Ctrl+k

Solve proportional reasoning problems using tables

A proportional table represents paired quantities whose ratio is constant, so each entry can be found by applying the same multiplicative scale factor or unit rate across the rows or columns. The learner uses equivalent ratios to determine missing values and distinguishes proportional relationships from those with merely equal additive changes, including contexts involving positive whole numbers, decimals, and simple fractions; more advanced treatments of generalized functions or complex algebraic cases are not included.

Detailed Explanation: 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 notebooks35812
Cost in dollars4.50$???

Step 1: Find the cost of 1 notebook

Divide the cost by the number of notebooks:

4.50Ă·3=1.504.50 \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:

5Ă—1.50=7.505 \times 1.50 = 7.50

For 8 notebooks:

8Ă—1.50=12.008 \times 1.50 = 12.00

For 12 notebooks:

12Ă—1.50=18.0012 \times 1.50 = 18.00

The completed table is:

Number of notebooks35812
Cost in dollars4.50$7.50$12.00$18.00$

Step 3: Check the ratio

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

4.50Ă·3=7.50Ă·5=12Ă·8=18Ă·12=1.504.50 \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.

Learn by doing: Solve proportional reasoning problems using tables

Click a topic below to practice the foundational skills you'll need, learn the steps, or master this skill

Practice with unlimited practice problems

Slope - Find Equivalent - X,Y Chart to Slope Zero Intercept Form


    ?