Multiplying fractions: printable worksheets

Multiply a whole number by a fraction and a fraction by a fraction, with bars and an area square, and cancel common factors first.

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Sample worksheet

The first 6 problems of a real worksheet, made the way the builder makes it. Open it in the builder to change the number of problems, the difficulty and the layout, then print.

\frac{5}{8} \times \frac{5}{8} = 00

\frac{1}{5} \times \frac{2}{3} = 00

\frac{2}{3} \times \frac{1}{2} = 00

\frac{1}{3} \times \frac{3}{4} = 00

\frac{1}{12} \times \frac{1}{6} = 00

\frac{1}{2} \times \frac{2}{5} = 00

Show answers

\frac{25}{64}

\frac{2}{15}

\frac{1}{3}

\frac{1}{4}

\frac{1}{72}

\frac{1}{5}

Multiplying a fraction by a number is really taking part of something, which is why the product of two fractions can be smaller than either factor. Fifth graders extend what they learned about multiplying a whole number by a fraction to a fraction of a fraction, and the area square makes that idea visible. This page practices both, with an answer key that shows the steps.

The sheet rotates through the types you select: multiply, repeated addition, compare without multiplying, word problems, and area with fraction sides. For products you pick which factors appear, from a whole number times a fraction to a mixed number times a mixed number. You also choose denominators from halves up to twelfths, the largest whole number, whether every fraction is a unit fraction, whether common factors are canceled first, and whether answers are mixed numbers or improper fractions. Models can be switched on, and word problems can use customary or metric units. The easy setting multiplies a whole number by a fraction with a model. The medium setting multiplies two fractions with no picture. The hard setting multiplies two fractions and cancels common factors before multiplying.

Smaller than you started with

Before multiplying, ask whether the product will be larger or smaller than the whole number.
Look for a numerator and a denominator, from different fractions, that share a factor, and cancel it before multiplying.

What students practise

I can describe shapes by their sides and corners and split a shape into equal shares.

Students tell the defining attributes of shapes, put shapes together, and partition circles and rectangles into equal shares named with the words halves, thirds and fourths.

Key words

half: one of two equal shares
third: one of three equal shares
fourth (quarter): one of four equal shares
equal shares: parts that are exactly the same size
side: a straight edge of a flat shape
vertex: the point where two sides meet

Common mistakes

Counts the parts without checking that they are the same size.
Thinks more parts means a bigger share.

Standards

Common Core State Standards this worksheet practises.

5.NF.B.4a: Interpret the product (a/b) x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a x q divided by b. For example, use a visual fraction model to show (2/3) x 4 = 8/3, and create a story context for this equation. Do the same with (2/3) x (4/5) = 8/15. (In general, (a/b) x (c/d) = ac/bd.)
5.NF.B.4b: Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.
5.NF.B.5a: Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.
5.NF.B.5b: Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n x a)/(n x b) to the effect of multiplying a/b by 1.
5.NF.B.6: Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.

Before this: Multiplying a fraction by a whole number (Grade 4)