Ratio Table
A table listing pairs of numbers that form equivalent ratios.
A ratio table is a chart used to compare two or more quantities and their relationships. It is a valuable tool to help understand and solve problems involving proportions, rates, and scaling.
To set up a ratio table, one or more variable quantities are listed in columns, and ratios of each quantity are calculated and entered into rows. The ratios are simplified, and common factors are identified so that the values in the table are in their simplest form.
For example, consider a recipe that calls for 3 cups of flour and 2 cups of sugar. To convert this recipe to make a larger or smaller amount, a ratio table can be used.
| Quantity | Flour | Sugar |
| ——– | —– | —– |
| Original | 3 | 2 |
| New | 6 | 4 |
In this ratio table, the quantities of flour and sugar in the original recipe are listed in the Original row. The New row lists the quantities for the same ingredients in a recipe that is twice as large. To find the new quantities of flour and sugar, the original quantities are multiplied by the scaling factor (in this case, 2) and entered into the table.
The ratios of flour to sugar in both recipes can be compared by dividing the quantity of flour by the quantity of sugar and simplifying the result. In the original recipe, the ratio is 3:2, or 1.5:1. In the new recipe, the ratio is 6:4, or 1.5:1 as well. This shows that the ratio of flour to sugar is the same in both recipes, even though the quantity of each ingredient has changed.
Ratio tables can also be used to solve problems involving rates, proportions, and scaling. By setting up the table and identifying the relationship between the quantities, unknown quantities can be calculated using simple cross-multiplication and division.
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