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Fractions, decimals and percentsGrades 5–6

Multiplying fractions worksheets

The generator prints fraction multiplication problems such as 3/4 × 2/9 with a blank for the product. Turn on mixed numbers for harder sets, set the largest denominator and print with an answer key showing each product in simplest form.

By Paul Gunder. Free to print for home, classroom and office use; see how our printables are made.

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  • Answer key on its own page
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4 to 20
8 to 30
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Tip: press N for new problems. The link always brings this exact sheet back.

Multiplying Fractions2 pages, answer key from page 2 · US Letter

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NameDateScoreMultiplying FractionsMultiply the numerators and multiply the denominators. Simplify your answer.1.1011 × 211 = 2.38 × 78 = 3.45 × 15 = 4.58 × 48 = 5.12 × 812 = 6.511 × 24 = 7.25 × 35 = 8.78 × 68 = 9.25 × 24 = 10.78 × 45 = 11.12 × 12 = 12.612 × 16 = 13.78 × 78 = 14.45 × 25 = 15.812 × 912 = 16.23 × 13 = 17.18 × 38 = 18.26 × 56 = 19.210 × 810 = 20.511 × 23 = PrintablePal.com · free printablesMultiplying Fractions
Worksheet, page 1
Multiplying Fractions: answer key1.1011 × 211 = 201212.38 × 78 = 21643.45 × 15 = 4254.58 × 48 = 5165.12 × 812 = 136.511 × 24 = 5227.25 × 35 = 6258.78 × 68 = 21329.25 × 24 = 1510.78 × 45 = 71011.12 × 12 = 1412.612 × 16 = 11213.78 × 78 = 496414.45 × 25 = 82515.812 × 912 = 1216.23 × 13 = 2917.18 × 38 = 36418.26 × 56 = 51819.210 × 810 = 42520.511 × 23 = 1033PrintablePal.com · free printablesAnswer key
Answer key, page 1

On this page

The easiest fraction operation to compute

Multiplication is the one operation where fractions behave more simply than expected: multiply the numerators, multiply the denominators, and you are nearly done. No common denominator is needed. The challenge is understanding what the answer means. Half of a third is a sixth, so the product of two proper fractions is smaller than either one, which surprises students who have learned that multiplication makes numbers bigger.

This work belongs in fifth grade and continues into sixth with division of fractions. If a student is still unsure how to reduce, begin with simplifying fractions, because nearly every product here needs it.

Settings

  • Skill is set to Multiply fractions. The same menu offers Divide fractions, which uses the keep-change-flip method and is worth trying later.
  • Denominators is set to A mix on this page, but it makes no real difference for multiplication, since denominators never need to match.
  • Use mixed numbers is the main difficulty control. When it is off, both factors are proper fractions. When it is on, both are mixed numbers, and the student must change them to improper fractions before multiplying.
  • Largest denominator ranges across 4 to 20. With mixed numbers on, the generator caps denominators at 10 to keep numbers manageable.
  • Number of problems is adjustable up to 30, down to 8. The default is 20.

The printed instruction says to multiply the numerators, multiply the denominators and simplify, and the key shows the final answer in simplest form (as a mixed number if the product is larger than 1).

Worked example: 3/4 × 2/9

Straight across.

  1. Multiply the numerators: 3 × 2 = 6.
  2. Multiply the denominators: 4 × 9 = 36.
  3. The product is 6/36. The greatest common factor of 6 and 36 is 6, so divide both: 1/6.

Cancel first. The same problem can be shortened by simplifying before multiplying.

  1. The 3 on top and the 9 on the bottom share a factor of 3. Divide both: 1 and 3.
  2. The 2 on top and the 4 on the bottom share a factor of 2. Divide both: 1 and 2.
  3. The problem is now 1/2 × 1/3 = 1/6.

Same answer, smaller numbers. Students who learn to cancel first avoid the last step of reducing a large fraction.

With mixed numbers. To find 1 1/2 × 2/3, change 1 1/2 to 3/2. Then 3/2 × 2/3 = 6/6 = 1. The product of a number and its reciprocal is always 1, which is a nice thing to point out.

Checking the key

  • Product not reduced. The student wrote 6/36 and stopped. The value is right; the form is not what the sheet asks for.
  • Common denominator found first. A student has confused this with addition. It still produces a correct answer if they continue correctly, but it wastes time.
  • Multiplying whole parts and fractions separately. For 1 1/2 × 2/3, a child multiplies 1 × 2 and 1/2 × 3, which gives nonsense. Convert to improper fractions first.
  • An answer larger than a factor. For proper fractions, the product should be smaller than each factor. If it is not, an error crept in.

For adding and subtracting, see subtracting fractions with unlike denominators. To prepare mixed numbers, practice with improper fractions and mixed numbers.

Sources

  1. Common Core State Standards: Grade 5 multiplying a fraction by a fraction or whole number (5.NF.B.4) thecorestandards.org
  2. Common Core State Standards: Grade 5 solving real-world problems that multiply fractions and mixed numbers (5.NF.B.6) thecorestandards.org