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C1. Ratio & proportion : inverse proportion. Vocabulary The quotient of two numbers or quantities showing their relative sizes is called their ratio. The ratio of a to b is written a:b or a/b. This ratio is often expressed using the smallest possible integers. Two variables, x and y, are in inverse proportion to one another if y is proportional to 1/x. We write y µ 1/x. These pairs of values of x and y display inverse proportion: (1,12), (2,6), (4,3), (6,2). Note that this relationship can also be written y=12/x or xy=12. Values that are in inverse proportion are often displayed in a table. x  2  4 16 y  8  4  1 Notice that if x is doubled, then y is halved. All the values fit the equation y=16/x. Whenever y µ 1/ x, you will be able to find an equation of the form y=m/x to fit the available information. An example y and x are in inverse proportion. If y=10 when x=4, find what y is when x=20. Solution using multipliers x has been increased by a multiplier of 5, so y should be decreased in the same way. So y=2 when x=20. Solution using equations The information given must fit an equation of the form y=m/x. In this case 10=m/4, so m=40, so the equation is y=40/x. When x=20, y=40/20=2.