Mr. B's Weebly - Grade 8 Mathematics
Extra Practice 1
|Lesson 3.1: What Is a Rational Number? |
|1. Which of the following numbers are equal to [pic]? |
|[pic] ____________________________________________ |
|2. Write the rational number represented by each letter as a decimal. |
|[pic] |
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|______________________________________________________________________ |
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|3. Write the rational number represented by each letter as a fraction. |
|[pic] |
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|______________________________________________________________________ |
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|4. Sketch a number line and mark each rational number on it. |
|Order the numbers from greatest to least. |
|–2.25, [pic], –1.5, [pic], 0.9 |
|5. In each pair, which rational number is greater? Explain how you know. |
|a) [pic] b) [pic] |
|c) [pic] d) [pic] |
|6. Diver A is 2.3 m below sea level. |
|Diver B is 1.7 m below sea level. |
|Diver C is 3.2 m below sea level. |
|a) Draw a vertical number line to show the location of the divers. |
|b) Which diver is farthest from the surface? Explain your thinking. |
Extra Practice 1
Lesson 3.1
1. [pic]
2. A: –1.8, B: –0.1, C: 0.6, D: –0.9
3. A: –1[pic], B: [pic], C: [pic]
4.
[pic], 0.9, [pic], –1.5, –2.25
5. a) –7.2 is greater because it is to the right
of –7.3 on a number line.
b) [pic] is greater because it is greater than 1 whereas [pic]is less than 1.
c) 1.2 is greater since it is positive.
d) One-eleventh is greater than one-thirteenth. So,[pic] is closer to 0 than [pic] on a number line. Since both numbers are negative, the number closer to 0, or farther to the right, is greater. So, [pic] is greater.
6. a)
b) Diver C because she is farthest from 0 on the number line
Extra Practice 2
|Lesson 3.2: Adding Rational Numbers |
|1. Write the addition statement that each number line represents. |
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|a) |
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|b) |
|2. Determine each sum. |
|a) [pic] b) [pic] |
|c) [pic] d) [pic] |
|3. Sarah borrowed $40.25 from her parents for a new sweater. She earns $17.50 for a night of baby-sitting and gives this to her parents. |
|a) Write an addition statement to represent this situation. _________________________ |
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|b) How much does Sarah now owe? __________________________________________ |
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|4. Determine each sum. |
|a) [pic] b) [pic] |
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|5. Use integers to estimate each sum. Then, determine each sum. |
|a) [pic] b) [pic] |
|c) [pic] d) [pic] |
Extra Practice 2
Lesson 3.2
1. a) [pic] 1[pic]1[pic]
b) [pic]
2. a) [pic]
b) [pic]
c) [pic]
d) [pic]
3. a) –40.25 + 17.50 = –22.75
b) Sarah now owes $22.75.
4. a) [pic]
[pic]
b) [pic]
[pic]
5. Estimates may vary.
a) –25.5
b) 1.59
c) –3.55
d) –7.38
Extra Practice 3
|Lesson 3.3: Subtracting Rational Numbers |
|1. Write the subtraction statement that each number line represents. |
|a) |
|[pic] |
|b) |
|[pic] |
|2. Determine each difference. Describe the strategies you used. |
|a) [pic] b) [pic] |
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|3. Two climbers leave base camp at the same time. Climber A ascends 20.4 m, while climber B descends 35.4 m. How far apart are the climbers? |
|Write a subtraction statement using rational numbers to solve the problem. |
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|4. Predict whether each difference is positive or negative. Determine each difference. |
|a) 3[pic]4[pic] b) [pic] |
|5. Use integers to estimate each difference. Then, determine each difference. |
|a) [pic] |
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|b) [pic] |
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|c) [pic] |
|6. Determine the missing rational number in each addition statement. |
|a) [pic]3[pic] b) [pic]–2[pic] |
Extra Practice 3
Lesson 3.3
1. a) 1[pic]
b) –1[pic]–2[pic]
2. a) I sketched a number line.
[pic]
[pic]
b) I used common denominators.
[pic]
[pic]
3. 20.4 – (–35.4) = 55.8; the distance between the climbers is 55.8 m.
4. a) Negative
[pic]
[pic]
b) Positive
[pic]
5. a) Estimate: –11; Calculate: –10.6
b) Estimate: 0; Calculate: –0.41
c) Estimate: –35; Calculate: –34.47
6. a) [pic]
b) [pic]
Extra Practice 4
|Lesson 3.4: Multiplying Rational Numbers |
|1. Predict the sign of each product. Determine each product. |
|a) [pic] b) [pic] |
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|c) [pic] d) [pic] |
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|2. Predict the sign of each product. Determine each product. |
|a) [pic] |
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|b) [pic] |
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|c) [pic] |
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|3. From November 12th to November 21st, the temperature in Burnaby, B.C. dropped an average of 1.7°C each day. Suppose the temperature on the |
|morning of November 12th was 11.4°C. What was the temperature on the morning of November 21st? |
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|4. Use integers to estimate each product then calculate each product. |
|a) [pic] b) [pic] |
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|5. Determine each product. |
|a) [pic] b) [pic] |
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Extra Practice 4
Lesson 3.4
1. a) Negative
(–1.2) × 0.3 = –0.36
b) Negative
0.34 × (–0.5) = –0.17
c) Positive
(–0.6) × (–0.15) = 0.09
d) Negative
0.9 × (–1.2) = –1.08
2. a) Negative
[pic]
b) Negative
[pic]
c) Positive
[pic]
3. [pic]
It was –3.9°C on the morning of Nov. 21.
4. a) Estimate: (1)(–13) = –13
Calculate: (1.19)(–13.2) = –15.708
b) Estimate: (–9)(–2) = 18
Calculate: (–8.65)(–1.6) = 13.84
5. a) [pic]
b) [pic]
Extra Practice 5
|Lesson 3.5: Dividing Rational Numbers |
|1. Determine each quotient. |
|a) i) [pic] ii) [pic] |
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|b) i) [pic] ii) [pic] |
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|2. Predict the sign of each quotient, then calculate each quotient. |
|a) [pic] b) [pic] |
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|c) [pic] d) [pic] |
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|3. A diver descends 3.2 m in 5 min. What was his average rate of descent in metres per minute? |
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|4. Use a calculator to determine each quotient. Round each answer to the nearest hundredth. |
|a) [pic] b) [pic] |
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|5. Determine each quotient. |
|a) [pic] b) [pic] |
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|6. Replace each [pic] with a rational number to make each equation true. |
|a) [pic] b) [pic] |
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Extra Practice 5
Lesson 3.5
1. a) i) 8
ii) –8
b) i) 20
ii) 0.2
2. a) Negative
[pic]
b) Negative
[pic]
c) Positive
[pic]
d) Negative
[pic]
3. [pic]; So, the average rate of descent is 0.64 m/min.
4. a) 16.4 ÷ (–5.5) [pic] –2.98
b) (–0.98) ÷ 12.4 [pic] –0.08
5. a) [pic]
[pic]
b) [pic]
[pic]
6. a) (–0.64) ( 2.5 = –1.6
b) [pic]
Extra Practice 6
|Lesson 3.6: Order of Operations with Rational Numbers |
|1. Evaluate. Do not use a calculator. |
|a) [pic] b) [pic] |
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|2. Evaluate. Do not use a calculator. |
|a) [pic] b) [pic] |
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|3. A formula for the area of a trapezoid is [pic]where b and c are the lengths of the parallel sides and a is the perpendicular distance |
|between these sides. Use the formula to determine the area of a trapezoid with: [pic]cm, [pic]cm, [pic]cm. |
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|4. Evaluate. |
|a) [pic] b) [pic] |
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|5. Evaluate this expression. Round the answer to the nearest hundredth. |
|[pic] |
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Extra Practice 6
Lesson 3.6
1. a) 4.5 + 5.1 ÷ 1.7 = 4.5 + 3 = 7.5
b) –5.8 – 3.1 × 0.5 = –5.8 – 1.55 = –7.35
2. a) [pic]
b) [pic]
[pic]
[pic]
[pic]
[pic]
[pic]
[pic]
3. Substitute.
A = [pic]
The area of the trapezoid is 24.15 cm2.
4. a) [pic]
[pic]
b) [pic]
[pic]
5. [pic]28.35
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Target A-1
Target A-2
Target A-2
Master 2.23
Target A-2
Target A-2
Target A-2
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