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