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CHAPTER
5.1 Ratio and Proportions
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2. Ratios as Fractions
A ratio is the quotient of two quantities. In fact, ratios are no different from fractions, except that ratios are sometimes written using a notation other than fractional notation. For example, the ratio of 1 to 2 can be written as 1 to 2 or or 1: 2 These ratios are all read as “the ratio of 1 to 2.”

3. Writing a Ratio as a Fraction
The order of the quantities is important when writing ratios. To write a ratio as a fraction, write the first number of the ratio as the numerator of the fraction and the second number as the denominator.
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4. Writing a Ratio as a Fraction
Write the ratio of 12 to 17 using fractional notation. Solution The ratio is
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5. Writing a Ratio as a Fraction in Simplest Form
Write each ratio as a fraction in simplest form. a. $15 to $10 b. 4 ft to 24 in. c. Solution Write each ratio as a fraction. Convert unlike units to like units. a. b. 2
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6. Writing a Ratio as a Fraction in Simplest Form
Write each ratio as a fraction in simplest form. a. $15 to $10 b. 4 ft to 24 in. c. Solution Write each ratio as a fraction. Convert unlike units to like units. c.
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7. Using Ratios in Geometry
Given the rectangle shown: a. Find the ratio of its width to its length. b. Find the ratio of its length to its perimeter. Solution a. ratio of width to length
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8. Using Ratios in Geometry
Given the rectangle shown: a. Find the ratio of its width to its length. b. Find the ratio of its length to its perimeter. Solution b. length to perimeter perimeter = = 24 feet
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Solving Proportions
An equation stating that two ratios are equal is called a proportion. The first and last numbers in a proportion are the extremes. The middle two numbers are the means. Cross products are the product of the means and also the product of the extremes.
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10. Theorem 5.1 Means-Extremes Property
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Solving a Proportion
Solve each proportion for the variable. a. b. Solution a. b.
The check is left to the student.
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Geometric Means
For any two positive numbers a and b, the geometric mean of a and b is the positive number x such that
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13. Finding the Geometric Mean
What is the geometric mean of 6 and 15? a. 90 b. c. d. 30 Solution Let x be the geometric mean. Use the definition of geometric mean to set up a proportion. Then solve for x.
The correct answer is b.
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14. Properties of Proportions
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15. Using Properties of Proportions
Use the Properties of Proportions to write three proportions equivalent to Solution Property 1: Write the reciprocal of each ratio: Property 2: Switch the means:
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16. Using Properties of Proportions
Use the Properties of Proportions to write three proportions equivalent to Property 3: In each ratio, add the denominator to the numerator:
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17. Writing Equivalent Proportions
In the diagram, What ratio completes the equivalent proportion Justify your answer. Solution a. Notice the positions of x and y in the first proportion. Now see where x and y appear in the second proportion. Using Property 2:
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18. Writing Equivalent Proportions
In the diagram, What ratio completes the equivalent proportion Justify your answer. Using cross products:
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19. Proportional Segments
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20. Proportional Segments
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