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Glacius
FoundationsConcept reference

Adding fractions

A fraction sum is found by rewriting the addends with a common denominator and adding their numerators.

1 min read1 figureSources & further reading
On this page 8 sections
  1. Overview
  2. Adding fractions combines quantities measured in the same-sized parts
  3. Check your understanding
  4. Check your understanding
  5. Key takeaway
  6. Further questions
  7. Sources & further reading
  8. Concept connections

01Adding fractions combines quantities measured in the same-sized parts#

Adding fractions combines quantities measured in the same-sized parts. Two quarters plus one quarter is three quarters. The part size stays a quarter.

Two quarters and one more quarter occupy three of the four equal parts of a whole.Two quarters and one more quarter occupy three of the four equal parts of a whole.
Figure 1Two quarters and one more quarter occupy three of the four equal parts of a whole.
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When denominators differ, rename the fractions using a common denominator. For 12+14\dfrac{1}{2}+\dfrac{1}{4}, one half equals two quarters.

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

Any shared denominator works. For thirds and sixths, use sixths: 13=26\dfrac{1}{3}=\dfrac{2}{6}. If none is obvious, multiplying the denominators always gives a shared one. Add the renamed numerators and keep that denominator.

Check your reasoning

Calculate 13+16\dfrac{1}{3}+\dfrac{1}{6}.

  1. A2/92/9
  2. B1/21/2
  3. C1/61/6
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1/21/2

Use sixths: 2/6+1/6=1/22/6+1/6=1/2.

02Check your understanding#

Check your reasoning

Complete: 25+15=?5\dfrac{2}{5}+\dfrac{1}{5}=\dfrac{?}{5}.

Show answer and explanation
3

Both quantities count fifths, so add 2 and 1 and keep the denominator 5.

03Check your understanding#

Check your reasoning

Two pieces measure 14\dfrac{1}{4} m and 12\dfrac{1}{2} m. Total length?

  1. A2/62/6 metre
  2. B1/81/8 metre
  3. C3/43/4 metre
Show answer and explanation
3/43/4 metre

One half is 2/42/4. Add to get 3/43/4 m.

Key takeaway

Use a common denominator, then add the numerators.

  • Add 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. “Adding fractions.” Math behind ML. /learn/f-fraction-add