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Chapter 5 - Ratio, Proportion, and Measurement

# Chapter 5 - Ratio, Proportion, and Measurement - Chapter 5...

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Chapter 5 Ratio, Proportion, and Measurement

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Martin-Gay, Basic College Mathematics with Early Integers 2 5.1 – Ratios 5.2 – Proportions 5.3 – Proportions and Problem Solving 5.4 – Length: U.S. and Metric Systems 5.5 – Weight and Mass: U.S. and Metric Systems 5.6 – Capacity: U.S. and Metric Systems 5.7 – Conversions between the U.S. and Metric Systems Chapter Sections
§ 5.1 Ratios

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Martin-Gay, Basic College Mathematics with Early Integers 4 Writing Ratios as Fractions EXAMPLE EXAMPLE SOLUTION SOLUTION Write the ratio of 7 to 12 as a fraction. 12 to 7 12 7 Remember that order is important while writing ratios. is not the same as 12 7 . 7 12
Martin-Gay, Basic College Mathematics with Early Integers 5 Writing Ratios in Simplest Form SOLUTION SOLUTION EXAMPLE EXAMPLE Write the ratio 25 to 150 as a fraction in it’s simplest form. 150 to 5 2 150 25 6 25 1 25 = = 6 1

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Martin-Gay, Basic College Mathematics with Early Integers 6 Writing Rates as Fractions Definition Example Rates : Used to compare different kinds of quantities. feet 15 shrubs 5 feet 3 shrubs 1
Martin-Gay, Basic College Mathematics with Early Integers 7 Finding Unit Rates Definition Example Unit Rate : A rate with a denominator of 1. 25 miles per hour EXAMPLE Write 275 miles in 11 hours as a unit rate. SOLUTION SOLUTION hours 11 miles 275 275 11 22 - 55 55 - 5 0 hour per miles 25 or hours 1 miles 5 2 2

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Martin-Gay, Basic College Mathematics with Early Integers 8 - Finding Unit Prices Definition Example Unit Price : When a unit rate is “money per item.” \$0.29 per apple EXAMPLE EXAMPLE Find the unit price of \$0.87 for 3 apples. SOLUTION SOLUTION apples 3 87 . 0 \$ 87 . 0 3 6 - 27 27 29 0 apple per \$0.29 or apples 1 29 . 0 \$ 2 . 0
§ 5.2 Proportions

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Martin-Gay, Basic College Mathematics with Early Integers 10 Writing Proportions Definition Example Proportion : A statement that 2 ratios or rates are equal. page 1 errors 1.5 pages 8 errors 12 =
Martin-Gay, Basic College Mathematics with Early Integers 11 Determining Whether Proportions Are True EXAMPLE EXAMPLE 7 4 12 7 = Determine whether is a true proportion by cross multiplying. SOLUTION SOLUTION 4 12 7 7 12 7 7 4 = ? 49 = 48 = Since the cross products are not equal, are not equivalent proportions. 7 4 and 12 7

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Martin-Gay, Basic College Mathematics with Early Integers 12 Finding Unknown Numbers in Proportions Definition Example Step 1 : Set the cross products equal to each other. Step 2 : Divide both sides of the resultant equation by the number multiplied by n. 3 n 9 12 = 12 3 9 = n 36 9 = n 9 9 4 = n
§ 5.3 Proportions and Problem Solving

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Martin-Gay, Basic College Mathematics with Early Integers 14 Solving Problems by Writing Proportions EXAMPLE EXAMPLE SOLUTION SOLUTION There are 76 milligrams of cholesterol in a 3-ounce serving of skinless chicken.
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Chapter 5 - Ratio, Proportion, and Measurement - Chapter 5...

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