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All courses Math Foundations · MF.RN.3 9 of 60
Multiply and divide fractions and mixed numbers and interpret the result in context.

Multiply two fractions

Problem
Calculate \(3/4~\times~2/5\) and give the product in simplest form.
Your answer
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Hint

Start by multiplying straight across: multiply the numerators together and the denominators together.

For fraction multiplication, you do not find common denominators or add across. Multiply top by top and bottom by bottom, then simplify.

Solution walkthrough

01

Use the multiplication rule

\[3/4~x~2/5~=~(3~x~2)/(4~x~5)\]

To multiply fractions, multiply the numerators together and the denominators together. No common denominator is needed.

02

Calculate the products

\[(3~x~2)/(4~x~5)~=~6/20\]

Three times 2 is 6, and 4 times 5 is 20.

03

Find a common factor

\[\mathrm{GCF}(6,~20)~=~2\]

The numerator and denominator of 6/20 share factor 2.

04

Simplify the product

\[6/20~=~(6~/~2)/(20~/~2)~=~3/10\]

Dividing both parts by 2 produces the equivalent fraction 3/10.

05

Check the size

\[3/10~<~2/5~\text{and}~3/10~<~3/4\]

Both original factors are positive and less than 1, so their product should be smaller than either factor; 3/10 satisfies that check.

06

State the simplified product

\[3/10\]

Three fourths times two fifths equals 3/10 in simplest form. This matches the correct choice.

+

Another way

  1. Cancel before multiplying: the factor 2 in the second numerator cancels with a factor 2 in denominator 4, leaving 3/(2 × 5) = 3/10.

!

Common mistake

Do not add across or search for a common denominator. Fraction multiplication uses numerator times numerator and denominator times denominator.

Solution walkthrough video