Free Printable Algebraic Expressions and Equivalences Study Guide

1.

Which of the sets of terms below does NOT include like terms?

a)

$14x,\ -0.5x,\ \frac{1}{3}x$

b)

$m,\ 3m,\ -3m$

c)

$\frac{1}{2},\ 28,\ -67$

d)

$4x,\ -3,\ -2x^2$

e)

$-2x,\ \frac{7}{8}y,\ 0.25z$

2.

Simplify the expression:

$14y+23-15y$

a)

$-y+23$

b)

$y+23$

c)

$22y$

d)

$-y^2+23$

3.

Which expression shows the perimeter of a rectangle with sides (7x-5) and (x-2)?

a)

$8x+7$

b)

$8x-7$

c)

$16x-14$

d)

$12x+6$

4.

Which is TRUE?

a)

$-10\left(x+5\right)$

is equivalent to $-10x+50$

b)

$-5.8\left(2n-10\right)$

is equivalent to

$11.6n+58$

c)

$\frac{1}{3}\left(9-6f\right)$

is equivalent to

$3-f$

d)

All of these are equivalent.

e)

$\left(3x-2\right)7$

is equivalent to

$3x-14$

5.

Simplify.

$-8\left(2x+10t-9n\right)$

6.

Simplify.

$12m-2\left(4m+11\right)$

7.

A rectangle has side lengths of $4x-6$ and $\frac{1}{2}$ . Simplify an expression for the area of the rectangle.

8.

Nyla purchased a new phone that cost $x$ dollars. Her brother, Nolan, purchased a new phone that cost 15% more than Nyla's. Which expressions could be used to represent the coat of Nolan's phone?

a)

$x+15x$

b)

$1.15x$

c)

$x-0.15x$

d)

$x+0.15$

e)

$x+0.15x$

9.

Simplify the expression:

$8x - 3 + 5x + 7$

a)

$-13x+4$

b)

$13x-10$

c)

$3x+10$

d)

$13x+4$

10.

Which is TRUE?

a)

$-3(2a-4)$

is equivalent to $-6a+4$

b)

$2(3x+5)$

is equivalent to $6x+7$

c)

$5(x+2)$

is equivalent to $5x+12$

d)

$4(y-6)$

is equivalent to $4y-24$

11.

Which expression shows the perimeter of a rectangle with sides (4y+3) and (2y-1)?

a)

$8y+4$

b)

$12y+8$

c)

$6y+2$

d)

$12y+4$

12.

Simplify by combining like terms.

$\left(4x+1\right)+\left(3+5x\right)$

13.

Simplify by combining like terms.

$\left(x+5\right)-\left(7x-4\right)$

14.

Match.

a)

$n+4$

1.

a number increased by 4

b)

$n-4$

2.

4 less than n

c)

$4-n$

3.

the difference of 4 and a number

d)

$4n$

4.

the product of 4 and a number

e)

$\frac{4}{n}$

5.

the quotient of 4 and a number

15.

Match each expression with the correct word problem.

a)

Kara scored 25 runs this season. Emily scored x more runs than Kara. How many runs did Emily score?

1.

$x+25$

b)

Ja'Quez gained 25 yards. Carson gained x fewer yards than Ja'Quez. How many yards did Carson gain?

2.

$25-x$

c)

Christian had some money. He spent $25 to buy snacks for all his friends during break. How much money does he have left?

3.

$x-25$

d)

Savannah bought x pairs of shoes. Each pair of shoes cost $25. How much did Savannah spend?

4.

$25x$

e)

Some friends went to the ballgame together. Their total to enter was $25. How much did each person have to pay?

5.

$\frac{25}{x}$

16.

Rewrite the expression factoring out the GCF.

$15y+20$

17.

Rewrite the expression factoring out the GCF.

$9y-54$

18.

Simplify by using the Distributive Property.

$\frac{1}{2}\left(y+18\right)$

19.

Simplify using the Distributive Property, then combine like terms.

$-8\left(2y-4\right)+11y$

20.

What is the constant in the expression?

$14.1x-7.7$

a)

$14$

b)

$7.7$

c)

$-7.7$

d)

$14.1x$

Algebraic Expressions and Equivalences Study Guide

Total questions: 20

Worksheet time: 26mins

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