Skill: Represent ratios with tape diagrams

A tape diagram shows a ratio by using equal-sized segments.

For a ratio of $3:5$:

• The first quantity is shown with $3$ equal segments.
• The second quantity is shown with $5$ equal segments.
• Each segment has the same value.

Suppose a class has boys and girls in a ratio of $3:5$. There are $32$ students altogether. How many boys and girls are there?

First, draw the ratio as two bars:

Boys:  [ ][ ][ ]

Girls: [ ][ ][ ][ ][ ]

The diagram has $3+5=8$ equal segments altogether. These $8$ segments represent the total of $32$ students.

Find the value of one segment:

$$32 \div 8=4$$

So, each segment represents $4$ students.

Now find each quantity:

• Boys: $3$ segments, so $3 \times 4=12$
• Girls: $5$ segments, so $5 \times 4=20$

Therefore, there are $\boxed{12}$ boys and $\boxed{20}$ girls.

The ratio $3:5$ tells how many equal units are in each bar. The numbers $3$ and $5$ are not the actual numbers of students; the common segment value, $4$, scales the ratio to the actual quantities.