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Multiplying and Dividing Expressions Worksheet

Multiplying and Dividing Expressions Worksheet
  • Page 1
 1.  
Which of the following represents the expression 1d × 11d25 in simplest form?
a.
11d5
b.
115d
c.
d5
d.
511d


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.]


Correct answer : (1)
 2.  
Which of the following represents the expression 9d23 × 244d in simplest form?
a.
18d
b.
16d
c.
20d
d.
18d


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.]


Correct answer : (1)
 3.  
Which of the following represents the expression - 5d - 6 × d - 610(d - 7), in simplest form?
a.
- 12d - 14
b.
- 12d + 14
c.
- 12d + 7
d.
12d - 7


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.]


Correct answer : (1)
 4.  
Which of the following represents the expression d5d2 + d - 12 × d + 43d3 in simplest form?
a.
d2(d - 2)
b.
d3d - 2
c.
d3d(d - 2)
d.
d23(d - 3)


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.]


Correct answer : (4)
 5.  
Which of the following represents the expression 81-d2d × 9d281+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.]


Correct answer : (4)
 6.  
Which of the following represents the expression 3d2d × 27d63d3 in simplest form?
a.
27d
b.
9d
c.
97d
d.
10d23d


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.]


Correct answer : (3)
 7.  
Which of the following represents the expression d2 -  8d + 155d × d2d2 -  25 in simplest form?
a.
d(d - 5)5(d - 3)
b.
d(d + 5)5(d + 3)
c.
d(d - 3)5(d + 5)
d.
d(d + 3)5(d - 5)


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.]


Correct answer : (3)
 8.  
Which of the following represents the expression 2d + 32 × 1010d + 15 in simplest form?
a.
2d
b.
1
c.
12d
d.
115d


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.]


Correct answer : (2)
 9.  
Which of the following represents the expression 32d3 + 20d2(5d - 20 ) × 2d - 88d + 5 in simplest form?
a.
8 5d
b.
8 5d4
c.
8 5d2
d.
d24


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.]


Correct answer : (3)
 10.  
Which of the following represents the expression d2 + 7d + 10d2 + 5d × 5d2d + 2 in simplest form?
a.
5d2
b.
5d
c.
d
d.
6d


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.]


Correct answer : (2)

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