Ratios and proportions are related mathematical concepts. Ratios compare similar things, like distances or time. Proportions are two equivalent ratios, such as traveling 80 miles in 90 minutes is proportional to traveling 160 miles in three hours. You calculate ratio and proportion by dividing.
A ratio shows a comparison or relationship between two similar things. For example, to find a ratio for measurements of time, such as two days and 12 hours, start by converting both numbers to the same unit. In this case, use hours. Write the expression as 48:12, then divide the first number by the second to get the ratio of 4:1, or 4 to 1. For another example, calculate the ratio between seven days and two weeks. There are 14 days in two weeks, so the ratio can be expressed as 7:14 and reduced to 1:2, or 1 to 2.
Ratios can be used to scale objects so they are bigger or smaller. If you have an 8-inch by 10-inch photograph and want to make a reprint that twice as big, no conversion is need since both measurements are in inches. The ratio is 8:10. To get the right size for the reprint, simply double the height and width, 16:20. If you want one half the original size, halve the height and width, 4:5.
Proportions are two equivalent ratios, such as 4:2 = 8:4 since both can be reduced to a ratio of 2:1. The examples in the introduction are proportional because both the elements of time and distance have ratios of 1:2, the miles being 80:160 and the minutes 90:180. Now consider a 20-foot table that weighs 60 pounds and a 10 foot table weighing 40 pounds. They are not proportional since 20:60 is not equivalent to 10:40.
You can use proportions to measure tall objects, like a flag pole, without a ladder. First, hold a yardstick upright on the ground and measure its shadow. Next, measure the shadow of the flag pole. If the yardstick has a one-foot shadow, its ratio would be 3:1. If the flag pole's shadow is 5 feet, its ratio would be x:5. To find out what x is when x:5 = 3:1, multiply across the known corners, then divide by the third number: x = (3x5) / 1, x = 15/1, x = 15. The flagpole is 15 feet tall.