Practice Unit Fraction in Math

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

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Quick Recap

A fraction with numerator 1, like $\frac{1}{3}$ or $\frac{1}{8}$ , representing exactly one equal part of a whole.

The building blocks of fractions— $\frac{1}{2}$ is one of two equal parts, $\frac{1}{4}$ is one of four.

Showing a random 20 of 50 problems.

Example 1

medium

A recipe uses

\dfrac{3}{4}

cup of flour. Express this as a sum of unit fractions using only

\dfrac{1}{2}

and

\dfrac{1}{4}

Example 2

medium

Express

\frac{2}{3}

as a sum of two different unit fractions.

Example 3

medium

Find a unit fraction between

\dfrac{1}{4}

and

\dfrac{1}{3}

Example 4

hard

Apply the greedy algorithm to start an Egyptian-fraction expansion of

\dfrac{2}{7}

: subtract the largest unit fraction

\le \dfrac{2}{7}

and report the remainder.

Example 5

medium

How many

\dfrac{1}{8}

s are in

\dfrac{3}{4}

Example 6

easy

What unit fraction is one of

5

equal parts of a whole?

Example 7

medium

How many unit-fraction pieces of

\frac{1}{12}

are in

\frac{1}{4}

Example 8

easy

Write

\frac{1}{10}

as a decimal.

Example 9

easy

What is one of

7

equal parts of a whole, as a unit fraction?

Example 10

medium

How many copies of

\dfrac{1}{12}

are in

\dfrac{1}{3}

Example 11

medium

\frac{1}{n} = 0.05

, find

n

Example 12

hard

Express

\dfrac{3}{4}

as a sum of two distinct unit fractions.

Example 13

medium

Express

\dfrac{2}{3}

as a sum of two distinct unit fractions.

Example 14

hard

What is the largest unit fraction less than

\dfrac{2}{7}

Example 15

challenge

Find four distinct unit fractions that sum to

1

Example 16

easy

What fraction is one part when a pizza is cut into

6

equal slices?

Example 17

medium

Compare

\dfrac{1}{5}

and

\dfrac{2}{9}

Example 18

medium

Order least to greatest:

\frac{1}{100}, \frac{1}{10}, \frac{1}{1000}

Example 19

easy

What fraction is one of

12

equal slices of a pie?

Example 20

easy

\frac{1}{2}

the same size as

\frac{1}{3}

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Related Concepts

Fractions Equivalent Fractions Adding Fractions