# Multiplying and Dividing Real Numbers Worksheet

Multiplying and Dividing Real Numbers Worksheet
• Page 1
1.
Find the quotient: ($11\frac{1}{5}$) ÷ (- 2)
 a. $\frac{1}{5}$ b. - $5\frac{3}{5}$ c. $\frac{3}{5}$ d. - $5\frac{5}{3}$

#### 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.

2.
Find the quotient: $7\frac{1}{8}$ ÷ 3
 a. $2\frac{8}{3}$ b. $2\frac{3}{8}$ c. $1\frac{8}{3}$ d. $\frac{3}{8}$

#### 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.

3.
Find the quotient: $13\frac{1}{2}$ ÷ 9
 a. 2 b. $2\frac{1}{2}$ c. $\frac{1}{2}$ d. $1\frac{1}{2}$

#### 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.

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

So, 4 x 2 = 8.

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.]

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. $d$ = -17$t$ b. $d$ = 17$t$ c. $d$ = 15$t$ d. $d$ = 19$t$

#### 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.]

7.
Reduce the quotient: (2$\frac{1}{2}$) -5
 a. - $\frac{1}{2}$ b. $\frac{2}{3}$ c. $\frac{1}{2}$ 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.]

8.
Evaluate: - 36 ÷ ($-1\frac{6}{12}$).
 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.]

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

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)