 12 sections.
a) or of a bag of popcorn
3 8
Then mark the fractions on the
3
number line.
8
2 3
Suggested answer: 3 2
I used grid paper to draw a number line. I chose 0 1 2
a whole with 24 sections.
3 1
is past 3 on the number line. 3
8
4
2 2
b) or of a container of juice The order from least to greatest
5 3
is 23, 34, and 32.
2

3
Suggested answer:
The numerators are the same, so the fraction with
the lower denominator is greater.
5 1
c) or of a length of string
7 2
5

7
Suggested answer:
I used grid paper to draw a number line. I chose a
whole with 14 sections.
5 1
is past on the number line.
7 2
Copyright © 2006 Nelson Answers Chapter 12: Fractions, Decimals, Ratios, and Percents 105

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CHAPTER 12
3 Fraction and Decimal Equivalents
Goal Relate fractions to decimals and determine equivalents.
1. Write an equivalent fraction for each decimal. At-Home Help
34 To write a fraction as a decimal,

a) 0.34 100 find an equivalent fraction with a
denominator of 10, 100, or 1000.
6 Then use place value to write the

b) 0.6 10 decimal equivalent.
7 For example:

c) 0.07 100 2 4

5 10
3
1 4 tenths
d) 1.3 10 0.4
37 To write a decimal as a fraction,
2
e) 2.37 100 use place value.
4 For example:
3
f) 3.04 100 2.1 2 ones 1 tenth
1
2
10
4
2. Explain how to write as a decimal.
5
Suggested answer:
I could divide a rectangle into 10 equal sections.
4
If I shade 4 rows, that represents .
5
4
of the rectangle is 8 sections.
5
4
So is the same as 0.8.
5
106 Answers Chapter 12: Fractions, Decimals, Ratios, and Percents Copyright © 2006 Nelson

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CHAPTER 12
4 Ratios
Goal Identify and model ratios to describe situations.
1. Write the ratio of grey items to white items. At-Home Help
a) 5 : 6 A ratio is a comparison of two
numbers or quantities measured
in the same units.
If you mix juice using 1 can of
concentrate and 3 cans of water,
the ratio of concentrate
to water is 1 : 3, or
1 to 3.
b) 2 : 5
c) 8 : 3 d) 0 : 6
2. Write the ratio of white to grey for each situation in Question 1.
a) 6 : 5 b) 5 : 2 c) 3 : 8 d) 6 : 0
3. a) What is the ratio of oats to raisins?
3:2
3 parts oats
b) What is the ratio of coconut to oats? 1 part coconut
1:3
2 parts raisins
c) What is the ratio of raisins to coconut?
2:1
Copyright © 2006 Nelson Answers Chapter 12: Fractions, Decimals, Ratios, and Percents 107

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CHAPTER 12
5 Equivalent Ratios
Goal Determine equivalent ratios and use them to solve problems.
1. Determine the missing number to make an At-Home Help
equivalent ratio. Equivalent ratios are two or
more ratios that represent the
a) 5 to 8 10 to 16
same comparison.
b) 12 : 100 3 : 25
1:3 2:6 3:9
c) 21 to 33 7 to 11
d) 18 : 6 9 :3
e) 75 : 24 25 : 8
f) 24 to 60 2 to 5
2. Kenton makes salsa by mixing tomatoes and peppers in a ratio of 5 to 2.
a) Write ratios equivalent to 5 : 2 in the ratio table.
Tomatoes 5 10 15 20 25 30
Peppers 2 4 6 8 10 12
b) If Kenton has 40 tomatoes, how many peppers does he need?
5 : 2 = 40 : 16
16 peppers
c) If Kenton has 20 peppers, how many tomatoes does he need?
5 : 2 = 50 : 20
50 tomatoes
3. Stacy makes one batch of muffins using muffin mix and water in a ratio of 3 : 1. She
needs to make 4 batches for school. How many cups of muffin mix will she need?
3 : 1 = 12 : 4
12 cups of muffin mix
108 Answers Chapter 12: Fractions, Decimals, Ratios, and Percents Copyright © 2006 Nelson

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CHAPTER 12
6 Percents as Special Ratios
Goal Understand the meaning of percent.
1. Write each as a ratio, a fraction, and a percent. At-Home Help
a) 10 to 25 c) 13 out of 20 A percent is a part-to-whole ratio
that compares a number or an
10 : 25 13 : 20 amount to 100.
10 40 13 65
= =
25 100 20 100 25% 25 : 100
= 40% = 65% 25

100
b) 0.07 d) 0.18 Percents are written with a percent
sign (%). The percent sign is like
7 : 100 18 : 100 writing “of each 100.” 25% is read
7 18
= 7% = 18% “25 percent” and means “25 of
100 100 each 100.”
2. Write each ratio as an equivalent fraction with 100% means the whole.
a denominator of 100, a decimal, and a percent.
9 33
a) = 45 b) = 66 c) 2 out of 5 d) 8 out of 25
20 100 50 100
= 0.45 = 0.66 2 40 8 32
= =
= 45% = 66% 5 100 25 100
= 0.40 = 0.32
= 40% = 32%
3. A survey at Jennifer’s school showed that 19 out of 25 students chose
pizza as their favourite lunch food.
a) What percent of students chose pizza?
19 out of 25 = 19 : 25
19
=
25
76
=
100
= 76%
b) What percent of students did not choose pizza?
Suggested answer: Out of 25 students, 25 – 19 = 6 students did not choose pizza.
6 out of 25 = 6 : 25
6
=
25
24
=
100
= 24%
Copyright © 2006 Nelson Answers Chapter 12: Fractions, Decimals, Ratios, and Percents 109

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CHAPTER 12
7 Relating Percents to Decimals
and Fractions
Goal Compare and order percents, fractions, and decimals.
1. Write each number as a percent. Order the At-Home Help
numbers from least to greatest. To compare fractions, decimals,
7 8 and percents, write all numbers
a) 0.6, , 0.07,
10 20 in the same form.
6 7 70 7 8 40 1
0.6 = = 0.07 = = For example, to compare , 0.11,
4
10 10 100 100 20 100 1
, and 30%, write each number as
60 = 70% = 7% = 40% 5
= a percent.
100
= 60% 1 25 11 1 20
0.11
4 100 100 5 100
8 7 25% 11% 20%
Order is 7%, 40%, 60%, 70% or 0.07, , 0.6, .
20 10
The order from least to greatest is
4 16 11%, 20%, 25%, 30% or
b) , 0.12, , 0.85
5 25 1 1
0.11, , , 30%.
5 4
4 80 12 16 64 85
= 0.12 = = 0.85 =
5 100 100 25 100 100
= 80% = 12% = 64% = 85%
16 4
Order is 12%, 64%, 80%, 85% or 0.12, , , 0.85.
25 5
2. An art show has paintings, sculptures, and sketches. Thirty-five percent
of the items are paintings and 0.13 of the items are sketches. What fraction
of the items are sculptures?
Suggested answer:
35% paintings
13
0.13 =
100
= 13% sketches
Percent of sculptures = 100% – (35% + 13%)
= 100% – 48%
= 52%
52
52% =
100
13
=
25
13
The fraction of items that are sculptures is .
25
110 Answers Chapter 12: Fractions, Decimals, Ratios, and Percents Copyright © 2006 Nelson

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CHAPTER 12
8 Estimating and Calculating Percents
Goal Estimate and calculate percents.
1. Estimate the percent of each number. At-Home Help
Show your work. To estimate the percent of a
number, use benchmarks such
a) 40% of 180
as 10%, 25%, 50%, and 75%.
Suggested answer: 1
10% is the same as .
50% of 180 is half of 180, or 90. 10
1
So 40% of 180 is a little less than 90 or about 75. 25% is the same as .
4
1
50% is the same as .
2
3
b) 30% of 90 75% is the same as .
4
Suggested answer: 100% is the same as 1 whole.
10% of 90 is 9. For example, to estimate 25% of
30% of 90 is 9 x 3 = 27. 500 km, use a number line.
0% 25% 50% 75% 100%
c) 50% of 412 0 about 250 500
100
Suggested answer:
50% of 500 km is half of 500
50% of 412 is half of 412, or about 200.
or 250 km.
So 25% is half of 250 km or
about 100 km.
d) 75% of 208
Suggested answer:
50% of 208 is half of 208, or about 100.
25% of 208 is about half of 100, or 50.
So 75% of 208 is about 100 + 50 = 150.
2. A store has a sign saying, “15% off all jackets.” Kenny wants to buy a leather
jacket that has a regular price of $360. About how much will Kenny save?
Suggested answer:
1
25% of $360 is of $360, or $90.
4
15% is about halfway between 0 and 25% but closer to 25%. So 15% of $360 is about half
of 90, or about $50.
So Kenny will save about $50.
Copyright © 2006 Nelson Answers Chapter 12: Fractions, Decimals, Ratios, and Percents 111

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CHAPTER 12
9 Unit Rates
Goal Represent relationships using unit rates.
1. Calculate the unit rate for each item. At-Home Help
a) 5 guitar picks for $1.00 A unit rate is a comparison of two
quantities where the second one is
Suggested answer: 20¢/pick described as one unit.
For example, a unit rate might be
30 km in 1 h or 4 tomatoes for $1.00.
Rates often have words like “per”
or “for” in them. A slash (/) is
b) 2 CDs for $15.00 sometimes used instead.
Suggested answer: For example, you read 100 km/h
2 : 15 = 1 : as “100 km per hour.”
= 7.5
$7.50/CD
c) 8 mini-muffins for $2.40 d) 3 tickets for $3.00
Suggested answer: 30¢/muffin Suggested answer:
3:3=1:
=1
$1.00/ticket
2. a) What is the price of one scoop of each type of ice cream?
Ice cream
Suggested answer:
Vanilla
(vanilla) 3 : 150¢ = 1 : (mango) 4 : 4 = 1 : 3 scoops for $1.50
= 50 =1
Chocolate
50¢/scoop $1.00/scoop 2 scoops for $1.40
Mango
(chocolate) 2 : 140¢ = 1 : (strawberry) 4 : 360¢ = 1 : 4 scoops for $4.00
= 70 = 90 Strawberry
70¢/scoop 90¢/scoop 4 scoops for $3.60
b) Which ice cream is the least expensive?
vanilla
c) Which ice cream is the most expensive?
mango
112 Answers Chapter 12: Fractions, Decimals, Ratios, and Percents Copyright © 2006 Nelson

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CHAPTER 12
10 Solving Problems Using Guess and Test
Goal Use a guess and test strategy to solve problems.
The ratio of flowers to herbs in Babak’s garden is 6 : 2. At-Home Help
He started with 80 plants. He wants to increase the Sometimes using a guess and
number of herbs in his garden so that 40% of his plants test strategy is a good way to
are herbs. How many more herb plants must he get? solve a problem.
Suggested answer: Use a chart to help you organize
the information you are given and
Understand the Problem what you want to calculate.
Babak started with 80 plants that made 100% of his garden. Remember to check if your answer
If Babak had 8 plants, 6 of them would be flowers and 2 is reasonable after guessing.
would be herbs.
0% 25% 50% 75% 100%
0 20 40 60 80
Make a Plan
I’ll set up a chart and use a guess and test strategy to determine how many
more herb plants Babak needs.
Carry Out the Plan
Number Number Total number of
Guess of flowers of herbs flowers and herbs Percent of herbs
20 1
start with 60 20 80 = = 25%
80 4
30 1
add 10 herbs 60 30 90 =
90 3
or about 30%
40
add 20 herbs 60 40 100 = 40%
100
Look Back
Babak will need 20 more herb plants to make his garden have 40% herbs.
I’ll check if my answer is correct. Babak started with 80 plants.
If he adds 20 plants, then he will have 80 + 20 = 100 plants altogether.
40% of 100 is 40. So he should have 60 flowers and 40 herbs.
He started out with 20 herbs. So 20 more herb plants will give 40 herb plants.
Copyright © 2006 Nelson Answers Chapter 12: Fractions, Decimals, Ratios, and Percents 113

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CHAPTER 12
Test Yourself Page 1
Circle the correct answer.
1. Which fraction is greatest?
4 2 3 3
, , ,
5 3 4 8
4 2 3 3
A. B. C. D.
5 3 4 8
2. What is the correct order of these fractions from least to greatest?
2 1 1 7 2
, , 1, ,
3 6 5 8 5
2 2 1 7 1 1 2 2 7 1
A. , , , , 1 C. , , , , 1
5 3 6 8 5 6 3 5 8 5
1 2 2 7 1 2 2 1 7 1
B. , , , , 1 D. , , , , 1
6 5 3 8 5 3 5 6 8 5
3. What is 1.03 as a fraction?
13 3 3 103
A. B. 1 C. 1 D.
100 10 100 1000
4. What is the ratio of white counters to grey counters?
A. 4 : 3 C. 4 : 7
B. 3 : 7 D. 3 : 4
5. Which ratios are equivalent to 6 out of 15?
i) 2 : 5 ii) 3 out of 10 iii) 4 out of 10 iv) 10 : 25 v) 20 : 45
A. i, ii, iii B. ii, iv, v C. i, iii, iv D. ii, iii, iv
6. What is the correct order of these numbers from least to greatest?
8 2
, 0.14, 30%, , 8%, 0.09
25 5
8 2 2 8
A. 8%, 0.09, 0.14, 30%, , C. 0.09, , 0.14, , 8%, 30%
25 5 5 25
2 8 2 8
B. 0.09, 0.14, , , 8%, 30% D. 8%, 0.09, , 0.14, , 30%
5 25 5 25
114 Answers Chapter 12: Fractions, Decimals, Ratios, and Percents Copyright © 2006 Nelson

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CHAPTER 12
Test Yourself Page 2
7. What is 0.3 as a ratio, a fraction, and a percent?
3
A. 3 : 100, , 30%
100
3
B. 3 : 10, , 30%
10
3
C. 3 : 10, , 3%
10
3
D. 3 : 10, , 3%
100
12
8. What is as an equivalent fraction with a denominator of 100, a decimal,
25
and a percent?
12
A. , 0.12, 12%
100
40
B. , 0.4, 40%
100
48
C. , 0.48, 48%
100
16
D. , 0.16, 16%
100
9. What is the best estimate for 25% of 212?
A. about 30 B. about 40 C. about 50 D. about 60
10. Which type of muffin is the least expensive?
Muffins
A. cinnamon raisin
Blueberry bran . . . . . 5 for $3.50
B. maple pecan Cranberry orange . . . 6 for $3.60
Crunchy oat . . . . . . . 8 for $3.20
C. cranberry orange
Maple pecan . . . . . . 3 for $2.70
D. crunchy oat Cinnamon raisin . . . . 5 for $2.50
11. A brand of light cheese says “20% less fat” on the label.
The regular version of the cheese has 85 g of fat. About
how many fewer grams of fat are in the light cheese?
A. about 10 g B. about 20 g C. about 30 g D. about 40 g
Copyright © 2006 Nelson Answers Chapter 12:Fractions, Decimals, Ratios, and Percents 115

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