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.4.a

Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b using a visual fraction model.

5.NF.4.b

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.