# Multiplying and Dividing Expressions Worksheet

Multiplying and Dividing Expressions Worksheet
• Page 1
1.
Which of the following represents the expression $\frac{1}{d}$ × $\frac{11{d}^{2}}{5}$ in simplest form?
 a. $\frac{11d}{5}$ b. $\frac{11}{5d}$ c. $\frac{d}{5}$ d. $\frac{5}{11d}$

#### Solution:

1d × 11d25
[Original expression.]

= 11d25d
[Multiply the numerators and denominators.]

= 11 × d × d5 × d
[Factor the numerator and denominator.]

= 11 × d5
[Divide out the common factors.]

= 11d5
[Simplify the expression.]

2.
Which of the following represents the expression $\frac{{9d}^{2}}{3}$ × $\frac{24}{4d}$ in simplest form?
 a. 18$d$ b. 16$d$ c. 20$d$ d. $\frac{18}{d}$

#### Solution:

9d23 × 244d
[Original expression.]

= 9×24d23×4d
[Multiply the numerators and denominators.]

= 3×3×4×6×d×d3×4×d
[Factor the numerator and denominator.]

= 3 × 6 × d
[Divide out the common factors.]

= 18d
[Simplify the expression.]

3.
Which of the following represents the expression × , in simplest form?
 a. b. c. d.

#### Solution:

- 5d - 6 × d - 610(d - 7)
[Original expression.]

= - 5(d -6)10(d - 6)(d - 7)
[Multiply the numerators and denominators.]

= - 5 × (d - 6)2 × 5 × (d - 6) × (d - 7)
[Factor the numerator and denominator.]

= - 12 × (d - 7)
[Divide out the common factors.]

= - 12d - 14
[Simplify the expression.]

4.
Which of the following represents the expression × in simplest form?
 a. b. c. d.

#### Solution:

d5d2 + d - 12 × d + 43d3
[Original expression.]

= d5(d - 3)(d + 4) × d + 43d3
[Factor the denominator.]

= d5(d + 4)3d3(d - 3)(d + 4)
[Multiply the numerators and denominators.]

= d23 × (d - 3)
[Divide out the common factors.]

= d23(d - 3)
[Simplify the expression.]

5.
Which of the following represents the expression $\frac{81-{d}^{2}}{d}$ × $\frac{9{d}^{2}}{81+9d}$ in simplest form?
 a. (9 - $d$) b. $d$(81 - $d$) c. $d$(9 + $d$) d. $d$(9 - $d$)

#### Solution:

81 -d2d × 9d281 + 9d
[Original expression.]

= (9 - d)(9 + d)d × 9d29(9 + d)
[Factor the numerator and denominator.]

= 9d2(9 - d)(9 + d)9d(9 + d)
[Multiply the numerators and denominators.]

= d(9 - d)
[Divide the common factors and simplify the expression.]

6.
Which of the following represents the expression $\frac{3{d}^{2}}{d}$ × $\frac{27d}{63{d}^{3}}$ in simplest form?
 a. $\frac{2}{7d}$ b. $\frac{9}{d}$ c. $\frac{9}{7d}$ d. $\frac{10{d}^{2}}{3d}$

#### Solution:

3d2d × 27d63d3
[Original expression.]

= 81d363d4
[Multiply the numerators and denominators.]

= 32×32×d332×7×d3×d
[Factor the numerator and denominator.]

= 3×37d
[Divide out the common factors.]

= 97d
[Simplify the expression.]

7.
Which of the following represents the expression × in simplest form?
 a. b. c. d.

#### Solution:

d2 -  8d + 155d × d2d2 -  25
[Original expression.]

= (d - 3)(d - 5)5d × d2(d - 5)(d + 5)
[Factor the numerator and denominator.]

= d2(d - 3)(d - 5)5d(d - 5)(d + 5)
[Multiply the numerators and denominators.]

= d(d - 3)5(d + 5)
[Divide out the common factors.]

8.
Which of the following represents the expression × in simplest form?
 a. 2$d$ b. 1 c. $\frac{1}{2d}$ d. $\frac{1}{15d}$

#### Solution:

2d + 32 × 1010d+15
[Original expression.]

= 2d + 32 × 105(2d + 3)
[Factor the denominator.]

= (2d + 3)1010(2d + 3)
[Multiply the numerators and denominators.]

= 1
[Divide out the common factors and simplify the expression.]

9.
Which of the following represents the expression × in simplest form?
 a. $\frac{8}{5}$$d$ b. $\frac{8}{5}$$d$4 c. $\frac{8}{5}$$d$2 d. $\frac{{d}^{2}}{4}$

#### Solution:

32d3 + 20d2(5d - 20 ) × 2d - 88d + 5
[Original expression.]

= 4d2(8d + 5)5(d - 4) × 2(d - 4)8d + 5
[Factor the numerators and denominators.]

= 8d2(8d + 5)(d - 4)5(d - 4)(8d + 5)
[Multiply the numerators and denominators.]

= 8 / 5d2
[Divide out the common factors.]

10.
Which of the following represents the expression × in simplest form?
 a. 5$d$2 b. 5$d$ c. $d$ d. 6$d$

#### Solution:

d2 + 7d + 10d2 + 5d × 5d2d + 2
[Original expression.]

= (d + 2)(d + 5)d(d + 5) × 5d2d + 2
[Factor the numerator and denominator.]

= 5d2(d + 2)(d + 5)d(d + 2)(d + 5)
[Multiply the numerators and denominators.]

= 5d
[Divide out the common factors and simplify the expression.]