Answer Keys: Operations with Rational Numbers

Student Concept Worksheet Answers

1

a) -13 | b) -5 | c) -7

a) Same signs: add and keep negative. b) Different signs: 12-7=5, larger is negative. c) Different signs: 15-8=7, larger is negative.

2

a) 6 + 4 = 10 | b) (-5) + (-8) = -13 | c) (-7) + 3 = -4

Keep, Change, Change: Change subtraction to addition and flip the sign of the second number.

3

a) -30 | b) 32 | c) -4 | d) 6

a) Different signs = negative. b) Same signs = positive. c) Different signs = negative. d) Same signs = positive.

4

a) 1/4 | b) 1/2 | c) -2.2 | d) -4.8

a) (-2/4)+(3/4)=1/4. b) (-2/3)x(-3/4)=6/12=1/2. c) Different signs. d) Different signs.

Practice Worksheet Answers

Part A: Adding Integers

1. -13

2. -5

3. -5

4. 0

5. 7

6. -35

Part B: Subtracting Integers

7. 11

8. -14

9. -3

10. -6

11. 0

12. 7

Part C: Multiplying and Dividing

13. -42

14. 72

15. -60

16. -64

17. -6

18. 8

19. -7

20. 4

Part D: Fractions and Decimals

#	Answer	Explanation
21	-5/4 or -1 1/4	(-2/4)+(-3/4)=-5/4
22	1/6	(-4/6)+(5/6)=1/6
23	1 or 4/4	(3/4)+(1/4)=4/4=1
24	-1/4	(-2/5)x(5/8)=-10/40=-1/4
25	-0.7	Different signs: 3.5-2.8=0.7, larger is negative
26	-2.5	(-4.2)+(1.7)=-2.5
27	-4	Different signs = negative
28	8	Same signs = positive

Part E: Word Problems

29

7°F

-8 + 15 = 7. Start at -8, rise (add) 15 degrees.

30

-475 feet

-350 + (-125) = -475. Descending means going more negative.

31

-$17

45 - 62 = -17. Withdrawing more than you have creates debt.

32

-$10.00

(-2.50) x 4 = -10. A negative change repeated 4 times.

33

-9°F

12 + ((-3.5) x 6) = 12 + (-21) = -9. Drop of 3.5 per hour for 6 hours = -21 total change.

Challenge Questions:

#34: (-3) + (-5) x 2 - (-8) = (-3) + (-10) + 8 = -13 + 8 = -5. Order of operations: multiply first, then add left to right.

#35: -45 + 120 - 85 + 65 = 75 + (-85) + 65 = -10 + 65 = 55 feet (above sea level)

FAST Practice Quiz Answers

1

B) -13

Same signs: add the numbers and keep the sign. (-8) + (-5) = -13. Common error: A (forgetting the negative sign).

2

C) 10

6 - (-4) = 6 + 4 = 10. Subtracting a negative = adding a positive. Common error: A (subtracting instead of adding).

3

C) 6°F

-12 + 18 = 6. Temperature "rising" means adding. Common error: D (subtracting instead of adding).

4

Select: (-4) x 3, 36 / (-3), and (-6) x 2

(-4) x 3 = -12 (different signs)
(-3) x (-4) = 12 (same signs = positive)
36 / (-3) = -12 (different signs)
(-48) / (-4) = 12 (same signs = positive)
(-6) x 2 = -12 (different signs)

5

A) -1/2

(-2/3) + (1/6) = (-4/6) + (1/6) = -3/6 = -1/2. Find common denominator, then add.

6

B) -$13.00

(-3.25) x 4 = -13.00. A negative change repeated 4 times. Different signs = negative result.

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