Slide 1 / 208 Slide 2 / 208 6th Grade Ratios, Proportions & Percents 2015-11-16 www.njctl.org Slide 3 / 208 Slide 4 / 208 Table of Contents Click on the topic to go to that section Writing Ratios Equivalent Ratios Rates & Unit Rates Using Ratios to Convert Measurements Writing Ratios Converting Unit Ratios Percents & Fractions Percents & Decimals Using Percents Glossary Return to Table of Contents Slide 5 / 208 Slide 6 / 208 Ratios Ratios Ratios can be written three different ways: What do you know about ratios ? _ a to b a : b a When have you seen or used ratios? b Each is read, "the ratio of a to b." Each ratio should be in simplest form .
Slide 7 / 208 Slide 8 / 208 Ratios Ratios The ratio of wings to beaks in the bird house at the zoo was: Click for Interactive Video 2 to 1 This is because for every 2 wings there was 1 beak. This can also be written as: 2:1 or 2 __ 1 Slide 9 / 208 Slide 10 / 208 Table for Questions 1 What is the ratio of lizards to bears at the zoo? This table shows the number of some of the animals at the zoo. Use the information in the table to answer the A 2 : 3 next several response questions. Answer animal number B 3 to 5 tigers 4 C 3 : 2 animal number lizards 3 D 3 : 24 bears 2 tigers 4 monkeys 6 lizards 3 birds 9 bears 2 monkeys 6 birds 9 Slide 11 / 208 Slide 12 / 208 2 What is the ratio of tigers to birds at the zoo? 3 What is the ratio of lizards to tigers at the zoo? animal number A 4 : 3 tigers 4 A The ratio of lizards to tigers is three to animal number lizards 3 B 4 to 9 four. tigers 4 bears 2 Answer B The ratio of tigers to lizards is four to C 9 to 4 lizards 3 monkeys 6 three. D 9 : 6 birds 9 bears 2 C The ratio of lizards to tigers is three to monkeys 6 seven. Answer birds 9 D There are three lizards and four tigers.
Slide 13 / 208 Slide 14 / 208 Simplest Form 4 What is the ratio of bears to tigers at the zoo? (Be sure your answer is in simplified form.) Ratios should always be written in simplest form. A animal number animal number The ratio of monkeys to birds is: 6 _ 9 tigers 4 tigers 4 Answer B This can be simplified by dividing lizards 3 lizards 3 each by 3. bears 2 bears 2 C 6 2 = monkeys 6 monkeys 6 9 3 birds 9 birds 9 D There are 2 monkeys for every 3 birds. Slide 15 / 208 Slide 16 / 208 Problem is from: 6.RP Games at Recess 5 What is the ratio of monkeys to tigers at the Click for link for commentary and solution. zoo? The students in Mr. Hill's class played games at recess. (Be sure your answer is in simplified form.) 6 boys played soccer A 2 : 3 Answer 4 girls played soccer animal number 2 boys jumped rope B 4 to 6 tigers 4 8 girls jumped rope C 6 to 4 lizards 3 Afterward, Mr. Hill asked the students to compare the boys D 3 : 2 bears 2 and girls playing different games. monkeys 6 Mika said, birds 9 "Four more girls jumped rope than played soccer." Chaska said, "For every girl that played soccer, two girls jumped rope." Slide 17 / 208 Slide 18 / 208 Mr. Hill said, "Mika compared the girls by looking at the B. Compare the number of boys who played soccer and difference and Chaska compared the girls using a ratio." jumped rope using a ratio. Write your answer as a sentence as Chaska did. A. Compare the number of boys who played soccer and 6 boys played soccer jumped rope using the difference. Write your answer as a 4 girls played soccer sentence as Mika did. 2 boys jumped rope 6 boys played soccer 8 girls jumped rope 4 girls played soccer 2 boys jumped rope 8 girls jumped rope
Slide 19 / 208 Slide 20 / 208 C. Compare the number of girls who played soccer to the 6 Which ratio matches this sentence? number of boys who played soccer using a ratio. Write your There are 7 girls for every 5 boys on the bus. answer as a sentence as Chaska did. 6 boys played soccer A 7 : 12 4 girls played soccer 2 boys jumped rope B 7 : 5 8 girls jumped rope C 12 : 5 D 5 : 7 Slide 21 / 208 Slide 22 / 208 7 Which ratio matches this sentence? 8 Which ratio matches this sentence? For every 9 students in line, there are 18 legs. The ratio of pencils to students is 3 to 1 A 9 to 18 A B 9 to 27 C 3 to 6 B D 1 to 2 C D Slide 23 / 208 Slide 24 / 208 Two Types of Ratios Ratios There are two types of ratios. Write the ratio for shaded parts to non-shaded parts. Part to Part 3 : 5 click and Part to Whole
Slide 25 / 208 Slide 26 / 208 Ratios 9 Dr. Ruiz has 7 snails and 3 fish in his aquarium. What is the ratio of fish to snails? Write the ratio for shaded to TOTAL number of parts. A 7 to 3 B 7 to 10 3 : 8 click C 3 to 7 D 3 to 10 Slide 27 / 208 Slide 28 / 208 11 10 Dr. Ruiz has 7 snails and 3 fish in his aquarium. If Dr. Ruiz adds 2 fish to this tank, what is the new ratio What is the ratio of snails to the total number of of guppies to the total number of animals? animals? A 7 to 3 A 1 to 2 B 7 to 10 B 5 to 12 C 3 to 7 C 3 to 7 D 3 to 10 D 3 to 10 Slide 29 / 208 Slide 30 / 208 12 Javier has stickers on the front of his folder. Use 13 Javier has stickers on the front of his folder. Use the stickers to answer the questions. the stickers to answer the questions. What is the What is the ratio of to ? ratio of to total number of stickers? A 6 : 1 A 4 : 15 B 1 : 6 B 4 : 19 C 1 : 2 C 1 : 5 D 6 : 7 D 4 : 9
Slide 31 / 208 Slide 32 / 208 14 Mrs. Heller's class has 14 girls and 13 boys. 15 At the playground there are 9 kids and 4 adults. What is the ratio of boys to total number of students? What is the ratio of adults to total number of people? A 4 to 9 A B 4 to 13 B C 9 to 4 D 9 to 13 C D Slide 33 / 208 Slide 34 / 208 16 The ratio of two people's height remains the same, 17 The ratio of two peoples ages remains the same, whether whether measured in feet or meters. they are compared this year, next year, or last year. True True False False Slide 35 / 208 Slide 36 / 208 Equivalent Ratios Equivalent ratios have the same value. 1 : 4 is equivalent to 2 : 8 Equivalent Ratios 3 to 2 is equivalent to 27 to 18 5 35 7 is equivalent to 49 Return to Table of Contents
Slide 37 / 208 Slide 38 / 208 Equivalent Ratios Equivalent Ratios There are two ways to determine if ratios are equivalent. 2. Cross Products 4 12 1. Common Factor 5 15 4 12 5 15 Since the cross products are equal, the ratios are x 3 equivalent. 4 12 4 x 15 = 5 x 12 5 15 60 = 60 x 3 Since the numerator and denominator were multiplied by the same value, the ratios are equivalent Slide 39 / 208 Slide 40 / 208 18 ) is equivalent to 19 ) is equivalent to True True False False Slide 41 / 208 Slide 42 / 208 20 ) is equivalent to 21 ) is equivalent to True True False False
Slide 43 / 208 Slide 44 / 208 23 Javier has stickers on the front of his folder. Use 22 Which ratio is equivalent to ? the stickers to answer the questions. Which two ratios below are equivalent? A B A to C B to C to D D to E to Slide 45 / 208 Slide 46 / 208 24 Mr. Smith's class has a girl to boy student ratio of 3:5. If 25 In the list below, what is the ratio of baking powder to salt. Write your answer in simplest form. Mr. Smith's class has 16 students, how many students are girls? Sugar Cookie Ingredients 1 1/2 c butter 3/4 tsp baking powder 2 c sugar 1 1/4 c flour 4 eggs 1/4 tsp salt Slide 47 / 208 Slide 48 / 208 Make a Table Make a Table You can also make a table of ratio values to find equivalent ratios. If the ratio of boys to girls in a school is 2 to 3. You can use this ratio to find the number of girls there would be for any number of boys. Cost of Strawberries First, determine the ratio. Quarts of Cost Strawberries Boys 2 20 200 220 400 How much will 1 $3.00 Girls 3 30 300 330 3 quarts of strawberries 2 $6.00 be? 3 How much will 4 4 quarts of If there are 400 boys, strawberries how many girls be? would there be?
Slide 49 / 208 Slide 50 / 208 Make a Table 26 Jude swims 1 lap for every 3 laps that Avery swims. Which table shows this relationship? Alexis wants some pink paint. In order to make the pink paint she needs 3 parts red paint to 1 part white paint. Answer Complete the chart showing the amounts she could use. Jude 1 5 9 13 A Avery 3 7 13 17 Red 1 3 9 15 30 60 150 Jude 1 5 9 13 B Avery 3 25 45 65 White 1/3 1 3 5 10 20 50 Jude 1 5 9 13 C Avery 3 15 27 39 Slide 51 / 208 Slide 52 / 208 27 What value goes in the empty box for 28 What value goes in the empty box for the ratio table below? the ratio table below? Answer Answer 1 2 3 4 2 4 6 8 5 10 ? 20 7 ? 21 28 Slide 53 / 208 Slide 54 / 208 29 Keyboards are made up of black and white keys. If the pattern shown continues, how many white keys will appear on a keyboard with 25 black keys? Rates & Unit Rates Return to Table of Contents
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