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 where b≠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 π rational? Briefly justify.

Example 3

medium
True or false: every terminating decimal is rational.

Example 4

medium
Convert 0.12‾ to a fraction in lowest terms.

Example 5

medium
Order from least to greatest: 12, 0.4, 35.

Example 6

challenge
Show that 0.9‾=1, and explain why this means 0.9‾ is rational.

Example 7

medium
Express 0.36‾ 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 a rational number? Justify in one sentence.

Example 11

medium
Express 0.27‾ as a fraction in simplest form.

Example 12

hard
Express 0.16‾ as a fraction in simplest form.

Example 13

easy
Is 34 a rational number?

Example 14

medium
Express 78 as a decimal and confirm it terminates.

Example 15

hard
Find a fraction equivalent to 1525 in lowest terms, and identify its decimal form.

Example 16

medium
Convert 1.6‾ to a fraction.

Example 17

medium
Show that 16 is rational but 20 is not.

Example 18

hard
Find the additive inverse and multiplicative inverse of −37.

Example 19

medium
Compute 23+14 and express as a fraction in lowest terms.

Example 20

easy
Is the decimal 0.5 rational?
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