Chapter 5 - Ratio and Proportion - 5.3 Proportions - 5.3 Exercises - Page 350: 19

A proportion sets two rates/fractions/ratios equal to each other. We can visualize the cross-multiplication as two arrows: one from 30 to 9 and the other from 6 to 45.

Work Step by Step

A proportion sets two rates/fractions/ratios equal to each other. For example, one might say that Jim is twice as tall as Bill. If Jim is 6 feet tall, then we can set up a proportion like so: $\frac{6}{x}=\frac{2}{1}$ This can be used to find $x$, Bill's height by cross-multiplication: $6*1=2*x$ $x=3$ In the fraction provided, we have: $\displaystyle \frac{30}{6}=\frac{45}{9}$ We can visualize the cross-multiplication as two arrows: one from 30 to 9 and the other from 6 to 45. The numbers multiply thus: $30*9=45*6$ $270=270$ This method can be used to solve for any variables (as was done in the above example).

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