Math Words: Ratio, Rate, Proportional, Estimate

Read the key words of middle-school math problems quickly and accurately.

Word problems are reading problems first. A ratio compares two quantities, like 3 cups of flour to 2 cups of water (3:2). A rate is a ratio of two different kinds of units, such as miles per hour or dollars per pound; a unit rate tells you the amount for one unit. Proportional means two quantities change at the same rate, so their ratio stays constant. To estimate is to find an approximate answer, often by rounding. Words like 'per', 'each', and 'for every' usually signal a rate or ratio.

Read carefully: 'A recipe uses 4 eggs for every 6 muffins. Estimate how many eggs are needed for 40 muffins, assuming the amounts are proportional. ' 'For every' signals a ratio of 4:6, or 2:3. 'Proportional' tells you the ratio holds. 'Estimate' tells you an approximate answer is acceptable: about 27 eggs. Missing one of these words changes the whole problem.

• 1A ratio compares two quantities; a rate compares different units.
• 2Proportional means the ratio stays constant.
• 3'Per', 'each', and 'for every' signal ratios and rates.