To multiply fractions, multiply the tops together and the bottoms together, then simplify. To divide, keep the first fraction, change the sign to multiply, and flip the second fraction over.
The steps, on one like it
What is 3⁄5 divided by 2⁄7? Give the answer in simplest form.
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Keep the first fraction exactly as it is: 3/5.
Only the fraction you are dividing by gets flipped.
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Flip the second fraction so 2⁄7 becomes 7/2.
7⁄2 is the reciprocal, and dividing by a number equals multiplying by its reciprocal.
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Change the divide sign to a multiply sign: 3⁄5 × 7/2.
Flipping and multiplying give the same result as dividing.
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Multiply the tops: 3 × 7 = 21. Multiply the bottoms: 5 × 2 = 10.
Fractions multiply straight across, top with top and bottom with bottom.
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Check that 21 and 10 share no factor, then write 21/10.
Nothing cancels, so the fraction is already in simplest form.
Answer: 21⁄10
The mistake people often make
Flipping the wrong fraction, so 3⁄5 divided by 2⁄7 becomes 5⁄3 × 2/7. Only the second fraction turns over.
Say it as you write it: keep, change, flip. The first fraction is kept exactly as given.
Another way to see it
Ask how many lots of 2⁄7 fit inside 3/5. Draw a bar and shade 3⁄5 of it. Now measure that shaded part in chunks of 2/7. Two whole chunks fit and only a sliver of a third one. The answer 21⁄10 is just over 2, which is exactly what the bar shows.
Words to know
- reciprocal
- A fraction turned upside down, so 2⁄7 becomes 7/2.