Understanding Ratios and Proportions in Chapter 7
Explore the concept of ratios and proportions in Chapter 7, focusing on writing ratios, solving proportions, and understanding extremes and means. Additional examples and practical applications are provided to enhance learning. Discover how to write equivalent proportions and solve real-world problems using these mathematical principles.
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Presentation Transcript
Chapter 7: Similarity
7-1 Ratios and Proportions Objective To write ratios and solve proportions
Ratio: A comparison of two numbers Notation: words, colon, fraction or decimal (b 0) a a: b to b a b Proportion: An equation stating two ratios are equal Example: 4= 2 Write the ratio in simplest form. 6 3
Solving a Proportion 56 x Steps: 1. Cross multiply 19= 133 x = 133 133 = 19 1064 56 2. Divide x = 8 x Solve the following proportions: x 30 5 18 = x 3 7 49 4 10 = = = 56 8 = 7 x x x x = 17 5 .
Additional Examples + 306 50 =x 51 23 =x 24 20 21 14 6120 = 24(x + 50) 714 = 21(x 23) 6120 = 24x + 1200 4920 = 24x 714 = 21x 483 1197 = 21x 205 = x 57 = x
Example 1 In a photograph, Dan is 2.5 inches tall and his sister Emma is 1.5 inches tall. Dan s actual height is 70 inches. What is Emma s actual height? Dan s actual height Dan s picture height 2.5 70 = x 1.5 Emma s actual height Emma s picture height 2.5x = 105 x = 42 inches
Extremes and Means The first and last numbers in a proportion are the extremes. The middle two numbers in a proportion are the means.
