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Understanding Ratios and Proportions in Mathematics

This chapter explores the concepts of ratios and proportions in mathematics. A ratio is defined as a comparison of two numbers and can be expressed in various forms including words, colons, fractions, and decimals. Proportions state that two ratios are equal. We discuss how to write ratios in simplest form and the steps to solve proportions through cross multiplication and division. The chapter also includes examples and practical applications, demonstrating how to solve real-world problems using these concepts.

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Understanding Ratios and Proportions in Mathematics

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  1. Chapter 7:Similarity

  2. 7-1Ratios and Proportions Objective To write ratios and solve proportions

  3. Ratio: • A comparison of two numbers • Notation: words, colon, fraction or decimal (b 0) Proportion: • An equation stating two ratios are equal • Example: Write the ratio in simplest form.

  4. Solving a Proportion Steps: 1. Cross multiply 2. Divide Solve the following proportions:

  5. Additional Examples 6120 = 24(x + 50) 714 = 21(x – 23) 6120 = 24x + 1200 714 = 21x – 483 4920 = 24x 1197 = 21x 205 = x 57 = x

  6. 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

  7. Extremes and Means The first and last numbers in a proportion are the extremes. The middle two numbers in a proportion are the means.

  8. Properties of Proportions

  9. Write an equivalent proportion. 7-1 p. 436: 15-31 odd

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