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Think-Pair-Share :

Think-Pair-Share : How are common fractions, decimals, percents , and ratios alike? How are they different?. Ratios and Proportions. I can define unit rate. I can compute unit rates, including those with fractions.

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Think-Pair-Share :

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  1. Think-Pair-Share: How are common fractions, decimals, percents, and ratios alike? How are they different?

  2. Ratios and Proportions I can define unit rate. I can compute unit rates, including those with fractions.

  3. I can define unit rate.I can compute unit rates, including those involving fractions.______________________________________________________________________________________________________________________________________________ Ratios × Ratio - A comparison of two numbers by division Ratios can be written three different ways: a to b a : b a b Each is read, "the ratio of a to b." Each ratio should be in simplest form. Find the ratio of boys to girls in this class

  4. I can define unit rate.I can compute unit rates, including those involving fractions.______________________________________________________________________________________________________________________________________________ There are 48 animals in the field. Twenty are cows and the rest are horses. Write the ratio in three ways: The number of cows to the number of horses The number of horses to the number of animals in the field Remember to write your ratios in simplest form!

  5. I can define unit rate.I can compute unit rates, including those involving fractions.______________________________________________________________________________________________________________________________________________ There are 27 cupcakes. Nine are chocolate, 7 are vanilla and the rest are strawberry. What is the ratio of vanilla cupcakes to strawberry cupcakes? A 7 : 9 7 27 B 7 11 C 1 : 3 D

  6. I can define unit rate.I can compute unit rates, including those involving fractions.______________________________________________________________________________________________________________________________________________ There are 27 cupcakes. Nine are chocolate, 7 are vanilla and the rest are strawberry. What is the ratio of chocolate cupcakes to total cupcakes? 7 9 A 7 27 B 9 27 C 1 3 D

  7. I can define unit rate.I can compute unit rates, including those involving fractions.______________________________________________________________________________________________________________________________________________ There are 27 cupcakes. Nine are chocolate, 7 are vanilla and the rest are strawberry. What is the ratio of total cupcakes to vanilla cupcakes? 27 to 9 A B 7 to 27 27 to 7 C D 11 to 27

  8. I can define unit rate.I can compute unit rates, including those involving fractions.______________________________________________________________________________________________________________________________________________ Equivalent Ratios Return to Table of Contents

  9. I can define unit rate.I can compute unit rates, including those involving fractions.______________________________________________________________________________________________________________________________________________ Equivalent ratios have the same value 3 : 2 is equivalent to 6: 4 1 to 3 is equivalent to 9 to 27 5 35 6 is equivalent to 42

  10. I can define unit rate.I can compute unit rates, including those involving fractions.______________________________________________________________________________________________________________________________________________ There are two ways to determine if ratios are equivalent. 1. Common Factor = 4 12 5 15 x 3 = 4 12 5 15 x 3 Since the numerator and denominator were multiplied by the same value, the ratios are equivalent

  11. I can define unit rate.I can compute unit rates, including those involving fractions.______________________________________________________________________________________________________________________________________________ 2. Cross Products = 4 12 5 15 Since the cross products are equal, the ratios are equivalent. 4 x 15 = 5 x 12 60 = 60

  12. I can define unit rate.I can compute unit rates, including those involving fractions.______________________________________________________________________________________________________________________________________________ 4 is equivalent to 8 ? 9 18 True False

  13. I can define unit rate.I can compute unit rates, including those involving fractions.______________________________________________________________________________________________________________________________________________ 5is equivalent to 30 ? 9 54 True False

  14. I can define unit rate.I can compute unit rates, including those involving fractions.______________________________________________________________________________________________________________________________________________ 1:7 is equivalent to 10,which is equivalent to 5 to 65? 70 True False

  15. I can define unit rate.I can compute unit rates, including those involving fractions.______________________________________________________________________________________________________________________________________________ Rates Return to Table of Contents

  16. I can define unit rate.I can compute unit rates, including those involving fractions.______________________________________________________________________________________________________________________________________________ Rates Rate: a ratio of two quantities measured in different units Examples of rates: 4 participants/2 teams 5 gallons/3 rooms 8 burgers/2 tomatoes

  17. I can define unit rate.I can compute unit rates, including those involving fractions.______________________________________________________________________________________________________________________________________________ Unit Rates Unit rate: Rate with a denominator of one Often expressed with the word "per" Examples of unit rates: 34 miles/gallon 2 cookies per person 62 words/minute

  18. I can define unit rate.I can compute unit rates, including those involving fractions.______________________________________________________________________________________________________________________________________________ Finding a Unit Rate Six friends have pizza together. The bill is $63. What is the cost per person? Hint: Since the question asks for cost per person, the cost should be first, or in the numerator. $63 6 people Since unit rates always have a denominator of one, rewrite the rate so that the denominator is one. $63 6 6 people 6 $10.50 1 person ÷ ÷ = The cost of pizza is $10.50 per person

  19. I can define unit rate.I can compute unit rates, including those involving fractions.______________________________________________________________________________________________________________________________________________ Sixty cupcakes are at a party for twenty children. How many cupcakes per person?

  20. I can define unit rate.I can compute unit rates, including those involving fractions.______________________________________________________________________________________________________________________________________________ The recipe calls for 6 cups of flour for every four eggs. How many cups of flour are needed for one egg?

  21. I can define unit rate.I can compute unit rates, including those involving fractions.______________________________________________________________________________________________________________________________________________ Sarah rode her bike 14 miles in hour. What is Sarah's unit rate in miles per hour?

  22. I can define unit rate.I can compute unit rates, including those involving fractions.______________________________________________________________________________________________________________________________________________ Red apples cost $3.40 for ten. Green apples cost $2.46 for six. Which type of apple is cheaper per apple? Show your work! Red apples A B Green apples

  23. Ratios and Proportions I can define unit rate. I can compute unit rates, including those with fractions. I can determine if two quantities have a proportional relationship.

  24. I can define unit rate.I can compute unit rates, including those involving fractions.______________________________________________________________________________________________________________________________________________ Tahira and Brendan going running at the track. Tahira runs 3.5 miles in 28 minutes and Brendan runs 4 miles in 36 minutes. Who runs at a faster pace (miles per minute)? Show your work! Tahira A B Brendan

  25. I can define unit rate.I can compute unit rates, including those involving fractions.______________________________________________________________________________________________________________________________________________ Textbook Practice Shoulder Partners Pages 276-277 #5-8 Check with a teacher before moving on. #12-14 Check with a teacher before moving on. #23-27

  26. Ratios and Proportions I can define unit rate. I can compute unit rates, including those with fractions. I can determine if two quantities have a proportional relationship.

  27. I can compute unit rates, including those involving fractions. I can determine if two quantities have a proportional relationship.______________________________________________________________________________________________________________________________________________ Proportions Return to Table of Contents

  28. I can compute unit rates, including those involving fractions. I can determine if two quantities have a proportional relationship.______________________________________________________________________________________________________________________________________________ Proportions A proportion is an equation that states that two ratios are equivalent. Example: 2 12 3 18 = = 5 15 9 27

  29. I can compute unit rates, including those involving fractions. I can determine if two quantities have a proportional relationship.______________________________________________________________________________________________________________________________________________ Cross out all of the ratios that are not equivalent.

  30. I can compute unit rates, including those involving fractions. I can determine if two quantities have a proportional relationship.______________________________________________________________________________________________________________________________________________ If one of the numbers in a proportion is unknown, mental math can be used to find an equivalent ratio. Example 1: = 2 6 3 x x 3 = 2 6 3 x Hint: To find the value of x, multiply 3 by 3 also. = 2 6 3 9 x 3

  31. I can compute unit rates, including those involving fractions. I can determine if two quantities have a proportional relationship.______________________________________________________________________________________________________________________________________________ If one of the numbers in a proportion is unknown, mental math can be used to find an equivalent ratio. Example : = 28 7 32 x ÷ 4 = Hint: To find the value of x, divide 32 by 4 also. 28 7 32 x = 28 7 328 ÷ 4

  32. I can compute unit rates, including those involving fractions. I can determine if two quantities have a proportional relationship.______________________________________________________________________________________________________________________________________________ Use mental math to solve the proportion using equivalent ratios.

  33. I can compute unit rates, including those involving fractions. I can determine if two quantities have a proportional relationship.______________________________________________________________________________________________________________________________________________ In a proportion, the cross products are equal. = 530 2 12 = 5 12 2 30 60 60 =

  34. I can compute unit rates, including those involving fractions. I can determine if two quantities have a proportional relationship.______________________________________________________________________________________________________________________________________________ Proportions can also be solved using cross products. = 4 12 5 x Cross multiply Solve for x 4x = 5 12 4x = 60 x = 15 Example 2 = 7 x 8 48 7 48 = 8x 336 = 8x 42 = x Cross multiply Solve for x

  35. I can compute unit rates, including those involving fractions. I can determine if two quantities have a proportional relationship.______________________________________________________________________________________________________________________________________________ Use cross products to solve the proportion.

  36. I can compute unit rates, including those involving fractions. I can determine if two quantities have a proportional relationship.______________________________________________________________________________________________________________________________________________ Textbook Practice Page 285 #1-8 Check with a teacher before moving on. Page 289 #1-5 Check with a teacher before moving on. Page 289 #28-31

  37. Ratios and Proportions I can define unit rate. I can compute unit rates, including those with fractions. I can determine if two quantities have a proportional relationship.

  38. Real-Life Proportions The Crayola crayon company can make 2400 crayons in 4 minutes. How many crayons can they make in 15 minutes? A scooter can travel 2 miles in 3 minutes. At that rate, how many minutes would it take to travel 62 miles? A can of tomato paste weighs 16 ounces and/or 452 grams. This depends on whether you use English measurement or SI.  Find the number of ounces in a kilogram (1000 grams).

  39. I can compute unit rates, including those involving fractions. I can determine if two quantities have a proportional relationship.______________________________________________________________________________________________________________________________________________ • A company can buy packages of 500 sheets of paper for $4. At that rate, how much paper can be bought for $2000? • Mixing 4 ml of red paint and 15 ml of yellow paint makes orange paint. How much red would be needed if you use 100 ml of yellow paint?  • A fast typist can type 120 words in 100 seconds. In 180 seconds, how many words could be typed? • Carol spends 17 hours in a 2-week period practicing her culinary skills. How many hours does she practice in 5 weeks? • In the year 2000, there were 8.7 deaths per 1000 residents in the United States. If there were 281,000,000 residents in the U.S. during 2000, how many people died that year? • In a shipment of 400 parts, 14 are found to be defective. How many defective parts should be expected in a shipment of 1000? • A piece of cable 8.5 cm long weighs 52 grams. What will a 10-cm length of the same cable weigh? • Mary can read 22 pages in 30 minutes. How long would it take her to read a 100 page book? Write your answer in hours and minutes and round to the nearest minute, if needed.

  40. I can compute unit rates, including those involving fractions. I can determine if two quantities have a proportional relationship.______________________________________________________________________________________________________________________________________________ • A company can buy packages of 500 sheets of paper for $4. At that rate, how much paper can be bought for $2000?

  41. I can compute unit rates, including those involving fractions. I can determine if two quantities have a proportional relationship.______________________________________________________________________________________________________________________________________________ • 2.) Mixing 4 ml of red paint and 15 ml of yellow paint makes orange paint. How much red would be needed if you use 100 ml of yellow paint? 

  42. I can compute unit rates, including those involving fractions. I can determine if two quantities have a proportional relationship.______________________________________________________________________________________________________________________________________________ • 3.) A fast typist can type 120 words in 100 seconds. In 180 seconds, how many words could be typed?

  43. I can compute unit rates, including those involving fractions. I can determine if two quantities have a proportional relationship.______________________________________________________________________________________________________________________________________________ • 4.) Carol spends 17 hours in a 2-week period practicing her culinary skills. How many hours does she practice in 5 weeks?

  44. I can compute unit rates, including those involving fractions. I can determine if two quantities have a proportional relationship.______________________________________________________________________________________________________________________________________________ • 5.) In the year 2000, there were 8.7 deaths per 1000 residents in the United States. If there were 281,000,000 residents in the U.S. during 2000, how many people died that year?

  45. I can compute unit rates, including those involving fractions. I can determine if two quantities have a proportional relationship.______________________________________________________________________________________________________________________________________________ • 6.) In a shipment of 400 parts, 14 are found to be defective. How many defective parts should be expected in a shipment of 1000?

  46. I can compute unit rates, including those involving fractions. I can determine if two quantities have a proportional relationship.______________________________________________________________________________________________________________________________________________ • 7.) A piece of cable 8.5 cm long weighs 52 grams. What will a 10-cm length of the same cable weigh?

  47. I can compute unit rates, including those involving fractions. I can determine if two quantities have a proportional relationship.______________________________________________________________________________________________________________________________________________ • 8.) Mary can read 22 pages in 30 minutes. How long would it take her to read a 100 page book? Write your answer in hours and minutes and round to the nearest minute, if needed.

  48. Ratios and Proportions I can define unit rate. I can compute unit rates, including those with fractions. I can determine if two quantities have a proportional relationship.

  49. I can compute unit rates, including those involving fractions. I can determine if two quantities have a proportional relationship.______________________________________________________________________________________________________________________________________________ • Review • There are a total of 44 phones for sale at the store. Use the following table to answer questions 1 and 2. • Color # of Phones • Pink 22 • Blue 19 • Silver ? • What is the ratio of blue phones to silver phones? • What is the ratio of pink phones to the number of phones for sale?

  50. I can compute unit rates, including those involving fractions. I can determine if two quantities have a proportional relationship.______________________________________________________________________________________________________________________________________________ • Review • Circle the ratios that are in simplest form. • Underline the ratios that are equivalent to 5 to 8 • 8:32 _7_ 15 to 24 • 14 • 4 to 10 30:48 _6_ • 9 • 9 to 8 15:12 _45_ • 72

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