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 13\frac{1}{3} or 18\frac{1}{8}, representing exactly one equal part of a whole.

The building blocks of fractions—12\frac{1}{2} is one of two equal parts, 14\frac{1}{4} is one of four.

Showing a random 20 of 50 problems.

Example 1

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A recipe uses 34\dfrac{3}{4} cup of flour. Express this as a sum of unit fractions using only 12\dfrac{1}{2} and 14\dfrac{1}{4}.

Example 2

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Express 23\frac{2}{3} as a sum of two different unit fractions.

Example 3

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Find a unit fraction between 14\dfrac{1}{4} and 13\dfrac{1}{3}.

Example 4

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Apply the greedy algorithm to start an Egyptian-fraction expansion of 27\dfrac{2}{7}: subtract the largest unit fraction ≤27\le \dfrac{2}{7} and report the remainder.

Example 5

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How many 18\dfrac{1}{8}s are in 34\dfrac{3}{4}?

Example 6

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What unit fraction is one of 55 equal parts of a whole?

Example 7

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How many unit-fraction pieces of 112\frac{1}{12} are in 14\frac{1}{4}?

Example 8

easy
Write 110\frac{1}{10} as a decimal.

Example 9

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What is one of 77 equal parts of a whole, as a unit fraction?

Example 10

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How many copies of 112\dfrac{1}{12} are in 13\dfrac{1}{3}?

Example 11

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If 1n=0.05\frac{1}{n} = 0.05, find nn.

Example 12

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Express 34\dfrac{3}{4} as a sum of two distinct unit fractions.

Example 13

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Express 23\dfrac{2}{3} as a sum of two distinct unit fractions.

Example 14

hard
What is the largest unit fraction less than 27\dfrac{2}{7}?

Example 15

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Find four distinct unit fractions that sum to 11.

Example 16

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What fraction is one part when a pizza is cut into 66 equal slices?

Example 17

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Compare 15\dfrac{1}{5} and 29\dfrac{2}{9}.

Example 18

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Order least to greatest: 1100,110,11000\frac{1}{100}, \frac{1}{10}, \frac{1}{1000}.

Example 19

easy
What fraction is one of 1212 equal slices of a pie?

Example 20

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Is 12\frac{1}{2} the same size as 13\frac{1}{3}?
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