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GRADE 5 / FRACTIONS

Multiplying fractions worksheets

Choose area models, proper fractions, whole numbers or mixed-number products. Each set has a student sheet and a worked answer key.

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Area models

4 questions · US Letter · one page per download

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Area models · US Letter · Edition 0SDVZ5J. First problem: 2/3 × 3/4.

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Area models. Student sheet with 4 problems. First problem: 2/3 × 3/4.
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Shade rows and columns of a unit square. Count the overlap and simplify.

  1. 2/3 × 3/4
  2. 5/6 × 1/4
  3. 5/6 × 2/3
  4. 1/3 × 2/5
Area models. Worked key with 4 problems. First problem: 2/3 × 3/4.
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Shade rows and columns of a unit square. Count the overlap and simplify.

  1. 2/3 × 3/4 — 6 of 12 equal cells overlap. Raw product 6/12. Divide both by 6 to get 1/2.
  2. 5/6 × 1/4 — 5 of 24 equal cells overlap. Raw product 5/24. This is already in simplest form.
  3. 5/6 × 2/3 — 10 of 18 equal cells overlap. Raw product 10/18. Divide both by 2 to get 5/9.
  4. 1/3 × 2/5 — 2 of 15 equal cells overlap. Raw product 2/15. This is already in simplest form.

CHECK THE SAME PROBLEMS

2/3 × 3/4

Question 1 of 4

Unmarked grid on a unit square of 3 rows and 4 columns

SEVEN STARTING POINTS

Choose what to practise

Area models

Shade rows and columns of a unit square. Count the overlap and simplify.

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Area models student pageLook inside this original setStudent sheet and worked key
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Area models · US Letter · Edition 0SDVZ5J. First problem: 2/3 × 3/4.

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Area models. Student sheet with 4 problems. First problem: 2/3 × 3/4.
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Shade rows and columns of a unit square. Count the overlap and simplify.

  1. 2/3 × 3/4
  2. 5/6 × 1/4
  3. 5/6 × 2/3
  4. 1/3 × 2/5
Area models. Worked key with 4 problems. First problem: 2/3 × 3/4.
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Shade rows and columns of a unit square. Count the overlap and simplify.

  1. 2/3 × 3/4 — 6 of 12 equal cells overlap. Raw product 6/12. Divide both by 6 to get 1/2.
  2. 5/6 × 1/4 — 5 of 24 equal cells overlap. Raw product 5/24. This is already in simplest form.
  3. 5/6 × 2/3 — 10 of 18 equal cells overlap. Raw product 10/18. Divide both by 2 to get 5/9.
  4. 1/3 × 2/5 — 2 of 15 equal cells overlap. Raw product 2/15. This is already in simplest form.
Original PDFs · Letter and A4

US Letter · Student / Key / Both

A4 · Student / Key / Both

Multiply proper fractions

Start with the four model problems, then work with denominators up to 12.

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Multiply proper fractions · US Letter · Edition 0N8C10D. First problem: 2/3 × 3/4.

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Multiply proper fractions. Student sheet with 8 problems. First problem: 2/3 × 3/4.
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Start with the four model problems, then work with denominators up to 12.

  1. 2/3 × 3/4
  2. 5/6 × 1/4
  3. 5/6 × 2/3
  4. 1/3 × 2/5
  5. 3/4 × 4/11
  6. 9/10 × 1/10
  7. 4/9 × 11/12
  8. 2/5 × 2/11
Multiply proper fractions. Worked key with 8 problems. First problem: 2/3 × 3/4.
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Start with the four model problems, then work with denominators up to 12.

  1. 2/3 × 3/4 — Raw product 6/12. Divide both by 6 to get 1/2.
  2. 5/6 × 1/4 — Raw product 5/24. This is already in simplest form.
  3. 5/6 × 2/3 — Raw product 10/18. Divide both by 2 to get 5/9.
  4. 1/3 × 2/5 — Raw product 2/15. This is already in simplest form.
  5. 3/4 × 4/11 — Raw product 12/44. Divide both by 4 to get 3/11.
  6. 9/10 × 1/10 — Raw product 9/100. This is already in simplest form.
  7. 4/9 × 11/12 — Raw product 44/108. Divide both by 4 to get 11/27.
  8. 2/5 × 2/11 — Raw product 4/55. This is already in simplest form.
Original PDFs · Letter and A4

US Letter · Student / Key / Both

A4 · Student / Key / Both

Products that need simplifying

Every product can be reduced. Half the problems also let you simplify a factor first.

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Products that need simplifying · US Letter · Edition 18S6XVF. First problem: 2/3 × 3/4.

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Products that need simplifying. Student sheet with 8 problems. First problem: 2/3 × 3/4.
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Every product can be reduced. Half the problems also let you simplify a factor first.

  1. 2/3 × 3/4
  2. 9/12 × 7/12
  3. 1/12 × 4/5
  4. 4/6 × 5/6
  5. 3/4 × 6/11
  6. 9/10 × 2/8
  7. 5/9 × 3/4
  8. 3/6 × 2/8
Products that need simplifying. Worked key with 8 problems. First problem: 2/3 × 3/4.
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Every product can be reduced. Half the problems also let you simplify a factor first.

  1. 2/3 × 3/4 — Raw product 6/12. Divide both by 6 to get 1/2.
  2. 9/12 × 7/12 — Raw product 63/144. Divide both by 9 to get 7/16.
  3. 1/12 × 4/5 — Raw product 4/60. Divide both by 4 to get 1/15.
  4. 4/6 × 5/6 — Raw product 20/36. Divide both by 4 to get 5/9.
  5. 3/4 × 6/11 — Raw product 18/44. Divide both by 2 to get 9/22.
  6. 9/10 × 2/8 — Raw product 18/80. Divide both by 2 to get 9/40.
  7. 5/9 × 3/4 — Raw product 15/36. Divide both by 3 to get 5/12.
  8. 3/6 × 2/8 — Raw product 6/48. Divide both by 6 to get 1/8.
Original PDFs · Letter and A4

US Letter · Student / Key / Both

A4 · Student / Key / Both

Fractions × whole numbers

Find a fraction of a whole number. Practise both integer and fractional answers.

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Fractions × whole numbers student pageLook inside this original setStudent sheet and worked key
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Fractions × whole numbers · US Letter · Edition 0OE1L3K. First problem: 2/3 × 6.

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Fractions × whole numbers. Student sheet with 8 problems. First problem: 2/3 × 6.
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Find a fraction of a whole number. Practise both integer and fractional answers.

  1. 2/3 × 6
  2. 7/12 × 5
  3. 8/11 × 11
  4. 1/6 × 8
  5. 1/3 × 3
  6. 9/10 × 11
  7. 5/7 × 7
  8. 4/5 × 8
Fractions × whole numbers. Worked key with 8 problems. First problem: 2/3 × 6.
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Find a fraction of a whole number. Practise both integer and fractional answers.

  1. 2/3 × 6 — Raw product 12/3. Divide both by 3 to get 4.
  2. 7/12 × 5 — Raw product 35/12. This is already in simplest form.
  3. 8/11 × 11 — Raw product 88/11. Divide both by 11 to get 8.
  4. 1/6 × 8 — Raw product 8/6. Divide both by 2 to get 4/3.
  5. 1/3 × 3 — Raw product 3/3. Divide both by 3 to get 1.
  6. 9/10 × 11 — Raw product 99/10. This is already in simplest form.
  7. 5/7 × 7 — Raw product 35/7. Divide both by 7 to get 5.
  8. 4/5 × 8 — Raw product 32/5. This is already in simplest form.
Original PDFs · Letter and A4

US Letter · Student / Key / Both

A4 · Student / Key / Both

Mixed number × proper fraction

Rewrite one mixed factor, multiply and simplify. Check whether a fraction of the starting amount makes sense.

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Mixed number × proper fraction · US Letter · Edition 03XVH5U. First problem: 2 1/2 × 2/3.

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Mixed number × proper fraction. Student sheet with 6 problems. First problem: 2 1/2 × 2/3.
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Rewrite one mixed factor, multiply and simplify. Check whether a fraction of the starting amount makes sense.

  1. 2 1/2 × 2/3
  2. 2 5/6 × 1/6
  3. 1 1/2 × 2/3
  4. 3 1/3 × 5/6
  5. 1 1/3 × 1/3
  6. 2 3/5 × 1/2
Mixed number × proper fraction. Worked key with 6 problems. First problem: 2 1/2 × 2/3.
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Rewrite one mixed factor, multiply and simplify. Check whether a fraction of the starting amount makes sense.

  1. 2 1/2 × 2/3 — Rewrite as 5/2 × 2/3. Raw product 10/6. Simplest form 5/3. Mixed form 1 2/3.
  2. 2 5/6 × 1/6 — Rewrite as 17/6 × 1/6. Raw product 17/36. Simplest form 17/36.
  3. 1 1/2 × 2/3 — Rewrite as 3/2 × 2/3. Raw product 6/6. Simplest form 1.
  4. 3 1/3 × 5/6 — Rewrite as 10/3 × 5/6. Raw product 50/18. Simplest form 25/9. Mixed form 2 7/9.
  5. 1 1/3 × 1/3 — Rewrite as 4/3 × 1/3. Raw product 4/9. Simplest form 4/9.
  6. 2 3/5 × 1/2 — Rewrite as 13/5 × 1/2. Raw product 13/10. Simplest form 13/10. Mixed form 1 3/10.
Original PDFs · Letter and A4

US Letter · Student / Key / Both

A4 · Student / Key / Both

Multiply two mixed numbers

Rewrite both factors as improper fractions. Record the raw product, then give its simplest whole or mixed value.

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Multiply two mixed numbers · US Letter · Edition 1LE3YI8. First problem: 1 1/2 × 2 1/3.

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Multiply two mixed numbers. Student sheet with 6 problems. First problem: 1 1/2 × 2 1/3.
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Rewrite both factors as improper fractions. Record the raw product, then give its simplest whole or mixed value.

  1. 1 1/2 × 2 1/3
  2. 2 5/6 × 1 4/5
  3. 1 1/2 × 1 1/3
  4. 3 1/3 × 1 5/6
  5. 1 1/3 × 2 1/3
  6. 2 3/5 × 3 1/2
Multiply two mixed numbers. Worked key with 6 problems. First problem: 1 1/2 × 2 1/3.
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Rewrite both factors as improper fractions. Record the raw product, then give its simplest whole or mixed value.

  1. 1 1/2 × 2 1/3 — Rewrite as 3/2 × 7/3. Raw product 21/6. Simplest form 7/2. Mixed form 3 1/2.
  2. 2 5/6 × 1 4/5 — Rewrite as 17/6 × 9/5. Raw product 153/30. Simplest form 51/10. Mixed form 5 1/10.
  3. 1 1/2 × 1 1/3 — Rewrite as 3/2 × 4/3. Raw product 12/6. Simplest form 2.
  4. 3 1/3 × 1 5/6 — Rewrite as 10/3 × 11/6. Raw product 110/18. Simplest form 55/9. Mixed form 6 1/9.
  5. 1 1/3 × 2 1/3 — Rewrite as 4/3 × 7/3. Raw product 28/9. Simplest form 28/9. Mixed form 3 1/9.
  6. 2 3/5 × 3 1/2 — Rewrite as 13/5 × 7/2. Raw product 91/10. Simplest form 91/10. Mixed form 9 1/10.
Original PDFs · Letter and A4

US Letter · Student / Key / Both

A4 · Student / Key / Both

Four parts of a mixed-number product

Split both mixed factors into whole and fractional parts. Fill four partial products, then add. Uses the first four questions from the two-mixed-number set.

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Four parts of a mixed-number product student pageLook inside this original setStudent sheet and worked key
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Four parts of a mixed-number product · US Letter · Edition 1PKAU50. First problem: 1 1/2 × 2 1/3.

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Four parts of a mixed-number product. Student sheet with 4 problems. First problem: 1 1/2 × 2 1/3.
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Split both mixed factors into whole and fractional parts. Fill four partial products, then add. Uses the first four questions from the two-mixed-number set.

  1. 1 1/2 × 2 1/3
  2. 2 5/6 × 1 4/5
  3. 1 1/2 × 1 1/3
  4. 3 1/3 × 1 5/6
Four parts of a mixed-number product. Worked key with 4 problems. First problem: 1 1/2 × 2 1/3.
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Split both mixed factors into whole and fractional parts. Fill four partial products, then add. Uses the first four questions from the two-mixed-number set.

  1. 1 1/2 × 2 1/3 — 1 × 2 = 2. 1 × 1/3 = 1/3. 1/2 × 2 = 1. 1/2 × 1/3 = 1/6. Sum: 2 + 1/3 + 1 + 1/6 = 3 1/2.
  2. 2 5/6 × 1 4/5 — 2 × 1 = 2. 2 × 4/5 = 8/5. 5/6 × 1 = 5/6. 5/6 × 4/5 = 2/3. Sum: 2 + 8/5 + 5/6 + 2/3 = 5 1/10.
  3. 1 1/2 × 1 1/3 — 1 × 1 = 1. 1 × 1/3 = 1/3. 1/2 × 1 = 1/2. 1/2 × 1/3 = 1/6. Sum: 1 + 1/3 + 1/2 + 1/6 = 2.
  4. 3 1/3 × 1 5/6 — 3 × 1 = 3. 3 × 5/6 = 5/2. 1/3 × 1 = 1/3. 1/3 × 5/6 = 5/18. Sum: 3 + 5/2 + 1/3 + 5/18 = 6 1/9.
Original PDFs · Letter and A4

US Letter · Student / Key / Both

A4 · Student / Key / Both

MIXED NUMBERS

Which pieces belong in a mixed-number product?

For 2 1/2 × 2/3, write 2 1/2 as 5/2. Multiply by 2/3 to get 10/6, or 1 2/3. The result is less than 2 1/2 because the multiplier is less than one. Try a mixed number times a proper fraction →

For 1 1/2 × 2 1/3, the single fractions are 3/2 and 7/3. Their product is 21/6 = 7/2 = 3 1/2. Splitting the same sides gives 2 + 1/3 + 1 + 1/6 = 3 1/2. If a paper shows 2 1/6, ask which two areas the learner added. The whole-by-fraction and fraction-by-whole pieces contribute another 1/3 and 1.

Print two mixed factors → · Print the same first four as partial-product boxes →

AT THE MARKING TABLE

Did the product change, or only its name?

For 2/3 × 3/4, split one square into 3 equal rows and 4 equal columns. Mark two rows and three columns. A horizontal dash marks a row and a vertical dash marks a column. Cells with both marks form the overlap, 6 of the 12 equal cells. Six cells have both marks and six do not, so the overlap covers exactly 1/2 of the square.

In the simplifying set, half the problems have a factor that can be reduced before multiplying. For example, 6/8 × 3/12 becomes 3/4 × 1/4, giving 3/16.

A child who writes 6/12 has found the right area. Ask for its simplest name. A child who writes 5/7 may have added both numerators and denominators. Ask them to count the overlap before repeating the calculation.

The area and proper-fraction sets share their first four questions when made with the same edition. The whole-number set alternates products that are whole numbers and products that have a fractional part. An improper fraction or a mixed number can describe the same answer.

This lesson practises selected fifth-grade fraction multiplication skills in Common Core 5.NF.B.4. To connect hundredths to area, use multiplying decimals worksheets. To practise the standard algorithm with whole numbers, use three-digit by two-digit multiplication.

To recover a printed edition, enter its F1 code in Find my worksheet.

Compare the sizes of products or print a mixed review in the fifth grade multiplication guide.

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