Skill: Solve proportional reasoning problems using tables

A proportional table shows two quantities that change at the same rate. To find a missing value:

1. Find the unit rate—the amount for 1 unit.
2. Multiply the unit rate by the missing number.
3. Check that the ratio stays constant.

Example

Three notebooks cost 4.50$. Use the table to find the missing costs.

Number of notebooks	3	5	8	12
Cost in dollars	4.50$	?	?	?

Step 1: Find the cost of 1 notebook

Divide the cost by the number of notebooks:

$$4.50 \div 3 = 1.50$$

The unit rate is 1.50$ per notebook.

Step 2: Find each missing cost

Multiply the number of notebooks by 1.50$:

For 5 notebooks:

$$5 \times 1.50 = 7.50$$

For 8 notebooks:

$$8 \times 1.50 = 12.00$$

For 12 notebooks:

$$12 \times 1.50 = 18.00$$

The completed table is:

Number of notebooks	3	5	8	12
Cost in dollars	4.50$	7.50$	12.00$	18.00$

Step 3: Check the ratio

Each cost divided by the number of notebooks equals 1.50$:

$$4.50 \div 3 = 7.50 \div 5 = 12 \div 8 = 18 \div 12 = 1.50$$

Because the unit rate is constant, the table represents a proportional relationship. The amounts do not need to increase by the same addition each time; instead, each cost is found by multiplying the number of notebooks by the same rate, 1.50$ per notebook.