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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
Find the product: 3/4 × 2/5. Write your answer in simplest form.
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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

Write the multiplication as one fraction

\[3/4~×~2/5~=~(3~×~2)/(4~×~5)\]

When you multiply fractions, you multiply the numerators together and the denominators together.

02

Multiply across

\[(3~×~2)/(4~×~5)~=~6/20\]

The numerators give 6, and the denominators give 20, so the product is 6/20.

03

Simplify the fraction

\[6/20~=~3/10\]

Both 6 and 20 are divisible by 2. Dividing top and bottom by the same number keeps the value the same but writes it in simplest form.

04

State the final product

\[3/4~×~2/5~=~3/10\]

So the product of 3/4 and 2/5 is 3/10 in simplest form.

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Another way

  1. You can simplify before multiplying: in (3 × 2)/(4 × 5), the 2 and 4 share a factor of 2, so 2/4 becomes 1/2. Then (3 × 1)/(2 × 5) = 3/10.

!

Common mistake

A common mistake is adding across and getting 5/9. In 3/4 × 2/5, you do not add numerators and denominators; you multiply them to get 6/20, then simplify to 3/10.