We want to describe

2

different ways that we can represent the given ratio using a tape diagram. In this ratio, the first quantity is

3

times the second quantity.

3 \times 4 ⇓ 12 : 4

To do this, we should draw two tapes, one for each quantity in the ratio, so that the lengths of these tapes represent the relationship described by the ratio. First, let's draw

2

tapes in which each part represents

1

unit. This means that the first tape will have

12

parts and the second tape will have

4

parts.

We can see that the length of the first tape is

3

times the length of the second tape. However, one part in the tape diagram does not necessarily have to represent

1

unit. Let's suppose that each part in a tape diagram represents

4

units. We can calculate the number of parts needed for each tape by dividing the original quantity from the ratio by the value of one part.

\frac{1 2}{4} \frac{4}{4} = 3 = 1

The first tape will have

3

parts and the second tape will have only

1

part.

Notice that these are only two example ways to represent the given ratio using a tape diagram. We can draw more tape diagrams as long as the first tape is $3$ times longer than the second tape.

Exercise