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Simplifying Variable Expressions Worksheet

Simplifying Variable Expressions Worksheet
  • Page 1
 1.  
Jason gets $14 a day by washing cars. He is paid an extra $4 for every car he washes after 6 p.m. Which of the following equations represents his total earnings for the day, if y represents his earnings per day and x represents the number of cars washed after 6 p.m.?
a.
y = 14 + 4x
b.
y = 4 + 14x
c.
y = 4 + 15x
d.
None of the above


Solution:

Total earnings = Daily wage + Earnings for washing cars after 6 P.M. = $14 + $(4 x number of cars)

So, the equation y = 14 + 4x represents his total earnings for the day.


Correct answer : (1)
 2.  
Which of the following expressions is the simplest form of 7m + 4(4 + h)?
a.
7m + 4h + 16
b.
7m + 16h + 16
c.
m + 16h + 4
d.
None of the above


Solution:

7m + 4(4 + h) = 7m + 4(4) + 4(h)
[Use distributive property of addition.]

= 7m + 16 + 4h
[Multiply.]

= 7m + 4h + 16
[Use commutative property of addition.]


Correct answer : (1)
 3.  
Which of the following expressions has two terms?
a.
7x
b.
xy
c.
x + y + xy
d.
6 + 7


Solution:

A term is a number or a variable or a product of numbers and variables.

x, y and xy are the three terms in the expression x + y + xy.

xy is the only term in the expression xy.

7x is the only term in the expression 7x.

6 and 7 are the two terms in the expression 6 + 7.

So, 6 + 7 is the expression, which has two terms.


Correct answer : (4)
 4.  
Which of the following expressions is equivalent to the expression 2 + 4(3 + s)?
a.
15 + 4s
b.
13 + 4s
c.
14 + 4s
d.
16 + 4s


Solution:

2 + 4(3 + s)
[Original expression.]

= 2 + 4(3) + 4(s)
[Use the distributive property of addition.]

= 2 + 12 + 4s
[Multiply.]

= 14 + 4s
[Combine like terms.]


Correct answer : (3)
 5.  
Which of the following expressions is the simplified form of 4x + 5x(3 + y)?
a.
19x + 5xy
b.
24xy
c.
19x + 5(x + y)
d.
19x + 15 + 5y


Solution:

4x + 5x(3 + y)
[Original expression.]

= 4x + 5x(3) + 5x(y)
[Use the distributive property of addition.]

= 4x + 15x + 5xy
[Multiply.]

= (4 + 15)x + 5xy
[Use the distributive property of addition.]

= 19x + 5xy
[Simplify inside the grouping symbols.]


Correct answer : (1)
 6.  
Which of the following expressions is equivalent to the expression 5h - 2h(x - m)?
a.
5h - 2hx
b.
5h - 2hx + 2hm
c.
5xhm
d.
h(x - m)


Solution:

5h - 2h(x - m)
[Original expression.]

= 5h - 2h(x) - 2h(- m)
[Use the distributive property of addition.]

= 5h - 2hx + 2hm
[Multiply.]


Correct answer : (2)
 7.  
Fill in the blanks.
7h + 3 - 4h - 3 - 9h + 3 = __ h + __
a.
-6, -3
b.
6, 3
c.
6, -3
d.
-6, 3


Solution:

L.H.S = 7h + 3 - 4h - 3 - 9h + 3

= 7h - 4h - 9h + 3 - 3 + 3
[Use the commutative property of addition.]

= (7 - 4 - 9)h + (3 - 3 + 3)
[Use the distributive property of addition.]

= -6h + 3
[Combine like terms.]

The coefficient of h is -6 and the constant is 3.

-6, 3 is the set of values that fill in the blanks in the equation.


Correct answer : (4)
 8.  
Which of the following is the simplest form of the expression given below?
(a + 3 - 4a - 3 + 5a - 2 + 3a)
a.
5a - 2
b.
5a + 2
c.
- 5a - 2
d.
- 5a + 2


Solution:

(a + 3 - 4a - 3 + 5a - 2 + 3a)
[Original expression.]

= (a - 4a + 5a + 3a) + (3 - 3 - 2)
[Use the commutative property of addition to reorder the terms.]

= 5a - 2
[Combine like terms.]

Among the choices, the expression 5a - 2 is the simplified form of the expression.


Correct answer : (1)
 9.  
Which expression has two variables?
a.
x + y + xy
b.
4 + x
c.
5x
d.
4 + 5


Solution:

Variable is a symbol, usually a letter, which stands for an unknown number.

Choice (A) consists of variables x and y.

Choice (B) consists of one variable x and one constant 4.

Choice (C) consists of one variable x.

Choice (D) consists of two constants 4 and 5.

Only choice A contains two variables.


Correct answer : (1)
 10.  
Which of the following gives the total money (expressed in dollars) spent by Nina, if she bought four toys for d dimes each, two cups for n nickels each and a basket for $1.63?
a.
$(d + n + 1.63)
b.
$(d + n - 1.63)
c.
$(4d + 0.1n + 1.63)
d.
$(0.4d + 0.1n + 1.63)


Solution:

Cost of 4 toys = 4 x d dimes = 4d dimes

10 dimes = 1 dollar
[Write dimes in terms of dollars.]

1 dime = 110 dollar
[Divide each side by 10.]

Cost of 4 toys = 4d x 110 = $0.4d

Cost of 2 cups = 2 x n nickels = 2n nickels

20 nickels = 1 dollar
[Write nickels in terms of dollars.]

1 nickel = 120 dollar
[Divide each side by 20.]

Cost of 2 cups = 2n x 120 = $0.1n

Total amount = $(0.4d + 0.1n + 1.63)
[Add.]

The total money spent on four toys, two cups and a basket is $(0.4d + 0.1n + 1.63).


Correct answer : (4)

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