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7-1 Ratios and Proportions

7-1 Ratios and Proportions. Writing a Ratio. A ratio is a comparison of two quantities by division. Ratios can be written 3 ways: a / b , a : b , and a to b . Usually a and b are expressed in the same unit and the ratio is in simplest form.

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7-1 Ratios and Proportions

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  1. 7-1 Ratios and Proportions

  2. Writing a Ratio • A ratio is a comparison of two quantities by division. • Ratios can be written 3 ways: a/b, a : b, and a to b. • Usually a and b are expressed in the same unit and the ratio is in simplest form. • The bonsai bald cypress tree is a small version of a full-size tree. A Florida bald cypress stands 118 ft tall. What is the ratio of the height of the bonsai to the full-size tree?

  3. Using a Ratio • The measures of two supplementary angles are in the ratio 1 : 4. What are the measures of the angles?  The measures of two complementary angles are in the ratio 1 : 3. What are the measures of the angles?

  4. Using an Extended Ratio • An extended ratio compares three (or more) numbers. • In the extended ratio a : b : c, the ratios a : b, b : c, and a : c are all equivalent. • The lengths of the sides of a triangle are in the extended ratio 3 : 5 : 6. The perimeter of the triangle is 98 in. What is the length of the longest side?

  5.  The lengths of the sides of a triangle are in the extended ratio 4 : 7 : 9. The perimeter is 60 cm. What are the lengths of the sides?

  6. Equivalent Ratios • If two ratios are equivalent, you can write an equation stating that they are equal. • This equation is called a proportion. • The first and last numbers in a proportion are the extremes. • The middle two numbers are the means. Cross Product Property: In a proportion, the product of the extremes equals the product of the means.

  7. Solving a Proportion • What is the solution of each proportion?

  8. What is the solution of each proportion?

  9. Geometric Mean (7-4) • For any two positive numbers a and b, the geometric mean is the positive number x such that • What is the geometric mean of 6 and 15? What is the geometric mean of 4 and 18?

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