7th Grade Number System: Multiplying and Dividing Rational Numbers
SHOW ALL WORK IN YOUR NOTEBOOK!
Multiplying Rational Numbers
1. (-1)(-8) =
11. (-9.12)(-7) =
2. (1)(-2) =
12. (-5.8)(3.1) =
3. (-7)(8) =
13. (4.87)(-1) =
4. (9)(1) =
14. (4.4)(4.4) =
1
5
2
3
20.  4 (5 ) 
2
5
21.  62 (51) 
2
3
22. 13 (60) 
5. (-6)(3) =
15. (-2.86)(9.2) =
6. (2)(-5) =
16. (9.3)(-9.3) =
7. (0)(-5) =
17. (-6.2)(-9.1) =
8. (7)(-3) =
18. (6.34)(2) =
9. (-8)(-2) =
19.  6 (4 ) 
1
5
3
4
1
1
(8 ) 
2
6
23. 36
3
8
24. 4 ( 80) 
25. (-10)(45) =
10. (-5.21)(-5.3) =
Dividing Rational Numbers
1. 5 ÷ -1 =
10. 49.2 ÷ -8.2 =
2. 24 ÷ 4 =
11. -78.72 ÷ 6 =
3. -3 ÷ -3 =
12. -2.4 ÷ -4 =
4. 0 ÷ 3 =
13. 0.128 ÷ 3.2 =
2
3
2
3
19.  14  (3 ) 
3
8
1
8
20. 24  (8 ) 
3
8
21. 35  (4 ) 
5. -10 ÷ 2 =
14. -1.53 ÷ 51 =
6. -6 ÷ 3 =
15. -1.92 ÷ -1.92 =
7. -40 ÷ -8 =
16. 6.64 ÷ -8
1
2
1
4
22.  5  ( 2 ) 
23. 20÷ -6 =
8. -4 ÷ 2 =
17. 57.6 ÷ -8 =
24. -212 ÷ -53 =
9. -25 ÷ -5 =
3
5
18.  5  (4) 
25. 4050 ÷ 75 =
7th Grade Number System: Multiplying and Dividing Rational Numbers
SHOW ALL WORK IN YOUR NOTEBOOK!
Operations with Rational Numbers
1.  24  6(4)
5. 17.4  (3)( 1.7)
2. [(-5) + (-3)] + [(-5)(-2 –
4)]
6.
3. [-7 – (-3) + 5] [-3(7 – 11)]
3
4
4 2  (2.4)(3.7)
 16  (20)
Converting Rational Numbers to Decimals
Convert each Rational Number to Decimal Form.
5
6
13.  23
10.  4
11. 15
12. 
1
9
7
8
7
11
14. 2
1
4
2
2
2
32  [8  3(5  2 )]
5
7
7
8.
4. -3.2(2.8) + [-2 – (-5)(-3)]
9.
1
4
7.  7(2  1 )  (4)( 2 )
3
8
15.  5
2
6
3
4
7th Grade Number System: Multiplying and Dividing Rational Numbers
SHOW ALL WORK IN YOUR NOTEBOOK!
Number System Review
PMI 7th Grade
Name ________________________
Multiple Choice– Choose the correct answer for each question. No partial credit will be given.
1. What is the opposite of 5?
a) 5
b) -5
c) 0
2. What is │23 │?
a) 23
b) -23
c) 0
3. What is │-7│?
NJ Center for Teaching and Learning
~3~
www.njctl.org
7th Grade Number System: Multiplying and Dividing Rational Numbers
SHOW ALL WORK IN YOUR NOTEBOOK!
a) 7
b) -7
c) 0
4.
-11
-10
a)
b) =
c)
5.
-20.0
-19.9
a)
b) =
c)
6.
-9
-9 ¼
a)
b) =
c)
7. If the temperature reading on a thermometer is -5°C, what will the new reading be if the
temperature rises 8.4°C?
a) -13.4°C
b) -3.4°C
c) 3.4°C
d) 13.4°C
8. A submarine is cruising at -40 meters (40 meters below the surface). It descends 20 meters;
then it rises 15
a) 15 3 8 m
meters. What is the submarine’s new depth?
b)  60 1 4 m
44 8 m
c)
d) None of the above
7
9. The temperature in North Dakota was 5°C at 4 A.M. It had risen 13°C since midnight. What was
the temperature at midnight?
a) -8°C
b) -4°C
c) 8°C
d) 18°C
10. Convert the subtraction problem into an addition problem.
a) -10 + 5
NJ Center for Teaching and Learning
~4~
10 – (- 5)
www.njctl.org
7th Grade Number System: Multiplying and Dividing Rational Numbers
SHOW ALL WORK IN YOUR NOTEBOOK!
b) -10 + (-5)
c) 10 + 5
d) 10 + (-5)
11. Convert the subtraction problem into an addition problem.
a) -8.75+ 4.3
b) -8.75 + (-4.3)
c) 8.75 + 4.3
d) 8.75 + (-4.3)
8.75 – 4.3
12. Simplify: -12 + 6 – (-3)
a) -3
b) -9
c) 9
d) 3
13. Simplify: 10 + (-2) – (-17) – 5
a) 25
b) 20
c) -14
d) 14
14. Simplify: -1 + 3.1(4 –6)
a) 0.1
b) -2.1
c) -1.1
d) -7.2
15. Simplify: 6 – 4[(5 ½)(-4) + (-3 ¼)]
a) -95.25
b) -95
c) -50.5
d) -107
Short Constructed Response – Write the correct answer for each question. No partial credit will be
given.
16. Name the two numbers that have 10 as their absolute value _________________
In 17-18, use a number line to illustrate the given problem.
NJ Center for Teaching and Learning
~5~
www.njctl.org
7th Grade Number System: Multiplying and Dividing Rational Numbers
SHOW ALL WORK IN YOUR NOTEBOOK!
17. -6 + 7
18. 9 + -3
19. Simplify. Show each step.
20. Convert the fraction into a decimal. Show all work.
Extended Constructed Response - Solve the problem, showing all work. Partial credit may be
given.
21. Mike had a balance of $175 in his bank account at the start of the week. He withdrew $65.00 on
Monday, $43.25 on Wednesday, and $56.45 on Thursday. On Friday he deposited $165.30.
 At the end of the week, does Mike have more or less money in his savings account than he
had at the beginning of the week?
 How much more or less?
 Show all of your work to support your answers.
NJ Center for Teaching and Learning
~6~
www.njctl.org
7th Grade Number System: Multiplying and Dividing Rational Numbers
SHOW ALL WORK IN YOUR NOTEBOOK!
22. In the first quarter of the game, the Giants gained 5 yards, lost 13 yards, gained 2 yards, gained 6
yards and, unfortunately, lost 12 yards in their final play.
 Use a number line to depict the Giants’ activity in the first quarter.
 Use addition only to illustrate the Giants’ activity in the first quarter.
 What was the net yardage for the Giants in the first quarter?
23. The temperature varied greatly throughout the evening. Mary’s bug farm cannot survive if the
temperature falls below 32°C at any time. The evening temperature was consistently 62 degrees,
until a storm passed through the town. The temperature dropped 24°, dropped another 5°, rose 2°,
dropped 11°, and rose 9°.
 Illustrate the temperature changes throughout the night using only addition
 What was the lowest temperature of the night?
 Did the bug farm survive the night? Explain your answer.
24. The test was worth 100 points. Each multiple choice question was worth 3 points, each short
answer was worth 4 points and each extended response question was worth 5 points. There was
a bonus question worth 6 points. Mark’s answers contained incorrect responses to the following: 2
multiple choice, 2 short answer, 1 extended response. Mark’s answer to the bonus question was
correct. Mark hoped to earn at least a “B” on the test, which means his score had to be between
80 – 89.



How many points did Mark lose due to incorrect answers?
Did Mark earn a “B” as he had hoped?
What would Mark’s score have been if his extended response answer was correct and he
had one more multiple choice answer incorrect?
NJ Center for Teaching and Learning
~7~
www.njctl.org
7th Grade Number System: Multiplying and Dividing Rational Numbers
SHOW ALL WORK IN YOUR NOTEBOOK!
Answers to Chapter 7 Review
1)
2)
3)
4)
5)
6)
B
A
A
C
C
A
7) C
8) D
9) A
10) C
11) D
12) A
13) B
14) D
15) B
16) 10, -10
17)
18)
19)
20)
922
12
21)
More
0.60
22) 5 + (-13) + 2 + 6 + (-12)
-12 yards
23) 62 + (-24) + (-5) + 2 + (-11) + 9
Lowest temp in the night was 24 degrees
The bug farm did not survive the night since the temp did drop below 32 degrees at one
point.
NJ Center for Teaching and Learning
~8~
www.njctl.org
7th Grade Number System: Multiplying and Dividing Rational Numbers
SHOW ALL WORK IN YOUR NOTEBOOK!
24)
19 points lost due to
incorrect answers
Yes, his score was an 81.
His score would have been an 89.
NJ Center for Teaching and Learning
~9~
www.njctl.org