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Ratios and Proportions

Keystone Geometry. Ratios and Proportions. Ratio. A ratio is a comparison of two numbers such as a : b. Ratio:. When writing a ratio, always express it in simplest form. ** Ratios must be compared using the same units. A ratio can be expressed: 1. As a fraction

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Ratios and Proportions

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  1. Keystone Geometry Ratios and Proportions

  2. Ratio A ratio is a comparison of two numbers such as a : b. Ratio: When writing a ratio, always express it in simplest form. ** Ratios must be compared using the same units. A ratio can be expressed: 1. As a fraction 2. As a ratio 3 : 7 3. Using the word “to” 3 to 7

  3. A 10 8 D 3.6 4.8 C B 6 Example: What is the ratio of side AB to side CB in the triangle? Now try to reduce the fraction. Example: What is the ratio of side DB to side CD in the triangle?

  4. Ratio: Decimal: Example ………. A baseball player goes to bat 348 times and gets 107 hits. What is the players batting average? Solution: Set up a ratio that compares the number of hits to the number of times he goes to bat. Convert this fraction to a decimal rounded to three decimal places. The baseball player’s batting average is 0.307 which means he is getting approximately one hit every three times at bat.

  5. Proportion • Definition: A proportion is an equation stating that two ratios are equal. • For example,

  6. Terms of a Proportion First Term Third Term Second Term Fourth Term Fourth Term First Term Third Term Second Term

  7. Means and Extremes • The first and last terms of a proportion are called extremes. • The middle terms are called the means. ** The product of the means is always equal to the product of the extremes.

  8. Properties of Proportions is equal to: Switching the means Add one to both sides Reciprocals

  9. Example: If , then… 5y = _____ 2x

  10. ** Special Note: The easiest way to decide if two proportions are equal is to apply the mean-extremes property (cross multiplication).However, all of the other properties work as well, provided your initial proportion is true.

  11. = 12 • 3 4 • x Proportions- examples…. Example 1: Solve the proportion using cross multiplication. 4x = 36 x = 9 4x = 36 4 4

  12. Some to try… 1. 2. 3. 4.

  13. x 2 ft 84 yards 356 yards Example 2: Use a proportion to solve for the missing piece of a triangle. Find the value of x. First! Multiply by 3 to change yards into feet. The units must be the same.

  14. Examples: Find the measure of each angle. • Two complementary angles have measures in the ratio 2 : 3. • Two supplementary angles have measures in the ratio 3 : 7. • The measures of the angles of a triangle are in a ratio of 2 : 2 : 5. • The perimeter of a triangle is 48cm and the lengths of the sides are in a ratio of 3 : 4 : 5. Find the length of each side. 36 and 54 54 and 126 40, 40, and 100 12cm, 16cm, and 20cm

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