Using Proportions

A ratio is a comparison of two numbers such as 4:5 A ratio is a comparison of two numbers such as 4:5. When writing a ratio, always express it in simplest form. A B C D 3.6 6 8 4.8 10 What is the ratio of segment AB to segment CB? AB CB = 10 6 Now try to reduce the fraction. Once reduced this is the ratio between the two sides. 10 6 = 5 3 Therefore, the ratio of segment AB to segment CB is 5:3. Type notes here

A baseball player goes to bat 348 times and gets 107 hits. What is the player’s batting average? To find a baseball player’s batting average a ratio is first set up. The ratio compares the number of hits to the number of times he goes to bat. In this problem, the ratio would be 107 to 348 or in fraction form 107/ 348. Now convert this fraction to a decimal by dividing the denominator into the numerator and then rounding to three decimal places. Ratio: 107 348 Decimal: 107 / 348 = 0.307 Type notes here The baseball player’s batting average is 0.307 which means roughly he is getting one hit every three times at bat.

a b c d Proportion: an equation that states that two ratios are equal. = Ratio Ratio Proportion Type notes here

= Solving a proportion: There are two common ways to describe the method: Cross-multiply Use cross-products a b = c d cross products a • d = b • c ad = bc Type notes here Now solve the resulting equation.

= Solving a proportion: x Example 5 6 8 = 8 • x 6 • 5 8x = 30 8x = 30 8 8 x = 3.75 Type notes here

Proportions The sides of these two triangles are proportional, Because all 3 ratios of corresponding sides are equal. Not drawn to scale! X 2 F e t Type notes here 356 yards 84 yards How tall is the cactus? (Note the different units.)

Review Terms: Ratio Proportion Cross product Cross-multiply 1. A ratio is _____________________________________. In the example above ______ and ______ are ratios. 2. A proportion is _________________________________________ Type notes here 3. To solve the above equation, take the _________________________ or ______________________.