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 + 4$x$ | ||

b. | $y$ = 4 + 14$x$ | ||

c. | $y$ = 4 + 15$x$ | ||

d. | None of the above |

So, the equation

Correct answer : (1)

2.

Which of the following expressions is the simplest form of 7$m$ + 4(4 + $h$)?

a. | 7$m$ + 4$h$ + 16 | ||

b. | 7$m$ + 16$h$ + 16 | ||

c. | $m$ + 16$h$ + 4 | ||

d. | None of the above |

[Use distributive property of addition.]

= 7

[Multiply.]

= 7

[Use commutative property of addition.]

Correct answer : (1)

3.

Which of the following expressions has two terms?

a. | 7$x$ | ||

b. | $\mathrm{xy}$ | ||

c. | $x$ + $y$ + $\mathrm{xy}$ | ||

d. | 6 + 7 |

7

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 + 4$s$ | ||

b. | 13 + 4$s$ | ||

c. | 14 + 4$s$ | ||

d. | 16 + 4$s$ |

[Original expression.]

= 2 + 4(3) + 4(

[Use the distributive property of addition.]

= 2 + 12 + 4

[Multiply.]

= 14 + 4

[Combine like terms.]

Correct answer : (3)

5.

Which of the following expressions is the simplified form of 4$x$ + 5$x$(3 + $y$)?

a. | 19$x$ + 5$x$$y$ | ||

b. | 24$x$$y$ | ||

c. | 19$x$ + 5($x$ + $y$) | ||

d. | 19$x$ + 15 + 5$y$ |

[Original expression.]

= 4

[Use the distributive property of addition.]

= 4

[Multiply.]

= (4 + 15)

[Use the distributive property of addition.]

= 19

[Simplify inside the grouping symbols.]

Correct answer : (1)

6.

Which of the following expressions is equivalent to the expression 5$h$ - 2$h$($x$ - $m$)?

a. | 5$h$ - 2$h$$x$ | ||

b. | 5$h$ - 2$h$$x$ + 2$h$$m$ | ||

c. | 5$x$$h$$m$ | ||

d. | $h$($x$ - $m$) |

[Original expression.]

= 5

[Use the distributive property of addition.]

= 5

[Multiply.]

Correct answer : (2)

7.

Fill in the blanks.

7$h$ + 3 - 4$h$ - 3 - 9$h$ + 3 = __ $h$ + __

a. | -6, -3 | ||

b. | 6, 3 | ||

c. | 6, -3 | ||

d. | -6, 3 |

= 7

[Use the commutative property of addition.]

= (7 - 4 - 9)

[Use the distributive property of addition.]

= -6

[Combine like terms.]

The coefficient of

-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 - 4$a$ - 3 + 5$a$ - 2 + 3$a$)

a. | 5$a$ - 2 | ||

b. | 5$a$ + 2 | ||

c. | - 5$a$ - 2 | ||

d. | - 5$a$ + 2 |

[Original expression.]

= (

[Use the commutative property of addition to reorder the terms.]

= 5

[Combine like terms.]

Among the choices, the expression 5

Correct answer : (1)

9.

Which expression has two variables?

a. | $x$ + $y$ + $x$$y$ | ||

b. | 4 + $x$ | ||

c. | 5$x$ | ||

d. | 4 + 5 |

Choice (A) consists of variables

Choice (B) consists of one variable

Choice (C) consists of one variable

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. | $(4$d$ + 0.1$n$ + 1.63) | ||

d. | $(0.4$d$ + 0.1$n$ + 1.63) |

10 dimes = 1 dollar

[Write dimes in terms of dollars.]

1 dime =

[Divide each side by 10.]

Cost of 4 toys = 4

Cost of 2 cups = 2 x

20 nickels = 1 dollar

[Write nickels in terms of dollars.]

1 nickel =

[Divide each side by 20.]

Cost of 2 cups = 2

Total amount = $(0.4

[Add.]

The total money spent on four toys, two cups and a basket is $(0.4

Correct answer : (4)