Subtracting Fractions with Unlike Denominators Examples in Math

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 34−13\frac{3}{4} - \frac{1}{3}, convert to twelfths: 912−412=512\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 34−16\frac{3}{4} - \frac{1}{6}.

Answer

712\frac{7}{12}

First step

1
Find the LCD of 44 and 66: LCD=12\text{LCD} = 12.

Full solution

  1. 2
    Convert: 34=912\frac{3}{4} = \frac{9}{12} and 16=212\frac{1}{6} = \frac{2}{12}.
  2. 3
    Subtract: 912−212=712\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 78\frac{7}{8} of a race, then stopped. If the race is 11 km long, what fraction of the race is left? If another runner has already finished 25\frac{2}{5} of the remaining distance, how much of the total race has that runner covered?

Example 3

hard
Subtract 78−23−16\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 56−14\frac{5}{6} - \frac{1}{4}.

Example 2

hard
Compute 1112−38−16\frac{11}{12} - \frac{3}{8} - \frac{1}{6}.

Example 3

easy
Subtract 12−14\frac{1}{2}-\frac{1}{4}.

Example 4

easy
Subtract 23−16\frac{2}{3}-\frac{1}{6}.

Example 5

easy
Subtract 34−12\frac{3}{4}-\frac{1}{2}.

Example 6

easy
Subtract 56−13\frac{5}{6}-\frac{1}{3}.

Example 7

easy
Subtract 710−15\frac{7}{10}-\frac{1}{5}.

Example 8

easy
Subtract 34−18\frac{3}{4}-\frac{1}{8}.

Example 9

easy
Subtract 23−12\frac{2}{3}-\frac{1}{2}.

Example 10

easy
Subtract 45−110\frac{4}{5}-\frac{1}{10}.

Example 11

medium
Subtract 34−23\frac{3}{4}-\frac{2}{3}.

Example 12

medium
Subtract 56−38\frac{5}{6}-\frac{3}{8}.

Example 13

medium
712−?4=13\frac{7}{12}-\frac{?}{4}=\frac{1}{3}. Find the missing numerator.

Example 14

medium
Subtract 214−232\frac{1}{4}-\frac{2}{3}.

Example 15

medium
Subtract 910−25\frac{9}{10}-\frac{2}{5}.

Example 16

medium
A board is 78\frac{7}{8} m. You cut off 13\frac{1}{3} m. How much remains?

Example 17

medium
Subtract 1−23−161-\frac{2}{3}-\frac{1}{6}.

Example 18

medium
Subtract 56−14\frac{5}{6}-\frac{1}{4}.

Example 19

medium
Subtract 1112−34\frac{11}{12}-\frac{3}{4} and simplify.

Example 20

challenge
Maria has 34\frac{3}{4} of a tank of gas. She uses 13\frac{1}{3} of a tank driving to work and 16\frac{1}{6} coming home. How much is left?

Example 21

challenge
Order from largest to smallest the differences 12−13\frac{1}{2}-\frac{1}{3}, 13−14\frac{1}{3}-\frac{1}{4}, 14−15\frac{1}{4}-\frac{1}{5}.

Example 22

challenge
Find xx if 56−x=14\frac{5}{6}-x=\frac{1}{4}.

Example 23

easy
Subtract 12−13\frac{1}{2} - \frac{1}{3}.

Example 24

easy
Subtract 35−110\frac{3}{5} - \frac{1}{10}.

Example 25

easy
Subtract 78−14\frac{7}{8} - \frac{1}{4}.

Example 26

easy
Subtract 46−13\frac{4}{6} - \frac{1}{3}.

Example 27

easy
Subtract 512−14\frac{5}{12} - \frac{1}{4}.

Example 28

easy
Compute 35−14\frac{3}{5} - \frac{1}{4}.

Example 29

easy
Subtract 58−16\frac{5}{8} - \frac{1}{6}.

Example 30

medium
Subtract 56−29\frac{5}{6} - \frac{2}{9}.

Example 31

medium
Subtract 710−14\frac{7}{10} - \frac{1}{4}.

Example 32

medium
Subtract 715−15\frac{7}{15} - \frac{1}{5}.

Example 33

medium
Subtract 38−112\frac{3}{8} - \frac{1}{12}.

Example 34

medium
A board is 45\frac{4}{5} m long. You cut 12\frac{1}{2} m off. How much is left?

Example 35

medium
Subtract 1−23−141 - \frac{2}{3} - \frac{1}{4}.

Example 36

medium
Subtract 312−1233\frac{1}{2} - 1\frac{2}{3}.

Example 37

medium
1112−?6=14\frac{11}{12} - \frac{?}{6} = \frac{1}{4}. Find the missing numerator.

Example 38

medium
Subtract 914−27\frac{9}{14} - \frac{2}{7}.

Example 39

medium
Subtract 79−16\frac{7}{9} - \frac{1}{6}.

Example 40

medium
Subtract 56−310\frac{5}{6} - \frac{3}{10}.

Example 41

hard
Solve for xx: 34−x=25\frac{3}{4} - x = \frac{2}{5}.

Example 42

hard
Subtract 416−1344\frac{1}{6} - 1\frac{3}{4}.

Example 43

hard
A water tank is 58\frac{5}{8} full. After use, it drops by 13\frac{1}{3} of a tank. How full is it now?

Example 44

challenge
Compute 12−13+14−15\frac{1}{2} - \frac{1}{3} + \frac{1}{4} - \frac{1}{5}.

Example 45

challenge
If a6−18=524\frac{a}{6} - \frac{1}{8} = \frac{5}{24}, find the whole number aa.
← Back to Subtracting Fractions with Unlike Denominators Formula Explained Practice Mode

Background Knowledge

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

subtracting fractions like denominatorsequivalent fractionsleast common multiple