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7 Math Vocabulary # 3 (Ratios and Proportions).notebook 7th Grade Math Vocabulary Ahrens Constant of Proportionality A constant ratio (unit rate) in any proportional relationship Equations: Ratios and Proportions (3 , 45) y = 5 x k = y x Ratios and Proportions Glossary y x y = kx or k = 5 y = kx 45 = k3 k = 15 Constant of Proportionality Equivalent Ratios Equivalent Ratios Ratios that have the same value Two ratios that have the same value, even though they represent different amounts. 3 6 = 1 2 = 4 8 4 12 4 1 = 4 3 Disagree Ratio 1out of 3 Ratio A comparison of two or more values. Can be written as a fraction, decimal, percent, or with a colon, the word "to" or the words "out of". 4 out of 5 4 to 1 4 5 .8 4:1 80% is equivalent to is equivalent to Equivalent Ratios Ratio Agree 10 to 25 = 2 to 5 Equivalent Ratios Dr. Opinions 3 out of 9 1 out of 5 1 to 4 1 5 .2 1:4 20% A comparison of two numbers by division 3 different ways: "the ratio of a to b" a to b a : b a b 20 to 48 There are 48 animals in the field. Twenty are cows and the rest are horses. What is the number of cows to the total number of animals? 20:48 20 48 Ratio 1 7 Math Vocabulary # 3 (Ratios and Proportions).notebook Ahrens Rate Rate A ratio that compares quantities in different units. A ratio of two quantities measured in different units One minute for every 60 seconds. min 1 2 3 $8 per adult movie ticket. sec 60 120 180 adults 1 $ 2 3 8 16 24 Expect to drive 35 miles for every hour you drive. 3 participants/2 teams 7 burgers/2 tomatoes 5 gallons/3 rooms Rate Rate Unit Rate Unit Rate A comparison of two measurements when one of the terms has a value of 1. Rate with a denominator of one One minute for every 60 seconds. 1 min:60 sec $8 per adult movie ticket. $8 1 adult 35 miles per 1 hour 62 words/minute 34 miles/gallon 3 cookies per person Unit Rate Unit Rate Proportion Part to Part Ratio An equation that states that two ratios are equivalent A comparison of part of a whole to the rest of the whole. 14 2 = 3 21 1 20 = 2 40 Proportion 5 x3 15 = 8 x3 x x = 24 1 ― 8 3:5 1 ― 8 1 ― 8 1 ― 8 1 ― 8 1 ― 8 1 ― 8 1 ― 8 red:white red white 3 5 Part to Part Ratio 2 7 Math Vocabulary # 3 (Ratios and Proportions).notebook 1 ― 8 Part to Whole Ratio Percent A comparison of part of a whole the total. A ratio which is always based on the total being 100. When broken down, percent means out of 100. 3:8 1 ― 8 1 ― 8 1 ― 8 1 ― 8 1 ― 8 1 ― 8 Ahrens 3 8 red:total 1 ― 8 red total Per = out of 25% 1 =1/100 Cent = 100 25 100 .25 or one hundredth $.01 Part to Whole Ratio Percent Conversion Factor Simplest Form A number used to multiply or divide a quantity to convert from one system of measurement to another. When the GCF of both parts of a ratio is one. 21 days = 3 weeks To convert days into weeks, divide by 7. Qts Pts 16 in 12 1.5 ft Divide by 2 4 12 4 1 = 4 3 3 out of 9 10 to 25 is the same as 1out of 3 Both are divisible by 5 9 qts = 8.5 pts = 2 to 5 Conversion Factor Simplest Form Similar Scale Two shapes that are the same shape but different sizes The ratio of a drawing to the real life measurement congruent drawing real life (actual) :10 1 Scale not similar! Drawn Horse 150mm high Real Horse 1500mm high Similar Scale 3 7 Math Vocabulary # 3 (Ratios and Proportions).notebook Ahrens Population Density A unit rate of people per square mile NJ = 8,791,894 people NJ = 7,790 square miles Population Area Population Area = 8,791,894 7,790 = 1,129 people per square mile Population Density 4