Practice Rational Numbers in Math

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

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Quick Recap

Numbers that can be expressed as a ratio of two integers (ab\frac{a}{b} where bโ‰ 0b \neq 0).

Any number you can write as a fraction, including decimals that end or repeat.

Showing a random 20 of 50 problems.

Example 1

medium
A decimal terminates exactly when its reduced denominator has only which prime factors?

Example 2

hard
Is ฯ€\pi rational? Briefly justify.

Example 3

medium
True or false: every terminating decimal is rational.

Example 4

medium
Convert 0.12โ€พ0.\overline{12} to a fraction in lowest terms.

Example 5

medium
Order from least to greatest: 12,ย 0.4,ย 35\frac{1}{2},\ 0.4,\ \frac{3}{5}.

Example 6

challenge
Show that 0.9โ€พ=10.\overline{9}=1, and explain why this means 0.9โ€พ0.\overline{9} is rational.

Example 7

medium
Express 0.36โ€พ0.\overline{36} as a fraction in simplest form.

Example 8

medium
Is the sum of two rational numbers always rational?

Example 9

challenge
Prove that the sum of a rational number and an irrational number is irrational.

Example 10

easy
Is 114\frac{11}{4} a rational number? Justify in one sentence.

Example 11

medium
Express 0.27โ€พ0.\overline{27} as a fraction in simplest form.

Example 12

hard
Express 0.16โ€พ0.1\overline{6} as a fraction in simplest form.

Example 13

easy
Is 34\frac{3}{4} a rational number?

Example 14

medium
Express 78\frac{7}{8} as a decimal and confirm it terminates.

Example 15

hard
Find a fraction equivalent to 1525\frac{15}{25} in lowest terms, and identify its decimal form.

Example 16

medium
Convert 1.6โ€พ1.\overline{6} to a fraction.

Example 17

medium
Show that 16\sqrt{16} is rational but 20\sqrt{20} is not.

Example 18

hard
Find the additive inverse and multiplicative inverse of โˆ’37-\frac{3}{7}.

Example 19

medium
Compute 23+14\frac{2}{3} + \frac{1}{4} and express as a fraction in lowest terms.

Example 20

easy
Is the decimal 0.50.5 rational?
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