Subtracting Fractions with Like 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 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 58\frac{5}{8} of a cake and eat 28\frac{2}{8}. Same size slices, so subtract the count: 38\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 710−310\frac{7}{10} - \frac{3}{10}.

Answer

25\frac{2}{5}

First step

1
Denominators are equal (1010), so subtract only the numerators: 7−3=47 - 3 = 4.

Full solution

  1. 2
    Result: 410\frac{4}{10}.
  2. 3
    Simplify: gcd⁡(4,10)=2\gcd(4, 10) = 2, so 410=25\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 912\frac{9}{12} of a metre long. A piece of 512\frac{5}{12} of a metre is cut off. What length remains?

Example 3

medium
A jug holds 11 L. Maya drinks 38\frac{3}{8} L. Then her friend drinks 18\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 1115−415\frac{11}{15} - \frac{4}{15}.

Example 2

hard
You need 138\frac{13}{8} cups of milk for a recipe, but only have 58\frac{5}{8} of a cup. How much more milk do you need? Express your answer as a mixed number.

Example 3

easy
Subtract 58−28\frac{5}{8}-\frac{2}{8}.

Example 4

easy
Subtract 79−49\frac{7}{9}-\frac{4}{9}.

Example 5

easy
Subtract 45−15\frac{4}{5}-\frac{1}{5}.

Example 6

easy
Subtract 67−27\frac{6}{7}-\frac{2}{7}.

Example 7

easy
Subtract 910−310\frac{9}{10}-\frac{3}{10}.

Example 8

easy
Subtract 1112−512\frac{11}{12}-\frac{5}{12}.

Example 9

easy
Subtract 34−14\frac{3}{4}-\frac{1}{4}.

Example 10

easy
Subtract 811−311\frac{8}{11}-\frac{3}{11}.

Example 11

medium
Subtract 1−371-\frac{3}{7}.

Example 12

medium
Subtract 136−56\frac{13}{6}-\frac{5}{6} and write as a mixed number.

Example 13

medium
1013−?13=413\frac{10}{13}-\frac{?}{13}=\frac{4}{13}. Find the missing numerator.

Example 14

medium
Subtract 315−1453\frac{1}{5}-1\frac{4}{5}.

Example 15

medium
Subtract 1415−415\frac{14}{15}-\frac{4}{15} and simplify.

Example 16

medium
A jug holds 78\frac{7}{8} L. You pour out 38\frac{3}{8} L. How much remains?

Example 17

medium
Subtract 2−562-\frac{5}{6}.

Example 18

medium
Subtract 1720−720\frac{17}{20}-\frac{7}{20} and simplify.

Example 19

medium
Subtract 416−2564\frac{1}{6}-2\frac{5}{6}.

Example 20

challenge
A relay is 1516\frac{15}{16} km. The first runner covers 616\frac{6}{16} km and the second 516\frac{5}{16} km. How far must the third runner go?

Example 21

challenge
For which whole number kk does k9−29\frac{k}{9}-\frac{2}{9} simplify to 13\frac{1}{3}?

Example 22

challenge
Half a pizza (48\frac{4}{8}) is left. Sam eats 38\frac{3}{8} of the whole pizza. Express what is left of the whole, and of the original half.

Example 23

easy
Subtract 613−213\frac{6}{13} - \frac{2}{13}.

Example 24

easy
Subtract 1017−317\frac{10}{17} - \frac{3}{17}.

Example 25

easy
Subtract 89−29\frac{8}{9} - \frac{2}{9}.

Example 26

easy
Maya has 710\frac{7}{10} of a chocolate bar. She gives 210\frac{2}{10} to her brother. How much does she have left?

Example 27

easy
Compute 1220−420\frac{12}{20} - \frac{4}{20} and simplify.

Example 28

easy
Subtract 1114−414\frac{11}{14} - \frac{4}{14}.

Example 29

medium
Subtract 1−591 - \frac{5}{9}.

Example 30

medium
Find the missing numerator: 1720−?20=12\frac{17}{20} - \frac{?}{20} = \frac{1}{2}.

Example 31

medium
Subtract 527−2475\frac{2}{7} - 2\frac{4}{7}.

Example 32

medium
Subtract 198−78\frac{19}{8} - \frac{7}{8} and write as a mixed number.

Example 33

medium
A pitcher holds 1112\frac{11}{12} L of juice. Maya pours out 512\frac{5}{12} L. How much remains?

Example 34

medium
Subtract 1518−318\frac{15}{18} - \frac{3}{18} and simplify.

Example 35

medium
Find 1315−415−215\frac{13}{15} - \frac{4}{15} - \frac{2}{15}.

Example 36

medium
Subtract 4310−17104\frac{3}{10} - 1\frac{7}{10}.

Example 37

medium
Sara reads 712\frac{7}{12} of a book on Monday and 212\frac{2}{12} more on Tuesday. How much of the book is left?

Example 38

medium
?12−512=14\frac{?}{12} - \frac{5}{12} = \frac{1}{4}. Find the missing numerator.

Example 39

hard
Subtract 219−892\frac{1}{9} - \frac{8}{9} and write as a mixed number.

Example 40

hard
What value of kk makes k12−312=23\frac{k}{12} - \frac{3}{12} = \frac{2}{3}?

Example 41

hard
Compute 2314−914\frac{23}{14} - \frac{9}{14} and express as a mixed number.

Example 42

hard
Three friends share a ribbon 1920\frac{19}{20} m long. The first cuts 720\frac{7}{20} m and the second cuts 620\frac{6}{20} m. How much is left for the third?

Example 43

challenge
Subtract 5211−2711−13115\frac{2}{11} - 2\frac{7}{11} - 1\frac{3}{11}.

Example 44

challenge
For which whole numbers nn between 11 and 2020 does n20−420\frac{n}{20} - \frac{4}{20} simplify to 14\frac{1}{4}?
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Background Knowledge

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

fractionssubtraction