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Multiplying fractions worksheets

Twenty problems multiplying two proper fractions, such as 2/3 × 3/4, in three versions with answer keys, in simplest form.

Fraction operations: multiply fractions

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Multiply. Write the answer in simplest form.

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Sheet AFree at teach.peabody.kids

Fraction operations: multiply fractions

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Multiply. Write the answer in simplest form.

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Sheet BFree at teach.peabody.kids

Fraction operations: multiply fractions

NameDate

Multiply. Write the answer in simplest form.

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Sheet CFree at teach.peabody.kids

Answer key

Sheet A

Sheet B

Sheet C

Answer keyFree at teach.peabody.kids

Fraction operations: 20 problems a sheet, 3 versions that do not repeat each other where the numbers allow.

How to use it

  1. Look at the sheet: it is a real, printable sheet. Switch between Sheet A, B and C, or press New numbers (N) for a fresh set.
  2. Change how many problems, how many versions, and whether the key prints. Settings stay in this browser; Share copies a link that rebuilds the same sheets.
  3. Press Print sheet A and key, or Print all. The answer key prints on its own page, so you can keep it back.

Ideas for class

  • Draw an area model for the first problem: split a square into thirds one way and fourths the other, and shade two by three.
  • Ask whether the answer should be bigger or smaller than each factor before computing, and check afterwards.
  • Introduce cross-canceling only after students can simplify at the end, since it is a shortcut for that step.

Related

Questions

Why is the product smaller than both fractions?

Because each fraction is less than one whole. Taking a part of a part leaves less than either. Students find this strange at first, and an area model helps.

Does the sheet include whole numbers or mixed numbers?

Not this one. For a whole number times a fraction, choose Multiply a fraction by a whole number in the maker. For division of fractions, see Fraction operations there as well.

Are the answer keys checked?

Each answer is worked out by the code that wrote the problem, and our tests recompute every answer a second way and compare. Please still look over the key before you grade a class set.

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What this worksheet covers

Multiplying fractions needs no common denominator: multiply the tops, multiply the bottoms, and simplify. Each problem here has two proper fractions with denominators from 2 to 9, so the product is always smaller than either factor, which surprises students who expect multiplication to make things bigger. The key gives every answer in lowest terms, and some problems simplify a good deal.

Who it is for

Fifth grade. Common Core 5.NF.B.4 asks students to multiply a fraction by a fraction and to interpret the product as a part of a part, with area models. Students need to simplify fractions to be able to read the key.

Multiplying two proper fractions · grade 5

A worked example

2/3 × 3/4. Multiply the tops: 6. Multiply the bottoms: 12. The result is 6/12, which simplifies to 1/2. A shortcut is to cancel the 3 on the top and bottom before multiplying, which gives 2/4 and then 1/2.

Mistakes to watch for

  • Finding a common denominator first, as for addition, then multiplying across the wrong way. Remind students that multiplication does not need one.
  • Forgetting to simplify, so 6/12 is left as it stands. Ask whether any number divides both.

Make it your own

This sheet is one setting of the math worksheet generator. Open it there to change the skill, the range of numbers or the heading, or to mix several skills on one sheet.