8.05 Multiply fractions by whole numbers

Lesson

Practice

Lesson

Are you ready?

Let's recall how any fraction can be thought of as a multiple of a unit fraction.

We are going to work out how to represent $4\times\frac{1}{3}$4×13 on the number line.

Mark $\frac{1}{3}$13 on the number line.
Now mark $4\times\frac{1}{3}$4×13 on this number line.

Learn

We can extend this to multiply any fraction by a whole number, by thinking of the fraction as a multiple of a unit fraction.

Let's see how we can do this, in the video.

Apply

Question

We are going to work out how to represent $3\times\frac{2}{5}$3×25 on the number line.

First mark $\frac{2}{5}$25 on the number line.
Now mark $3\times\frac{2}{5}$3×25 on this number line.

Remember!

We can multiply a fraction by a whole number by thinking of it as a multiple of a unit fraction. For example:

$5\times\frac{3}{8}$5×38	$=$=	$5\times3\times\frac{1}{8}$5×3×18
	$=$=	$15\times\frac{1}{8}$15×18
	$=$=	$\frac{15}{8}$158

Outcomes

5.NF.B.4

Apply and extend previous understandings of multiplication to multiply a fraction by a whole number and a fraction by a fraction.

5.NF.B.4a

A. Interpret the product (a/b) x q as a parts of a partition of q into b equal parts. For example, use a visual fraction model to show (2/3) x 4 = 8/3, and create a story context for this equation.

5.NF.B.4b

B. Interpret the product of a fraction multiplied by a fraction (a/b) x (c/d). Use a visual fraction model and create a story context for this equation. For example, use a visual fraction model to show (2/3) x (4/5) = 8/15, and create a story context for this equation. In general, (a/b) x (c/d) = ac/bd.