Warm Up Write each fraction in lowest terms

Warm Up Write each fraction in lowest terms. 1. 14 16 7 8 3. 9 72 1 8 2. 24 64 3 8

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

Vocabulary fraction rational number ratio equivalent ratios

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

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). n d Any fraction can be written as a decimal by dividing the numerator by the denominator. for example. . . 1 2 = 1 ÷ 2 = 0. 5

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

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

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

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.

Partner Example: Determining Whether Two Ratios Are Equivalent Simplify to tell whether the ratios are equivalent. A. 3 and 2 27 18 3 3÷ 3 1 = = 27 27 ÷ 3 9 2 2÷ 2 1 = = 18 18 ÷ 2 9 1 1 Since = , 9 9 the ratios are equivalent. B. 12 and 27 15 36 12 12 ÷ 3 4 = 15 15 ÷ 3 = 5 4 3 Since , 5 4 the ratios are not equivalent. 27 27 ÷ 9 3 = 36 36 ÷ 9 = 4

Individual Practice: Determining Whether Two Ratios Are Equivalent Simplify to tell whether the ratios are equivalent. A. 3 and 9 15 45 B. 14 and 16 49 36 3 3÷ 3 = = 15 15 ÷ 3 9 9÷ 9 = = 45 45 ÷ 9 1 5 14 14 ÷ 7 2 = 49 49 ÷ 7 = 7 16 16 ÷ 4 4 = 36 36 ÷ 4 = 9 1 1 Since = , 5 5 the ratios are equivalent. 2 4 Since , 7 9 the ratios are not equivalent.