1. Warm Up Write each fraction in lowest terms. 14 16 1. 9 72 3. 24 64 2. 7878 3838 1818

2. Unit 1: Ratios and Propotional Reasoning Lesson 1: “Ratios”

3. Vocabulary fraction rational number ratio equivalent ratios

4. A fraction is an equal part of a whole The top number is the numerator... 3434 The bottom number is the denominator... for example......this tells you how many equal pieces there are present....this tells you how many equal pieces the fraction is broken into. 4 equal pieces... 3 are present

5. n d Any fraction can be written as a decimal by dividing the numerator by the denominator. 1212 1 ÷ 2 A rational number is any number that can be written as a fraction, as long as both the numerator and denominator are integers and d  0 (because you can't divide anything by zero). = =0.5 for example...

6. A ratio is a comparison of two quantities. Ratios can be written in three ways. 7575 Each of these name the same ratio! First number “ to” second 7 to 5 First number “:” second 7:5 As a fraction, with the first number over second

7. Class Example: Writing Ratios in Simplest Form Write the ratio 15 bikes to 9 skateboards in simplest form. 15 9 5353 The ratio of bikes to skateboards is, 5:3, or 5 to 3. 15 ÷ 3 9 ÷ 3 Write the ratio as a fraction. = = Simplify. 5353 bikes (Start by writing the words as a fraction; the first is the numerator, the second is the denominator.) skateboards

8. Partner Example: Writing Ratios in Simplest Form Write the ratio 24 shirts to 9 jeans in simplest form. 24 9 8383 The ratio of shirts to jeans is, 8:3, or 8 to 3. = shirts jeans 24 ÷ 3 9 ÷ 3 Write the ratio as a fraction. = = Simplify. 8383

9. Ratios that make the same comparison are equivalent ratios. Equivalent ratios represent the same point on the number line. One way to check whether two ratios are equivalent is to write both in simplest form.

10. Partner Example: Determining Whether Two Ratios Are Equivalent Simplify to tell whether the ratios are equivalent. 12 15 B. and 27 36 3 27 A. and 2 18 Since, the ratios are equivalent. 1919 = 1919 1919 = 3 ÷ 3 27 ÷ 3 3 27 = 1919 = 2 ÷ 2 18 ÷ 2 2 18 = 4545 = 12 ÷ 3 15 ÷ 3 12 15 = 3434 = 27 ÷ 9 36 ÷ 9 27 36 = Since, the ratios are not equivalent. 4545  3434

11. Individual Practice: Determining Whether Two Ratios Are Equivalent Simplify to tell whether the ratios are equivalent. 14 49 B. and 16 36 Since, the ratios are equivalent. 1515 = 1515 1515 = 3 ÷ 3 15 ÷ 3 3 15 = 1515 = 9 ÷ 9 45 ÷ 9 9 45 = 2727 = 14 ÷ 7 49 ÷ 7 14 49 = 4949 = 16 ÷ 4 36 ÷ 4 16 36 = Since, the ratios are not equivalent. 2727  4949 3 15 A. and 9 45