9-1: Using Ratios and Proportions

R ATIO : A comparison of two numbers by division ▫ Ratios can be written a variety of ways  45 to 340  45:340  45 / 340  45  340 ▫ All ratios should be written in simplest form.  In the above examples, because both 45 and 340 can be divided by 5, the proper ratio is 9 / 68

9-1: Using Ratios and Proportions Write each ratio in simplest form ▫ Six days to two weeks  In order to write a ratio, both units of measure must be the same, so an equivalent statement would be ▫ Six days to fourteen days ▫ The ratio is therefore 6:14 = 3:7

9-1: Using Ratios and Proportions Your Turn ▫W▫Write each ratio in simplest form ▫1▫1 8 / 24 33 /4 ▫1▫10 km to 20,000 m 11 to 2 ▫6▫6 inches : 2 feet 11:4

Proportion: An equation that shows two equivalent ratios. Every proportion has two cross products ▫ In the example above, 20 and 3 are called the extremes, 30 and 2 are called the means.  20(3) = 30(2) ▫ Explain reason for names  20:30 = 2:3

9-1: Using Ratios and Proportions Example ▫ Solve  15(2x + 1) = 35(3)Cross multiply  30x + 15 = 105Distribute  30x = 90Subtract 15  x = 3Divide by 30

9-1: Using Ratios and Proportions Your Turn ▫ Solve  b = 12 x = 4

9-1: Using Ratios and Proportions Assignment ▫ Worksheet #9-1