Cross ProductsDate: 02/28/99 at 10:32:16 From: Sarah Harvard Subject: Cross-products I am having trouble understanding cross-products. Will you please explain them to me? Date: 02/28/99 at 12:47:52 From: Doctor Reno Subject: Re: Cross-products Hi, Sarah! Cross-products can be used for three purposes: to compare fractions, to determine whether a proportion is true, and to solve a proportion. Fractions that represent the same quantity are called equivalent fractions. For example: 3/6, 4/8, and 5/10 are all equivalent fractions for 1/2. You can use cross-products as a shortcut method to find whether two fractions are equivalent. If the cross-products are equal, then the fractions are equivalent; if the cross-products are not equal, then the fractions are not equivalent. Are 3/10 and 15/50 equivalent? 3 x 50 = 150 10 x 15 = 150, so the fractions are equivalent. What about 7/14 and 5/8? Are they equivalent? 7 x 8 = 56 14 x 5 = 70, so the fractions are NOT equivalent. A proportion is a statement that two ratios are equal. You can determine whether a proportion is true by using cross-products. A proportion is true if the two fractions are equivalent and the cross-products are equal. Is the proportion 3/12 = 8/32 true or false? (We read 3/12 = 8/32 like this: "three is to twelve as eight is to thirty-two.") 3 / 3 1 ------ = --- 12 / 3 4 8 / 8 1 ------- = --- 32 / 8 4 So we know the fractions are equivalent. Are the cross-products equal? Does 3 x 32 = 8 x 12? 3 x 32 = 96 8 x 12 = 96 So YES, the proportion is TRUE. Cross-products can also be used to solve proportions when one of the numbers is unknown: 5 n ---- = ---- What is n? 20 48 We know from what we have learned above that 5 x 48 must equal 20 x n: 20 x n = 5 x 48 20 x n = 240 If you don't know how to solve for n yet, you can think: what number multiplied by 20 gives me 240? n = 12 We check this value for n by substituting it back into the proportion: 5 12 --- = ---- 20 48 Are the two fractions equivalent? 5 / 5 1 ------ = --- 20 / 5 4 12 / 12 1 ------- = --- 48 / 12 4 So the proportion is true; our value of 12 for n was correct. I hope this has helped, Sarah. If you have any more questions, please ask Dr. Math! - Doctor Reno, The Math Forum http://mathforum.org/dr.math/ |
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