Extra Practice 1
Lesson 3.1: Fractions to Decimals1.a) Write each fraction as a decimal.
i)ii)ii)iv)v)
b) Identify the decimals in part a as terminating or repeating.
2. Write each decimal as a fraction in simplest form.
a) 0.02b) 0.625c)d)
3. For each fraction, write an equivalent fraction with denominator 10, 100, or 1000. Then, write the fraction as a decimal.
a)b)c)d)
4. Write the first 6 fractions as decimals. What patterns do you see?
Use the patterns to write the remaining fractions as decimals.
Extra Practice 2
Lesson 3.2: Comparing and Ordering Fractions and Decimals1.Draw a number line.
Order these fractions on the line.
Explain your strategy.
, , , 1,
2.Order each set of numbers from least to greatest.
Use a different method for each set.
Explain the method you used each time.
a) 3.75, 3, b) , 2,
3.Identify the number that has been place incorrectly.
Explain how you know.
a), 0.75, , 0.83b), , , 1.15
4.Find a number between each pair of numbers.
a), b), 0.8c) 0.21, 0.22
5.Several students purchased ribbon for their craft projects.
Student Name / Andrea / Jocelyn / Cam / Jesse
Ribbon purchased
(m) / 1 / 1.6 / 1
a) Use a number line to order the ribbon purchased from greatest to least.
b) Who purchased the most ribbon?
c) Who purchased the least amount of ribbon?
d) Use a different method. Verify your answers in parts b and c.
Extra Practice 3
Lesson 3.3: Adding and Subtracting Decimals1.Use front-end estimation to estimate each sum or difference.
a) 9.043 + 0.9 + 1.15 b) 2.09 + 4.6 + 1.8
c) 9.6 – 7.4d) 50.4 – 5.04
2.Add or subtract. Use estimation to check the answers are reasonable.
a)7.56 + 0.07 + 122.7 b) 7.85 – 6.93
c) 2.2 – 1.68d) 83.07 + 0.42 + 7.7
3.Althea bought 3.6 kg of beef, 1.7 kg of cheese, 3 kg of fish and 2.28 kg of rice. What was the total mass she had to carry?
Estimate to check your answer is reasonable.
4.The Andersons can take one of two routes to their cabin on the lake.
If they take the highway route, the distance from their home to the cabin
is 156.7 km. If they take the more scenic route, the distance is 189.4 km.
How much longer is the scenic route than the highway route?
5.One summer, the average price for a litre of gasoline in Edmonton was $1.147 while the average price for a litre of gasoline in Victoria was $1.234.
How much more did a litre of gasoline cost in Victoria than in Edmonton that summer? Write your answer to the nearest cent.
6.Find two numbers with a sum of 254.791.
7.A student added 2.35 + 4.256 and got the sum 4.491.
a) What mistake did the student make?
b) What is the correct answer?
Extra Practice 4
Lesson 3.4: Multiplying Decimals1. Use Base Ten Blocks to find each product.
Record your work on a grid paper.
a)1.6 1.2b)2.1 0.8c)1.4 2.3
2. Multiply. Estimate first.
a)7.3 2.5b)6.9 0.4c)0.9 0.9
3.a) Multiply: 14 53
b) Use only the result from part a and estimation.
Find each product.
i) 1.4 5.3ii)14 5.3iii)1.4 530
4.Dustin earns $26.85 for each overtime hour he works.
How much does he earn when he works 3.5 h of overtime?
5.Find the cost of each item at the grocery store.
a) 1.89 kg of peaches at $2.89/kg
b) 0.65 kg of cheese at $7.49/kg
c) 2.27 kg of carrots at $1.79/kg
6.A skating rink is rectangular.
Its dimensions are 19.8 m by 46.3 m.
What is the area of the rink?
Estimate to check your answer is reasonable.
7.The product of 2 decimals is 0.48.
What might the decimals be?
Find as many answers as you can.
Extra Practice 5
Lesson 3.5: Dividing Decimals1.Estimate to place the decimal point in each quotient.
a) 17.5 2.5 = 7000
b) 124.6 0.8 = 15575
c) 57.96 4.6 = 1260
2.Divide.
a)9.45 0.3
b) 92.34 0.6
c) 1.8 0.2
3.a) Divide 428 16.
b) Use only the result from part a and estimation.
Find each quotient.
i) 42.8 1.6ii)4280 160iii)4.28 0.16
c) What do you notice about your answers in part b?
Explain.
4.Cameron has a board 3.8 m long.
He wants to make shelves for his room.
Each shelf is to be 0.6 m long.
a)How many shelves will Cameron get from this board?
b)He needs 4 shelves. How much board is left over?
c)Cameron’s sister wants 2 shelves.
She makes them from the leftover board.
How long will each shelf be?
What assumptions do you make?
5.Anita bought 5.7 m of curtain material.
It cost $170.94. What is the cost of 1 m of material?
6.The area of the top of a rectangular picnic table is 1.26 m2.
The width of the tabletop is 0.7 m.
What is its length?
Extra Practice 6
Lesson 3.6: Order of Operations with Decimals1. Evaluate.
a) 2.8 + 3.9 – 4.2
b) 78.9 – 9.6 0.2
c) 57.2 + 28.1 4
d) 72.9 0.3 3
2. Evaluate.
a) (23.92 – 16.46) 1.8
b) (32.7 + 6.4) 0.4
c) 6.8 (3.2 – 2.4)
d) 8.7 (1.84 + 2.66)
3.Evaluate.
a)41.6 – 3.4 (7.8 + 0.9)
b)41.6 – 3.4 7.8 + 0.9
c)(41.6 – 3.4) (7.8 + 0.9)
4.What do you notice about the expressions and answers in question 3?
Explain.
5.Evaluate.
a)3.26 + (4.85 0.05) – 3.75 4.2
b)1.899 0.012 + 3.496 1.15
c)9.342 2.5 – 3.86 2.3
6. Use the numbers 12.2, 13.3, 14.4, and 15.5, and any operations or brackets to write two expressions whose answers are 1.
Extra Practice 7
Lesson 3.7: Relating Fractions, Decimals, and Percents1.Write each fraction as a decimal and a percent.
a)b)c)d)e)
f)g)h) i)j)
2.Ruth’s test scores were: , , and .
Write each test score as a percent.
Order the test scores from greatest to least.
Which was Ruth’s best test? How do you know?
3.Write each percent as a fraction and a decimal.
Sketch number lines to show how the numbers are related.
a) 18%b) 37%c) 86%d) 99%
4.In 5 min, Benjamin completed 27 of 30 multiple-choice questions.
Madison completed 83% of the questions.
Who completed more questions?
How do you know?
5.Barney created a design on a grid.
He coloured of the grid red.
He coloured 0.375 of the grid green.
He coloured 40% of the grid blue.
He coloured the rest of the grid purple.
What percent of the grid is purple?
How do you know?
Extra Practice 8
Lesson 3.8: Solving Percent Problems1.Calculate.
a) 10% of 78b) 15% of 60c) 20% of 120
d) 65% of 84e) 87% of 118f) 37% of 215
2.Ms. Leitch has 27 students in her class.
About 30% of the students in Ms. Leitch’s class enjoy playing soccer.
a)About how many students enjoy playing soccer?
b)The school has a total of 539 students.
Assume 30% of all students in the school enjoy playing soccer.
About what percent of the school’s population enjoys playing soccer?
3.The regular price of a skateboard is $74.99.
Find the sale price before taxes when the skateboard is on sale for:
a) 30% offb) 25% off
c) 60% offd) 50% off
4.Find the tip left by each customer at a restaurant.
a) Wally: 15% of $25.73
b) Priya: 25% of $19.48
c) Alyssa: 10% of $48.22
5.The Goods and Services tax (GST) is currently 6%.
For each item below:
i) Find the GST.
ii) Find the cost of the item including GST.
a) package of 5 mechanical pencils: $4.49
b) backpack: $29.99
c) box of golf balls: $32.49
Extra Practice Sample Answers
Extra Practice 1 – Master 3.21
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Lesson 3.1
1. a) i) 0.75, terminating ii), repeatingiii) 0.6, terminating
iv) 0.875, terminatingv), repeating
2. a)b)c) d)
3. a) , 0.8 b), 0.06c), 0.35d) , 0.095
4., , , , , ,
The repeating digits in the decimals in the even-numbered positions are multiples of 9.
The decimals in the odd-numbered positions start at 0.045 and increase by 0.091 each time.
The last two digits repeat each time.
, , , 0.5, , ,
Extra Practice 2 – Master 3.22
Lesson 3.2
1. From least to greatest: , , , 1,
I wrote the mixed number as an improper fraction.
Since all fractions have denominator 6, I compared the numerators.
I ordered the numerators from least to greatest.
Students’ answers should include a number line.
2. a) 3, , 3.75; I wrote each number as a decimal, then used place value to order the decimals:
From least to greatest: , 3.5, 3.75
b)2, 2, ; I wrote each number as a mixed number, then wrote an equivalent fraction with denominator 18 for each fraction part. I compared the whole numbers and the fractions: = 3 = 3; 2, 2 = 2
From least to greatest: 2, 2, 3
3.a) = , which is greater than 0.83
b) The numbers are ordered from greatest to least. = 1.1, which is less than 1.15
4.Answers will vary. For example: a)b)0.7c) 0.212
5. a)Students’ answers should include a number line.
I wrote each number as a decimal, then used place value to order the decimals.
1, 1, 1.6,
b) Jesse
c)Cam
d) Answers will vary.
I wrote each number as a fraction with denominator 120, then compared the numerators.
Extra Practice 3 – Master 3.23
Lesson 3.3
1. a) 10b)7c)2d) 45
2. a) 130.33b)0.92c)0.52d) 91.19
3. 10.58 kg
4. 32.7 km
5. $0.09
6. Answers will vary. For example: 1.584 and 253.207, or 125.081 and 129.71
7. a) The student did not align the digits correctly. The student did not add digits with the same place value.
b) 6.606
Extra Practice 4 – Master 3.24
Lesson 3.4
1. a) 1.92b)1.68c)3.22
2. a)7 2 = 14, 18.25b)7 0.5 = 3.5, 2.76 c) 1 1 = 1,0.81
3. a)742
b) i) 7.42ii)74.2iii)742
4.$93.98
5.a) $5.46b) $4.87c) $4.06
6. 916.74 m2; 20 m 45 m = 900 m2
7. Answers will vary. For example: 0.6 0.8; 0.12 4
Extra Practice 5 – Master 3.25
Lesson 3.5
1. a) 7.000b)155.75c)12.60
2. a) 31.5b)153.9c)9
3. a) 26.75
b) i) 26.75ii)26.75iii)26.75
c) The answers are all the same. All of the division statements are equivalent. In part i, both the divisor and the dividend are divided by 10; in part ii, they are multiplied by 10; in part iii, they are divided by 100. So, the quotient does not change each time.
4.Assume that no wood is lost when each cut is made.
In practice, this does not happen.
a) 6 boards b) 1.4 m c) 0.7 m
5.$29.99
6.1.8 m
Extra Practice 6 – Master 3.26
Lesson 3.6
1. a)2.5b)30.9c)169.6d) 729
2.a)13.428b)97.75c)8.5d) 39.15
3. a) 12.02b)15.98c)332.34
4.All answers are different. All questions contain the same numbers, in the same order,
and the same operations. But, the operations are performed in different orders.
5. a) 84.51b)161.29c)14.477
6.(14.4 – 12.2) ÷ (15.5 – 13.3) or (15.5 14.4) ÷ (13.3 – 12.2)
1
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Master 3.30
Extra Practice 7 – Master 3.27
Lesson 3.7
1.a)0.6, 60%b)0.7, 70%
c)0.5, 50%d)0.75, 75%
e)0.09, 9%f)0.95, 95%
g)0.64, 64%h)0.8, 80%
i)0.18, 18%j)0.9, 90%
2.85%, 75%, 80%
From greatest to least: 85%, 80%, 75%
Ruth’s best test score was ; 85% is the greatest percent.
3.a), 0.18b) , 0.37c) , 0.86d) , 0.99
Students’ answers should include number lines.
4.Benjamin: = 90%; 90% > 83%
5.10%; = 0.125, 40% = 0.4
0.125 + 0.4 + 0.375 = 0.9
1.0 – 0.9 = 0.1, or 10%
Extra Practice 8 – Master 3.28
Lesson 3.8
1.a)7.8b) 9c) 24d) 54.6e) 102.66f) 79.55
2. a) About 8 studentsb) About 162 students
3. a) $52.49b) $56.24c) $30.00d) $37.50
4. a)$3.86b) $4.87c) $4.82
5. a) i) $0.27ii) $4.76
b) i) $1.80ii) $31.79
c) i) $1.95 ii) $34.44
Activating Prior Knowledge: Unit 3
The right to reproduce this page is restricted to purchasing schools.
This page may have been modified from its original. Copyright © 2007 Pearson Education Canada