Skip to content
Glacius
FoundationsConcept reference

Subtracting fractions

A fraction difference is found by rewriting both fractions with a common denominator and subtracting their numerators in order.

1 min read1 figureSources & further reading
On this page 8 sections
  1. Overview
  2. Subtracting fractions removes one quantity from another
  3. Check your understanding
  4. Check your understanding
  5. Key takeaway
  6. Further questions
  7. Sources & further reading
  8. Concept connections

01Subtracting fractions removes one quantity from another#

Subtracting fractions removes one quantity from another. Start with three quarters and remove two quarters. One quarter remains; the size of each part stays the same.

Removing two quarters from three quarters leaves one quarter of the same whole.Removing two quarters from three quarters leaves one quarter of the same whole.
Figure 1Removing two quarters from three quarters leaves one quarter of the same whole.
Link to this figure ↗Download SVGDownload PNG

Give both fractions a common denominator before subtracting. For 34−12\dfrac{3}{4}-\dfrac{1}{2}, rewrite the half as two quarters.

34−12=34−24=14\frac{3}{4}-\frac{1}{2}=\frac{3}{4}-\frac{2}{4}=\frac{1}{4}

Subtract in the stated order. If the second quantity is larger, the result is negative: 14−34=−24=−12\dfrac{1}{4}-\dfrac{3}{4}=-\dfrac{2}{4}=-\dfrac{1}{2}. Subtracting equal fractions gives zero.

Check your reasoning

Calculate 56−13\dfrac{5}{6}-\dfrac{1}{3}.

  1. A4/34/3
  2. B2/32/3
  3. C1/21/2
Show answer and explanation
1/21/2

Use sixths: 5/6−2/6=1/25/6-2/6=1/2.

02Check your understanding#

Check your reasoning

Complete: 15−35=?5\dfrac{1}{5}-\dfrac{3}{5}=\dfrac{?}{5}.

Show answer and explanation
-2

Subtract the numerators in order: 1−3=−21-3=-2.

03Check your understanding#

Check your reasoning

A ribbon is 78\dfrac{7}{8} m. Cut off 14\dfrac{1}{4} m. Length left?

  1. A5/85/8 metre
  2. B6/46/4 metre
  3. C3/83/8 metre
Show answer and explanation
5/85/8 metre

One quarter is 2/82/8. Subtract to get 5/85/8 m.

Key takeaway

Use a common denominator, then subtract the second numerator from the first.

  • Subtract two fractions using a common denominator

Further questions

Should I simplify the final fraction?
Equivalent forms have the same value. A simplified form is usually easier to read; the app accepts the equivalent choice shown.

Sources & further reading

  1. [1]

Reference this concept

Link to this page, a section, or an individual figure.

Glacius. “Subtracting fractions.” Math behind ML. /learn/f-fraction-subtract