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.
A proportional table shows two quantities that change at the same rate. To find a missing value:
Three notebooks cost 4.50$. Use the table to find the missing costs.
| Number of notebooks | 3 | 5 | 8 | 12 |
|---|---|---|---|---|
| Cost in dollars | 4.50$ | ? | ? | ? |
Divide the cost by the number of notebooks:
The unit rate is 1.50$ per notebook.
Multiply the number of notebooks by 1.50$:
For 5 notebooks:
For 8 notebooks:
For 12 notebooks:
The completed table is:
| Number of notebooks | 3 | 5 | 8 | 12 |
|---|---|---|---|---|
| Cost in dollars | 4.50$ | 7.50$ | 12.00$ | 18.00$ |
Each cost divided by the number of notebooks equals 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.
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