Ratio & Proportion
A ratio is a way to compare two or more quantities of the same kind. It tells us how many times one value contains another value. For example, if you have 10 apples and 5 oranges, the ratio of apples to oranges is 10 to 5. We write this as 10:5. We can simplify this ratio by dividing both numbers by 5 to get 2:1. This means for every 2 apples, there is 1 orange. Proportion is simply a statement that says two ratios are equal. If a/b = c/d, we say that a, b, c, and d are in proportion.
Concepts (3)
Four numbers a, b, c, and d are in proportion if the first ratio equals the second ratio. In the equation a/b = c/d, 'a' and 'd' are the extremes, while 'b' and 'c' are the means.
Four numbers a, b, c, and d are in proportion if the first ratio equals the second ratio. In the equation a/b = c/d, 'a' and 'd' are the extremes, while 'b' and 'c' are the means. The most important rule is that the product of extremes equals the product of means (a * d = b * c). For example, in 2:4 :: 3:6, we see 2 * 6 = 12 and 4 * 3 = 12.
To find which ratio is larger, convert them into fractions. For example, to compare 2:3 and 5:8, write them as 2/3 and 5/8. Cross-multiply the numerators and denominators: 2*8 = 16 and 3*5 = 15.
To find which ratio is larger, convert them into fractions. For example, to compare 2:3 and 5:8, write them as 2/3 and 5/8. Cross-multiply the numerators and denominators: 28 = 16 and 35 = 15. Since 16 is greater than 15, the ratio 2:3 is greater than 5:8. This is a quick way to compare values without finding decimals.
This is the most useful tool for solving ratio problems. When a ratio like 5:7 is given, the actual numbers are 5x and 7x. Here, 'x' is a common multiplier. If the sum of these numbers is 60, you can write 5x + 7x = 60. This gives 12x = 60, so x = 5.
This is the most useful tool for solving ratio problems. When a ratio like 5:7 is given, the actual numbers are 5x and 7x. Here, 'x' is a common multiplier. If the sum of these numbers is 60, you can write 5x + 7x = 60. This gives 12x = 60, so x = 5. Now you can find the actual numbers: 55=25 and 75=35.
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Start Lesson: Properties of Proportion