Subtracting Fractions with Unlike Denominators Examples

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Subtracting Fractions with Unlike Denominators.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.

Concept Recap

Subtracting fractions with different denominators by first rewriting them with a common denominator, then subtracting numerators.

To find $\frac{3}{4} - \frac{1}{3}$ , convert to twelfths: $\frac{9}{12} - \frac{4}{12} = \frac{5}{12}$ . Same idea as addition, just subtract.

Read the full concept explanation →

How to Use These Examples

Read the first worked example with the solution open so the structure is clear.
Try the practice problems before revealing each solution.
Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: A difference of fractions makes sense only once both share a common denominator.

Common stuck point: The procedure for subtracting fractions with unlike denominators is the easy part; the trap is subtracting numerators and denominators separately. Asking "Do the fractions have different denominators that must be matched before subtracting?" first is what keeps a correct-looking calculation from being attached to the wrong concept.

Sense of Study hint: Ask: Do the fractions have different denominators that must be matched before subtracting?

Worked Examples

Example 1

easy

Subtract

\frac{3}{4} - \frac{1}{6}

Compare the two fractions before finding a common denominator

Answer

\frac{7}{12}

First step

Find the LCD of

4

and

6

\text{LCD} = 12

Full solution

2
Convert: $\frac{3}{4} = \frac{9}{12}$ and $\frac{1}{6} = \frac{2}{12}$ .
3
Subtract: $\frac{9}{12} - \frac{2}{12} = \frac{7}{12}$ .

Just as with addition of unlike fractions, you must first find equivalent fractions with a common denominator. Once the pieces are the same size, subtracting numerators gives the result.

Example 2

medium

A runner completed

\frac{7}{8}

of a race, then stopped. If the race is

1

km long, what fraction of the race is left? If another runner has already finished

\frac{2}{5}

of the remaining distance, how much of the total race has that runner covered?

Example 3

hard

Subtract

\frac{7}{8} - \frac{2}{3} - \frac{1}{6}

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy

Compute

\frac{5}{6} - \frac{1}{4}

Compare 5/6 and 1/4 before subtracting

Example 2

hard

Compute

Example 13

medium

\frac{7}{12}-\frac{?}{4}=\frac{1}{3}

. Find the missing numerator.

Example 14

medium

Subtract

2\frac{1}{4}-\frac{2}{3}

Example 15

medium

Subtract

\frac{9}{10}-\frac{2}{5}

Convert 2/5 to 4/10, then subtract from 9/10

Example 16

medium

A board is

\frac{7}{8}

m. You cut off

\frac{1}{3}

m. How much remains?

Example 17

medium

Subtract

1-\frac{2}{3}-\frac{1}{6}

Example 18

medium

Subtract

\frac{5}{6}-\frac{1}{4}

LCM of 6 and 4 is 12; convert both fractions

Example 19

medium

Subtract

\frac{11}{12}-\frac{3}{4}

and simplify.

Example 20

challenge

Maria has

\frac{3}{4}

of a tank of gas. She uses

\frac{1}{3}

of a tank driving to work and

\frac{1}{6}

coming home. How much is left?

Example 21

challenge

Order from largest to smallest the differences

\frac{1}{2}-\frac{1}{3}

\frac{1}{3}-\frac{1}{4}

\frac{1}{4}-\frac{1}{5}

Example 22

challenge

Find

x

\frac{5}{6}-x=\frac{1}{4}

Example 23

easy

Subtract

\frac{1}{2} - \frac{1}{3}

Both halves and thirds convert to sixths

Example 24

easy

Subtract

\frac{3}{5} - \frac{1}{10}

Convert 3/5 to 6/10 to match the denominator

Example 25

easy

Subtract

\frac{7}{8} - \frac{1}{4}

Convert 1/4 to 2/8, then subtract from 7/8

Example 26

easy

Subtract

\frac{4}{6} - \frac{1}{3}

Example 27

easy

Subtract

\frac{5}{12} - \frac{1}{4}

Convert 1/4 to 3/12 to subtract from 5/12

Example 28

easy

Compute

\frac{3}{5} - \frac{1}{4}

Example 29

easy

Subtract

\frac{5}{8} - \frac{1}{6}

Example 30

medium

Subtract

\frac{5}{6} - \frac{2}{9}

Example 31

medium

Subtract

\frac{7}{10} - \frac{1}{4}

Example 32

medium

Subtract

\frac{7}{15} - \frac{1}{5}

Convert 1/5 to 3/15 to subtract from 7/15

Example 33

medium

Subtract

\frac{3}{8} - \frac{1}{12}

Example 34

medium

A board is

\frac{4}{5}

m long. You cut

\frac{1}{2}

m off. How much is left?

Example 35

medium

Subtract

1 - \frac{2}{3} - \frac{1}{4}

Example 36

medium

Subtract

3\frac{1}{2} - 1\frac{2}{3}

Example 37

medium

\frac{11}{12} - \frac{?}{6} = \frac{1}{4}

. Find the missing numerator.

Example 38

medium

Subtract

\frac{9}{14} - \frac{2}{7}

Example 39

medium

Subtract

\frac{7}{9} - \frac{1}{6}

Example 40

medium

Subtract

\frac{5}{6} - \frac{3}{10}

Example 41

hard

Solve for

x

\frac{3}{4} - x = \frac{2}{5}

Example 42

hard

Subtract

4\frac{1}{6} - 1\frac{3}{4}

Example 43

hard

A water tank is

\frac{5}{8}

full. After use, it drops by

\frac{1}{3}

of a tank. How full is it now?

Example 44

challenge

Compute

\frac{1}{2} - \frac{1}{3} + \frac{1}{4} - \frac{1}{5}

Example 45

challenge

\frac{a}{6} - \frac{1}{8} = \frac{5}{24}

, find the whole number

a

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Related Concepts

Subtracting Fractions with Like Denominators Equivalent Fractions Least Common Multiple Adding Fractions with Unlike Denominators

Background Knowledge

These ideas may be useful before you work through the harder examples.

subtracting fractions like denominatorsequivalent fractionsleast common multiple