Question 1

Which of the following fractions is equivalent to $$\frac{3}{5}$$?

Accepted Answer

$$\frac{9}{15}$$

Question 2

Simplify the fraction $$\frac{28}{56} to $$its lowest terms.

Accepted Answer

$$\frac{1}{2}$$

Question 3

A pizza is cut into 12 equal slices. If 8 slices are eaten, what fraction of the pizza remains?

Accepted Answer

$$\frac{1}{3}$$

Question 4

Evaluate the expression $$(-3)^3.$$

Accepted Answer

$$-27$$

Question 5

Which of the following is the correct exponential form for $$8 	imes 8 	imes 8 	imes 8$$?

Accepted Answer

$$8^4$$

Question 6

Evaluate the algebraic expression $$2x + 5$$ when $$x = 4.$$

Accepted Answer

$$13$$

Question 7

Translate the phrase 'the sum of 17 and a number $$x$$' into an algebraic expression.

Accepted Answer

$$17 + x$$

Question 8

Write an equation for the following scenario: 'Seven more than twice a number is equal to 19.' Let $$x be $$the number.

Accepted Answer

$$2x + 7 = 19$$

Question 9

Use the distributive property to simplify $$4(x - 8).$$

Accepted Answer

$$4x - 32$$

Question 10

Combine like terms in the expression $$3x + 7x - 2.$$

Accepted Answer

$$10x - 2$$

Question 11

A water tank contains 10 liters of water and is being filled at a rate of $$r$$ liters per minute. Write an expression for the amount of water in the tank after $$t$$ minutes.

Accepted Answer

$$10 + rt$$

Question 12

Evaluate $$\frac{1}{2}a + 4b$$ when $$a = 10$$ and $$b = -6.$$

Accepted Answer

$$-19$$

Question 13

Which of the following is a proper fraction?

Accepted Answer

$$\frac{2}{5}$$

Question 14

Simplify the expression $$2(x + 3) + 4x.$$

Accepted Answer

$$6x + 6$$

Question 15

Evaluate $$-8y^3$$ when $$y = 2.$$

Accepted Answer

$$-64$$

Question 16

Which of the following expressions represents 'negative three times the value of $$x$$ increased by 5'?

Accepted Answer

$$-3x + 5$$

Question 17

If $$x = -2$$, what is the value of $$x^2 + 4x + 6$?

Accepted Answer

$$2$$

Question 18

Which of the following is the correct translation for 'the quotient of a number $$x$$ and 6 subtracted from 9 is equal to 1'?

Accepted Answer

$$9 - \frac{x}{6} = 1$$

Question 19

Use the distributive property to expand and simplify $$-2(3x - 4y + 5).$$

Accepted Answer

$$-6x + 8y - 10$$

Question 20

Combine like terms and simplify: $$5a - 3b + 2a + 7b.$$

Accepted Answer

$$7a + 4b$$

Intermediate Algebra Study Guide: Real Numbers and Algebraic Expressions

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