One way to teach students proportions is to show them how to find a unit ratio and then to use multiplication to derive the desired result. Another method is to use cross-multiplication to find the unknown quantity in a pair of ratios. To illustrate the idea of proportions, it's best to tie the concept to a real-world situation rather than presenting it as an abstract pair of fractions. An example is to find the cost of two sets of items.
Continue ReadingFor an example exercise, assume you have a set of two items that costs $14 and that you want the student to find out how much three of those items would cost. Have the student find the unit price by dividing the total price by the number of units, then multiplying by the number to buy. In this case, 14 divided by 2 gives 7 as the unit price. A set of three items would cost $21.
Cross-multiplication works by a similar principle and is frequently used in algebra. To teach cross-multiplication, have the student write the two ratios as an equation. Multiply one denominator by the opposite numerator, and do the same for the opposites. For example, 2/3 = 4/x simplifies to 12 = 2x, or x = 6.
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