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. | - $5\frac{5}{3}$ |

[Write the expression.]

= (

[Write improper fractions.]

= (

[Multiply by the reciprocal of -

=

= -

[Find the products.]

= -

[Write as a mixed number.]

The quotient of (

Correct answer : (2)

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. | $\frac{3}{8}$ |

[Write the expression.]

= (

[Write improper fractions.]

= (

[Multiply by the reciprocal of

=

=

=

[Write as a mixed number.]

The quotient of

Correct answer : (2)

3.

Find the quotient: $13\frac{1}{2}$ ÷ 9

a. | 2 | ||

b. | $2\frac{1}{2}$ | ||

c. | $\frac{1}{2}$ | ||

d. | $1\frac{1}{2}$ |

[Write the expression.]

= (

[Write improper fractions.]

= (

[Multiply by the reciprocal of

=

=

[Write as a mixed number.]

The quotient of

Correct answer : (4)

4.

Using repeated addition, find the product of 4 and 2.

a. | 8 | ||

b. | 6 | ||

c. | 10 | ||

d. | 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 |

[Original expression.]

= 20

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

= 20 (-2)

[Substitute -2 for

= -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. | $d$ = -17$t$ | ||

b. | $d$ = 17$t$ | ||

c. | $d$ = 15$t$ | ||

d. | $d$ = 19$t$ |

[Formula.]

[As the kite is moving up, the velocity is indicated by positive value.]

[Algebraic model.]

Correct answer : (2)

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 |

[Original expression.]

= (

[Write the fraction as a division.]

= (

[Write in improper fraction.]

= (

[Use reciprocal to write a division expression as a product.]

=

[

= -

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

Correct answer : (1)

8.

Evaluate: - 36 ÷ ($-1\frac{6}{12}$).

a. | 24 | ||

b. | 34 | ||

c. | -24 | ||

d. | 29 |

[Writing in improper fraction.]

= -36 x (

[Use reciprocal to write a division expression as a product.]

= -36 x

[

= 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 |

[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 |

[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)