Skill: Represent ratios on double number lines

A double number line shows two quantities that change together. The values that match are placed above and below each other. Start with $0$ paired with $0$, then use the same multiplicative relationship for every pair.

Example: Three notebooks cost 6$. How much do five notebooks cost?

1. Label the two lines.

$$\begin{array}{c} \text{Number of notebooks}\\ \text{Cost in dollars} \end{array}$$

2. Pair zero with zero, and place the known values together.

$$\begin{array}{c|c|c|c} \text{Number of notebooks} & 0 & 3 & 5\\ \hline \text{Cost} & \$0 & \$6 & ? \end{array}$$

3. Find the cost of $1$ notebook by dividing both quantities in the known pair by $3$:

$$3\text{ notebooks}\div 3=1\text{ notebook}$$ $$\$6\div 3=\$2$$

So, $1$ notebook costs 2$.

4. Use that unit rate to find the cost of $5$ notebooks:

$$5\text{ notebooks}\times \$2\text{ per notebook}=\$10$$

5. Fill in the missing value:

$$\begin{array}{c|c|c|c} \text{Number of notebooks} & 0 & 3 & 5\\ \hline \text{Cost} & \$0 & \$6 & \$10 \end{array}$$

Therefore, **five notebooks cost 10}$**. The values are related multiplicatively: each notebook costs$$2$, rather than adding a fixed dollar amount to move from one pair to the next.