Practice Equivalence in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

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Quick Recap

When two expressions, numbers, or objects represent the same value or are interchangeable in every relevant context.

$\frac{1}{2}$ , $0.5$ , and $50\%$ are equivalent—different forms, same value.

Showing a random 20 of 50 problems.

Example 1

medium

Are

\frac{5}{8}

and

0.625

equivalent?

Example 2

medium

Find a value of

n

that makes

4 \times n = 2 \times 10

true. Explain what equivalence means here.

Example 3

medium

Are

\frac{a}{b}

and

\frac{2a}{2b}

equivalent for nonzero

b

? Why?

Example 4

medium

Are

x^2

and

2x

equivalent? Test more than one value.

Example 5

easy

\frac{4}{6}

equivalent to

\frac{2}{3}

Example 6

challenge

For what values of

x

are

\frac{x^2 - 1}{x - 1}

and

x + 1

equivalent?

Example 7

easy

15 + 7

equivalent to

11 + 11

? Show your work.

Example 8

medium

Find

n

such that

5 \times 8 = n + 20

Example 9

easy

0.25

equivalent to

\frac{1}{4}

Example 10

medium

Find

n

so that

\frac{4}{6} = \frac{n}{18}

Example 11

medium

Convert

\frac{7}{8}

to a decimal and confirm equivalence.

Example 12

hard

Order from smallest to largest by finding equivalents:

\frac{2}{3}, \frac{5}{8}, 0.7

Example 13

easy

25\%

equivalent to

\frac{1}{4}

Example 14

easy

Are

\frac{5}{10}

and

\frac{1}{2}

equivalent?

Example 15

medium

Fill in:

\frac{2}{3} = \frac{?}{15}

Example 16

easy

6+5

equivalent to

7+4

Example 17

challenge

Prove

\frac{1}{2}+\frac{1}{3}

is equivalent to

\frac{5}{6}

Example 18

challenge

Show

\frac{x^2-1}{x-1}

is equivalent to

x+1

for

x\ne 1

, and explain the restriction.

Example 19

medium

Are

\frac{3}{5}

and

\frac{12}{20}

equivalent?

Example 20

easy

Write

\frac{1}{5}

as a percent.

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Related Concepts

Equal Equivalent Fractions