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Glacius
FoundationsConcept reference

Multiplying fractions

The product of two fractions has the product of their numerators over the product of their denominators.

1 min read1 figureSources & further reading
On this page 8 sections
  1. Overview
  2. Multiplying by a fraction takes that fraction of an amount
  3. Check your understanding
  4. Check your understanding
  5. Key takeaway
  6. Further questions
  7. Sources & further reading
  8. Concept connections

01Multiplying by a fraction takes that fraction of an amount#

Multiplying by a fraction takes that fraction of an amount. Half of 34\dfrac{3}{4} is 38\dfrac{3}{8}: halve each selected quarter to get three selected eighths.

Half of three quarters is three eighths; each selected quarter is halved.Half of three quarters is three eighths; each selected quarter is halved.
Figure 1Half of three quarters is three eighths; each selected quarter is halved.
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Multiply numerator by numerator and denominator by denominator. A common denominator is unnecessary.

12×34=1×32×4=38\frac{1}{2}\times\frac{3}{4}=\frac{1\times3}{2\times4}=\frac{3}{8}

The usual sign rule still applies. In −23×34-\dfrac{2}{3}\times\dfrac{3}{4}, multiply the numerators to get −6-6 and the denominators to get 1212. The result is −12-\dfrac{1}{2}. A zero numerator makes the product zero.

Check your reasoning

Calculate 23×14\dfrac{2}{3}\times\dfrac{1}{4}.

  1. A37\dfrac{3}{7}
  2. B27\dfrac{2}{7}
  3. C16\dfrac{1}{6}
Show answer and explanation
16\dfrac{1}{6}

Multiply to get 2/12, which is 1/6.

02Check your understanding#

Check your reasoning

Complete: 35×27=?35\dfrac{3}{5}\times\dfrac{2}{7}=\dfrac{?}{35}.

Show answer and explanation
6

The numerator is 3×2=63\times2=6.

03Check your understanding#

Check your reasoning

A tray holds 23\dfrac{2}{3} kg. Use 34\dfrac{3}{4} of it. How much?

  1. A1/21/2 kilogram
  2. B5/75/7 kilogram
  3. C8/98/9 kilogram
Show answer and explanation
1/21/2 kilogram

Multiply: (2×3)/(3×4)=1/2(2\times3)/(3\times4)=1/2 kg.

Key takeaway

Multiply the numerators together and the denominators together.

  • Multiply two fractions

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. “Multiplying fractions.” Math behind ML. /learn/f-fraction-multiply