Stewdent.eu
β–Ύ

Subtracting Fractions

How to subtract fractions with the same and different denominators, including mixed numbers.

Last updated: 29 December 2025

β˜…β˜†β˜†β˜†β˜† Level 1FractionsAlgebraLowest Common Denominatorsubtraction3 min read

Report an error

Same Denominator

When fractions have the same denominator, subtract the numerators and keep the denominator.

Same Denominator

acβˆ’bc=aβˆ’bc\frac{a}{c} - \frac{b}{c} = \frac{a - b}{c}

5/8 βˆ’ 3/8

58βˆ’38=5βˆ’38=28=14\dfrac{5}{8} - \dfrac{3}{8} = \dfrac{5-3}{8} = \dfrac{2}{8} = \dfrac{1}{4}

Different Denominators

Find the Lowest Common Denominator (LCD), convert both fractions, then subtract.

  1. 1

    Find the LCD

    Find the smallest number that both denominators divide into.

  2. 2

    Convert both fractions

    Multiply numerator and denominator to get the LCD.

  3. 3

    Subtract the numerators

    Keep the LCD as the denominator and simplify if possible.

3/4 βˆ’ 1/6

LCD of 4 and 6 = 12

34=912\dfrac{3}{4} = \dfrac{9}{12} and 16=212\dfrac{1}{6} = \dfrac{2}{12}

912βˆ’212=712\dfrac{9}{12} - \dfrac{2}{12} = \dfrac{7}{12}

Mixed Numbers

Subtract the whole number parts and fraction parts separately. If the fraction part would be negative, borrow 1 from the whole number.

3ΒΎ βˆ’ 1Β½

334βˆ’124=(3βˆ’1)+(34βˆ’24)=2143\dfrac{3}{4} - 1\dfrac{2}{4} = (3-1) + \left(\dfrac{3}{4} - \dfrac{2}{4}\right) = 2\dfrac{1}{4}

4ΒΌ βˆ’ 1ΒΎ (borrowing)

14βˆ’34\dfrac{1}{4} - \dfrac{3}{4} is negative, so borrow 1 from 4:

414β†’3544\dfrac{1}{4} \to 3\dfrac{5}{4}

354βˆ’134=(3βˆ’1)+(54βˆ’34)=224=2123\dfrac{5}{4} - 1\dfrac{3}{4} = (3-1) + \left(\dfrac{5}{4} - \dfrac{3}{4}\right) = 2\dfrac{2}{4} = 2\dfrac{1}{2}

Real-World Applications

Real world: remaining ingredients

A recipe needs 34\dfrac{3}{4} cup of milk. You have already poured 13\dfrac{1}{3} cup. How much more do you need?

LCD(4, 3) = 12: 34=912\dfrac{3}{4} = \dfrac{9}{12}, 13=412\dfrac{1}{3} = \dfrac{4}{12}.

912βˆ’412=512\dfrac{9}{12} - \dfrac{4}{12} = \dfrac{5}{12} cup still needed.

Real world: fuel used on a journey

A motorbike tank was 78\dfrac{7}{8} full before a drive. After the trip it was 38\dfrac{3}{8} full. How much fuel was used?

78βˆ’38=48=12\dfrac{7}{8} - \dfrac{3}{8} = \dfrac{4}{8} = \dfrac{1}{2} β€” exactly half a tank.

Real world: time left for homework

A student has 2342\dfrac{3}{4} hours of homework. After finishing maths (1121\dfrac{1}{2} hours), how much time is left?

234βˆ’112=234βˆ’124=1142\dfrac{3}{4} - 1\dfrac{1}{2} = 2\dfrac{3}{4} - 1\dfrac{2}{4} = 1\dfrac{1}{4} hours (75 minutes) remaining.

Tip

Where do you see this? Tracking remaining ingredients, monitoring fuel or battery charge, scheduling study blocks, and reading progress bars all involve subtracting fractions.

Practice Problems

Calculate: 7/9 βˆ’ 2/9

Show answer
(7 βˆ’ 2)/9 = 5/9.

Calculate: 5/6 βˆ’ 3/8

Show answer
LCD = 24. 20/24 βˆ’ 9/24 = 11/24.

Calculate: 5β…“ βˆ’ 2β…”

Show answer
Borrow: 4⁴⁄₃ βˆ’ 2β…” = 2β…”... Actually: 5β…“ = 5 2/6, 2β…” = 2 4/6. Borrow: 4 8/6 βˆ’ 2 4/6 = 2 4/6 = 2β…”.