Slide 1 / 206 Slide 2 / 206 7th Grade Ratios and Proportions 2015-11-18 www.njctl.org Slide 3 / 206 Slide 4 / 206 Table of Contents Click on the topic to go to that section Writing Ratios Equivalent Ratios Rates Proportions Writing Ratios Direct & Indirect Relationships in Tables & Graphs Constant of Proportionality Writing Equations for Proportions Understanding Graphs of Proportions Problem Solving Scale Drawings Return to Similar Figures Table of Glossary Contents Slide 5 / 206 Slide 6 / 206 Ratios Ratios Ratio - A comparison of two numbers by division What do you know about ratios? Ratios can be written three different ways: a to b a : b a b Each is read, "the ratio of a to b." When have you seen or used ratios? Each ratio should be in simplest form. Find the ratio of boys to girls in this class
Slide 7 / 206 Slide 8 / 206 Ratios Video Writing Ratios There are 48 animals in the field. Twenty are cows and the rest are horses. Click for a ratios video Write the ratio in three ways: a. The number of cows to the number of horses b. The number of horses to the number of animals in the field Remember to write your ratios in simplest form! Slide 9 / 206 Slide 10 / 206 Remember to write your ratios in simplest form! Remember to write your ratios in simplest form! 1 There are 27 cupcakes. Nine are chocolate, 7 are 2 There are 27 cupcakes. Nine are chocolate, 7 are vanilla and the rest are strawberry. What is the ratio vanilla and the rest are strawberry. What is the ratio of Answer of vanilla cupcakes to strawberry cupcakes? Answer chocolate & strawberry cupcakes to vanilla & chocolate cupcakes? A 7 : 9 A 20 7 B 16 27 11 B 7 C 7 11 5 C D 1 : 3 4 16 D 20 Slide 11 / 206 Slide 12 / 206 Remember to write your ratios in simplest form! Remember to write your ratios in simplest form! 4 There are 27 cupcakes. Nine are chocolate, 7 are 3 There are 27 cupcakes. Nine are chocolate, 7 are vanilla and the rest are strawberry. What is the ratio vanilla and the rest are strawberry. What is the ratio Answer of total cupcakes to vanilla cupcakes? Answer of chocolate cupcakes to total cupcakes? 7 A A 27 to 9 9 7 B 7 to 27 B 27 9 C 27 to 7 C 27 1 D 11 to 27 D 3
Slide 13 / 206 Slide 14 / 206 Equivalent Ratios Equivalent ratios have the same value. Equivalent Ratios 3 : 2 is equivalent to 6: 4 1 to 3 is equivalent to 9 to 27 Return to Table of 5 35 Contents 6 is equivalent to 42 Slide 15 / 206 Slide 16 / 206 Equivalent Ratios Equivalent Ratios There are two ways to determine if ratios are equivalent. 2. Cross Products 1. Common Factor 4 12 4 12 5 15 5 15 x 3 4 12 Since the cross products are equal, the ratios are 5 15 equivalent. 4 x 15 = 5 x 12 x 3 60 = 60 Since the numerator and denominator were multiplied by the same value, the ratios are equivalent Slide 17 / 206 Slide 18 / 206 5 4 is equivalent to 8 6 5 is equivalent to 30 9 18 9 54 True True Answer Answer False False
Slide 19 / 206 Slide 20 / 206 7 8 18:12 is equivalent to 9, which is equivalent to 36 2 is equivalent to 10 , which is equivalent to 40 6 24 24 120 480 Answer Answer True True False False Slide 21 / 206 Slide 22 / 206 9 1:7 is equivalent to 10 , which is equivalent to 5 to 65 70 Answer Rates True False Return to Table of Contents Slide 23 / 206 Slide 24 / 206 Rates Video Rates Rate : a ratio of two quantities measured in different units Click for video Examples of rates: 4 participants/2 teams 5 gallons/3 rooms 8 burgers/2 tomatoes
Slide 25 / 206 Slide 26 / 206 Finding a Unit Rate Unit Rates Six friends have pizza together. The bill is $63. Unit rate : Rate with a denominator of one Often expressed with the word "per" What is the cost per person? Hint: Since the question asks for cost per person, Examples of unit rates: the cost should be first, or in the numerator. $63 34 miles/gallon 6 people click 2 cookies per person Since unit rates always have a denominator of one, rewrite the rate so that the denominator is one. 62 words/minute $63 ÷ 6 click to reveal 6 people ÷ 6 The cost of pizza is $10.50 per person $10.50 1 person Slide 27 / 206 Slide 28 / 206 Click for Practice 10 Sixty cupcakes are at a party for twenty children. How many cupcakes per person? Answer Slide 29 / 206 Slide 30 / 206 11 John's car can travel 94.5 miles on 3 gallons of gas. 12 The snake can slither 240 feet in half a day. How many feet can the snake move in an hour? How many miles per gallon can the car travel? Answer Answer
Slide 31 / 206 Slide 32 / 206 13 There are five chaperones at the dance of 100 14 The recipe calls for 6 cups of flour for every four eggs. students. How many students per chaperone are How many cups of flour are needed for one egg? there? Answer Answer Slide 33 / 206 Slide 34 / 206 15 Sarah rode her bike miles in hour. 16 An airplane's altitude changed -378 feet over 7 minutes. What was the mean change of altitude in feet per What is Sarah's unit rate in miles per hour? minute? Answer From PARCC PBA sample test non-calculator #3 Slide 35 / 206 Slide 36 / 206 17 A -ounce hamburger patty has grams of 18 Rosy waxes of her car with bottle of car wax. protein, and 6 ounces of fish has 32 grams of protein. At this rate, what fraction of the bottle of car wax will Determine the grams of protein per ounce for each type Rosy use to wax her entire car? of food. A hamburger patty has approximately _____________ A 0.2 grams of protein per ounce. B 4.5 The fish has approximately C 5.7 _____________ grams of protein D 21.0 F 0.2 per ounce. E 25.5 G 5.3 H 6.0 I 26.0 J 32.0 From PARCC EOY sample test calculator #4 From PARCC PBA sample test calculator #1
Slide 37 / 206 Slide 38 / 206 Compare Rates Compare Rates We often use unit rates to easily compare rates. Jim traveled 480 miles on a full tank of gas. His gas tank holds 15 gallons. Example: Sebastian and Alexandra both work during the summer. Tara traveled 540 miles on a full tank of gas. Her gas Sebastian worked 26 hours one week and earned tank holds 18 gallons. $188.50 before taxes. Alexandra worked 19 hours and earned $128.25 before taxes. Who earns more per hour Which person's car gets better gas mileage? at their job? Sebastian Alexandra Jim Tara click click Sebastian earned more per hour Slide 39 / 206 Slide 40 / 206 19 Tahira and Brendan going running at the track. Tahira 20 Red apples cost $3.40 for ten. Green apples cost $2.46 for six. runs 3.5 miles in 28 minutes and Brendan runs 4 miles in 36 minutes. Who runs at a faster pace (miles per Which type of apple is cheaper per apple? hour)? Answer Answer Show your work! Show your work! A Tahira A Tahira B Brendan B Brendan Slide 41 / 206 Slide 42 / 206 21 Fruity Oats is $2.40 for a 12 oz. box. 22 Two families drive to their vacation spot. The Jones Snappy Rice is $3.52 for a 16 oz. box. family drives 432 miles and used 16 gallons of gas. The Which cereal is cheaper per ounce? Alverez family drives 319 miles and uses 11 gallons of gas. Which family got more miles per gallon of gas? Answer Answer Show your work! Show your work! A Fruity Oats B Snappy Rice A Jones Family B Alverez Family
Slide 43 / 206 Slide 44 / 206 23 Mariella typed 123 words in 3 minutes. Population Density Enrique typed 155 words in 5 minutes. Who typed more words per minute? Answer Show your work! Population Density : A unit rate of people per square mile This data is compiled by the US Census Bureau every 10 years and is used when determining the number of Representatives each state gets in the House of Representatives. A Mariella B Enrique Slide 45 / 206 Slide 46 / 206 Click for National Geographic Web Site Population Density Slide 47 / 206 Slide 48 / 206 Population Density Population Density We know that New Jersey has a population density of 1,129 people To calculate population density: per square mile. Use the links below to compare this data with two other states. Population Population Density = Find the population of the state. · Area Click here for population data Click here for area data NJ = 8,791,894 people Find the area of the state. · NJ = 7,790 square miles Divide · Population 8,791,894 = 1,129 people per square mile = Area 7,790
Slide 49 / 206 Slide 50 / 206 24 The population of Newark, NJ is 278,980 25 The population of Moorestown, NJ is people in 24.14 square miles. What is its 19,509 people in 15 square miles. What is population density? its population density? Answer Answer Newark, NJ Moorestown, NJ Slide 51 / 206 Slide 52 / 206 26 The population of Waco, TX is 124,009 27 The population of Argentina is 40,091,359 people in 75.8 square miles. What is its people and Argentina is 1,042,476 square population density? miles. What is t he population density? Answer Answer Waco Slide 53 / 206 Slide 54 / 206 28 The population of San Luis, Argentina is 432,310 people and the Provence is 29,633 square miles. What is the population density? Answer Proportions Return to Table of Contents San Luis, Argentina
Recommend
More recommend
