Subtracting Fractions with Like Denominators Examples

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Subtracting Fractions with Like 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 that share the same denominator by subtracting the numerators and keeping the denominator.

You have $\frac{5}{8}$ of a cake and eat $\frac{2}{8}$ . Same size slices, so subtract the count: $\frac{3}{8}$ remains.

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: The denominator stays because the size of each piece does not change.

Common stuck point: The procedure for subtracting fractions with like denominators is the easy part; the trap is subtracting the denominators. Asking "Are both amounts measured in the same fractional unit?" first is what keeps a correct-looking calculation from being attached to the wrong concept.

Sense of Study hint: Ask: Are both amounts measured in the same fractional unit?

Worked Examples

Example 1

easy

Subtract

\frac{7}{10} - \frac{3}{10}

The full bar is 7/10. Remove the 3/10 piece — what remains?

Answer

\frac{2}{5}

First step

Denominators are equal (

10

), so subtract only the numerators:

7 - 3 = 4

Full solution

2
Result: $\frac{4}{10}$ .
3
Simplify: $\gcd(4, 10) = 2$ , so $\frac{4}{10} = \frac{2}{5}$ .

Subtracting like-denominator fractions mirrors adding them: operate only on the numerators and keep the denominator fixed. Always check whether the result simplifies.

Example 2

medium

A board is

\frac{9}{12}

of a metre long. A piece of

\frac{5}{12}

of a metre is cut off. What length remains?

Example 3

medium

A jug holds

1

L. Maya drinks

\frac{3}{8}

L. Then her friend drinks

\frac{1}{8}

L. How much is left in the jug?

Practice Problems

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

Example 1

easy

Compute

\frac{11}{15} - \frac{4}{15}

The full bar is 11/15. Remove 4/15 — what fraction remains?

Example 2

hard

You need

\frac{13}{8}

cups of milk for a recipe, but only have

\frac{5}{8}

of a cup. How much more milk do you need? Express your answer as a mixed number.

Example 3

easy

Subtract

\frac{5}{8}-\frac{2}{8}

The full bar is 5/8. Remove the 2/8 piece — what fraction remains?

Example 4

easy

Subtract

\frac{7}{9}-\frac{4}{9}

7/9 minus 4/9: the result 3/9 simplifies to 1/3.

Example 5

easy

Subtract

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

The full bar is 4/5. Remove 1/5 — what fraction remains?

Example 6

easy

Subtract

\frac{6}{7}-\frac{2}{7}

The full bar is 6/7. Remove 2/7 — what fraction remains?

Example 7

easy

Subtract

\frac{9}{10}-\frac{3}{10}

9/10 minus 3/10: the result 6/10 simplifies to 3/5.

Example 8

easy

Subtract

\frac{11}{12}-\frac{5}{12}

11/12 minus 5/12: the result 6/12 simplifies to 1/2.

Example 9

easy

Subtract

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

3/4 minus 1/4: the result 2/4 simplifies to 1/2.

Example 10

easy

Subtract

\frac{8}{11}-\frac{3}{11}

The full bar is 8/11. Remove 3/11 — what fraction remains?

Example 11

medium

Subtract

1-\frac{3}{7}

Example 12

medium

Subtract

\frac{13}{6}-\frac{5}{6}

and write as a mixed number.

Example 13

medium

\frac{10}{13}-\frac{?}{13}=\frac{4}{13}

. Find the missing numerator.

Example 14

medium

Subtract

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

Example 15

medium

Subtract

\frac{14}{15}-\frac{4}{15}

and simplify.

Example 16

medium

A jug holds

\frac{7}{8}

L. You pour out

\frac{3}{8}

L. How much remains?

The jug holds 7/8 L. After pouring out 3/8 L, how much remains? (4/8

Example 17

medium

Subtract

2-\frac{5}{6}

Example 18

medium

Subtract

\frac{17}{20}-\frac{7}{20}

and simplify.

Example 19

medium

Subtract

4\frac{1}{6}-2\frac{5}{6}

Example 20

challenge

A relay is

\frac{15}{16}

km. The first runner covers

\frac{6}{16}

km and the second

\frac{5}{16}

km. How far must the third runner go?

Example 21

challenge

For which whole number

k

does

\frac{k}{9}-\frac{2}{9}

simplify to

\frac{1}{3}

Example 22

challenge

Half a pizza (

\frac{4}{8}

) is left. Sam eats

\frac{3}{8}

of the whole pizza. Express what is left of the whole, and of the original half.

Example 23

easy

Subtract

\frac{6}{13} - \frac{2}{13}

The full bar is 6/13. Remove 2/13 — what fraction remains?

Example 24

easy

Subtract

\frac{10}{17} - \frac{3}{17}

The full bar is 10/17. Remove 3/17 — what fraction remains?

Example 25

easy

Subtract

\frac{8}{9} - \frac{2}{9}

8/9 minus 2/9: the result 6/9 simplifies to 2/3.

Example 26

easy

Maya has

\frac{7}{10}

of a chocolate bar. She gives

\frac{2}{10}

to her brother. How much does she have left?

Maya has 7/10 of a chocolate bar. She gives 2/10 to her brother — how much does she have left? (5/10

Example 27

easy

Compute

\frac{12}{20} - \frac{4}{20}

and simplify.

Example 28

easy

Subtract

\frac{11}{14} - \frac{4}{14}

11/14 minus 4/14: the result 7/14 simplifies to 1/2.

Example 29

medium

Subtract

1 - \frac{5}{9}

Example 30

medium

Find the missing numerator:

\frac{17}{20} - \frac{?}{20} = \frac{1}{2}

Example 31

medium

Subtract

5\frac{2}{7} - 2\frac{4}{7}

Example 32

medium

Subtract

\frac{19}{8} - \frac{7}{8}

and write as a mixed number.

Example 33

medium

A pitcher holds

\frac{11}{12}

L of juice. Maya pours out

\frac{5}{12}

L. How much remains?

The pitcher holds 11/12 L. After pouring out 5/12 L, how much remains? (6/12

Example 34

medium

Subtract

\frac{15}{18} - \frac{3}{18}

and simplify.

Example 35

medium

Find

\frac{13}{15} - \frac{4}{15} - \frac{2}{15}

Example 36

medium

Subtract

4\frac{3}{10} - 1\frac{7}{10}

Example 37

medium

Sara reads

\frac{7}{12}

of a book on Monday and

\frac{2}{12}

more on Tuesday. How much of the book is left?

Example 38

medium

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

. Find the missing numerator.

Example 39

hard

Subtract

2\frac{1}{9} - \frac{8}{9}

and write as a mixed number.

Example 40

hard

What value of

k

makes

\frac{k}{12} - \frac{3}{12} = \frac{2}{3}

Example 41

hard

Compute

\frac{23}{14} - \frac{9}{14}

and express as a mixed number.

Example 42

hard

Three friends share a ribbon

\frac{19}{20}

m long. The first cuts

\frac{7}{20}

m and the second cuts

\frac{6}{20}

m. How much is left for the third?

Example 43

challenge

Subtract

5\frac{2}{11} - 2\frac{7}{11} - 1\frac{3}{11}

Example 44

challenge

For which whole numbers

n

between

1

and

20

does

\frac{n}{20} - \frac{4}{20}

simplify to

\frac{1}{4}

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Related Concepts

Fractions Subtraction Subtracting Fractions with Unlike Denominators Adding Fractions with Like Denominators

Background Knowledge

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

fractionssubtraction