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Ratios, Rates & Proportions

Mathematics, Grade 8

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Ratios & Rates Geometric Proportions Using Conversion Factors Ordering Ratios Equivalent Ratios Numerical Proportions corresponding angles • Numerical Proportions compare two numbers. • Cross products are used to find a missing quantity in a proportion. • A ratio is a comparison of two quantities measured in the same units. • Ratios are used to solve proportions, to find dimensions in similar figures and to determine distances in travel maps. • To order ratios, convert them to decimals or fractions. • Order them from least to greatest: 0.875, 1.20, 1.33 and 1.5 • A conversion factor is a ratio that represents the same quantity but uses different units. The ratios of 1,200 ft per minute into miles per hour and are equivalent. • Rates are used to compare quantities measured with different units. • A unit rate has a denominator of 1. Zoe rode her bike 6 miles in 48 minutes. Example: Convert: • Geometric proportions compare two similar figures. • Similar figures have equal corresponding angles and corresponding sides that are in proportion. • The triangles are similar since their corresponding sides are equivalent. • A cross product is the product of the numerator in one ratio and the denominator in the other ratio. Cross Product Rule • When two ratios are equal, then the cross products, a•d and b•c, are equal. 3 6 1 2 = a b c d = 5 10 1 2 1 2 = = = = 3 5 6 10 = 5 • 6 = 30 3 • 10 = 30 G I H 3 cm 6 cm 4 cm K J L 24 cm 12 cm 16 cm • An equation with two equal ratios is called a proportion. 5 ÷ 10 10 ÷ 10 5 10 5 10 25 50 25 50 = , = 5 • 5 10 • 5 3:2 1.5 = = = • • = 4:3 1.33 = = 7:8 0.875 = = 6:5 1.20 3 2 4 3 7 8 1,200 ft 1,200 • 60 mi 13.63 mi/h 5,280 h 1 min 1,200 ft 5,280 ft 1 min 60 min 1 mi 1 h 6 5 = 6 mi 48 min. 48 min. 6 mi Rate or = 0.125 mi 1 min. 8 min. 1 mi Unit Rate or corresponding sides © Copyright NewPath Learning. All Rights Reserved. 93-4806 www.newpathlearning.com Ratios, Rates & Proportions

\|xiBAHBDy01683qzZ Ratios & Rates Geometric Proportions Using Conversion Factors Ordering Ratios Equivalent Ratios Numerical Proportions • Numerical Proportions compare numbers. • Cross products are used to find a missing quantity in a proportion. • A ratio is a comparison of • Ratios are used to • To order ratios, convert them to decimals or fractions. • Order them from least to greatest: 0.875, 1.20, 1.33 & 1.5 • A conversion factor is a ratio that represents the same quantity but uses different units. The ratios of 1,200 ft per minute into miles per hour and are equivalent. • Rates are used to • A unit rate has a denominator of 1 . Zoe rode her bike 6 miles in 48 minutes. Example: Convert: • Geometric proportions compare two similar figures. • Similar figures have equal corresponding angles and corresponding sides that are in proportion. • A cross product is the product of the numerator in one ratio and denominator in the other ratio. 3 6 = 5 10 1 2 = = = = 3 5 6 10 = 5 • 6 = 30 3 • 10 = 30 • An equation with two equal ratios is called a proportion. 5 ÷ 10 10 ÷ 10 5 10 5 10 = , = 5 • 5 10 • 5 3:2 = = = • • = 4:3 = = 7:8 = = 6:5 3 2 4 3 7 8 6 5 = Rate or = Unit Rate or . . . G I H 3 cm 6 cm 4 cm K J L 24 cm 12 cm 16 cm . • The triangles are since their corresponding sides are equivalent. . • corresponding angle • corresponding side • cross product numerator • denominator • equation • equivalent ratio • geometric proportion Key Vocabulary Terms • numerical proportion • proportion • rate • ratio • similar figures • unit rate © Copyright NewPath Learning. All Rights Reserved. 93-4806 www.newpathlearning.com Ratios, Rates & Proportions

Ratios, Rates & Proportions

Mathematics, Grade 8

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