To get the best deal on Tutoring, call 1-855-666-7440 (Toll Free)

Multiplying and Dividing Real Numbers Worksheet

Multiplying and Dividing Real Numbers Worksheet
  • Page 1
 1.  
Find the quotient: (111 5) ÷ (- 2)
a.
1 5
b.
- 53 5
c.
3 5
d.
- 55 3


Solution:

(111 / 5) ÷ (- 2)
[Write the expression.]

= (56 / 5) ÷ (- 2 / 1)
[Write improper fractions.]

= (565) · (- 12)
[Multiply by the reciprocal of - 2 / 1.]

= 56(- 1)52

= - 285
[Find the products.]

= - 535
[Write as a mixed number.]

The quotient of (111 / 5) ÷ (- 2) is - 53 / 5.


Correct answer : (2)
 2.  
Find the quotient: 71 8 ÷ 3
a.
28 3
b.
23 8
c.
18 3
d.
3 8


Solution:

71 / 8 ÷ 3
[Write the expression.]

= (57 / 8) ÷ (3 / 1)
[Write improper fractions.]

= (578) · (13)
[Multiply by the reciprocal of 3 / 1.]

= 57183

= 198

= 238
[Write as a mixed number.]

The quotient of 71 / 8 ÷ 3 is 23 / 8.


Correct answer : (2)
 3.  
Find the quotient: 131 2 ÷ 9
a.
2
b.
21 2
c.
1 2
d.
11 2


Solution:

131 / 2 ÷ 9
[Write the expression.]

= (27 / 2) ÷ (9 / 1)
[Write improper fractions.]

= (272) · (19)
[Multiply by the reciprocal of 9 / 1.]

= 32

= 112
[Write as a mixed number.]

The quotient of 131 / 2 ÷ 3 is 11 / 2.


Correct answer : (4)
 4.  
Using repeated addition, find the product of 4 and 2.
a.
8
b.
6
c.
10
d.
2


Solution:

4 x 2 = 2 + 2 + 2 + 2
[Multiplication by a positive integer can be modeled as repeated addition.]

= 8
[Use the addition rules.]

So, 4 x 2 = 8.


Correct answer : (1)
 5.  
Evaluate -4(-5)(y) for y = -2.
a.
-40
b.
40
c.
-42
d.
-20


Solution:

-4(-5)(y)
[Original expression.]

= 20y
[The product is positive as there are even number of negative factors.]

= 20 (-2)
[Substitute -2 for y.]

= -40
.
[Since there is one negative factor, the product is negative.]


Correct answer : (1)
 6.  
A kite is moving up with a velocity of 17 ft per second. Write an algebraic model for its displacement, d (in feet) after t seconds.
a.
d = -17t
b.
d = 17t
c.
d = 15t
d.
d = 19t


Solution:

Displacement = Velocity x Time
[Formula.]

d = 17 x t
[As the kite is moving up, the velocity is indicated by positive value.]

d = 17t
[Algebraic model.]


Correct answer : (2)
 7.  
Reduce the quotient: (212) -5
a.
- 1 2
b.
2 3
c.
1 2
d.
None of the above


Solution:

(212) - 5
[Original expression.]

= (212) ÷ - 5
[Write the fraction as a division.]

= (52) ÷ - 5
[Write in improper fraction.]

= (52) × (1- 5)
[Use reciprocal to write a division expression as a product.]

= 52 × - 15
[a- b = - a / b]

= - 12
[Since there is one negative factor, the product is negative.]


Correct answer : (1)
 8.  
Evaluate: - 36 ÷ (-16 12).
a.
24
b.
34
c.
-24
d.
29


Solution:

-36 ÷ ( -16 / 12 ) = -36 ÷ ( -18 / 12 )
[Writing in improper fraction.]

= -36 x ( 12-18)
[Use reciprocal to write a division expression as a product.]

= -36 x -1218
[a / -b = -a / b.]

= 24
[Two negative factors, so product is positive.]


Correct answer : (1)
 9.  
Find the product of 5 and (- 8) by using repeated addition.
a.
- 43
b.
- 37
c.
- 40
d.
40


Solution:

5(- 8) = (- 8) + (- 8) + (- 8) + (- 8) + (- 8)
[Multiplication by a positive integer can be modeled as repeated addition.]

= - 40
[Use the addition rules.]


Correct answer : (3)
 10.  
Using the definition of opposites and repeated addition, evaluate - 2(4).
a.
8
b.
-8
c.
4
d.
10


Solution:

-2(4) = -(2)(4)
[Use the definition of opposites.]

= -(4 + 4)
[Multiplication by a positive integer can be modeled as repeated addition.]

= - (8)
[Use the addition rules.]

= - 8
[A product is negative if it has odd number of negative factors.]


Correct answer : (2)

*AP and SAT are registered trademarks of the College Board.