Multiplying a fraction by a whole number: printable worksheets

Multiply a whole number by a fraction as repeated addition and as a product, with fraction bars and number-line hops.

Sample worksheet

The first 4 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{2}{3} + \frac{2}{3} + \frac{2}{3} + \frac{2}{3} = 00

\frac{5}{12} + \frac{5}{12} + \frac{5}{12} + \frac{5}{12} + \frac{5}{12} = 00

\frac{3}{5} + \frac{3}{5} = 00

\frac{1}{3} + \frac{1}{3} + \frac{1}{3} = 00

Show answers

2 \frac{2}{3}

2 \frac{1}{12}

1 \frac{1}{5}

4.1

Multiplying a fraction by a whole number starts out as repeated addition: three groups of one fourth is one fourth added three times. Fourth graders learn to see that, record it as a product, and then recognize that the numerator is what gets multiplied while the piece size stays put. Getting that picture right now makes later work with fractions times fractions far less mysterious.

The sheet can pose multiplication, repeated addition, a comparison where the child decides if a product is bigger or smaller than a number without calculating, word problems, and area with fraction sides. Factor forms include a whole number times a fraction, and also a fraction times a fraction or mixed numbers. You can choose denominators, set the largest whole number between two and ten, restrict fractions to unit fractions, and ask for canceling first. A model setting draws bars for whole-number products, number-line hops for repeated addition, a square for a fraction of a fraction, or tiles for an area. Answers can be mixed numbers or improper fractions, and word problems use customary or metric units.

The easy setting uses unit fractions with a model, and whole numbers up to five. Medium is repeated addition with the model. Hard multiplies by whole numbers as large as ten and leaves the model out.

Pictures that help

When a child cannot see why the answer is a mixed number, draw the bars together and count how many wholes are filled.

Practice repeated addition before moving to the product form.
Ask whether the answer should be more or less than one before solving.

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.

4.NF.B.4a: Understand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 as the product 5 x (1/4), recording the conclusion by the equation 5/4 = 5 x (1/4).
4.NF.B.4b: Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number. For example, use a visual fraction model to express 3 x (2/5) as 6 x (1/5), recognizing this product as 6/5. (In general, n x (a/b) = (n x a)/b.)
4.NF.B.4c: Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. For example, if each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?

Before this: Adding and subtracting fractions (Grade 4)
Next: Multiplying fractions (Grade 5)