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Ratios, Unit Rate, and Proportions

Ratios, Unit Rate, and Proportions. Constructed Response Assessment October 17th. 7 5. Day 1: Ratios. A ratio is a comparison of two quantities using division. . Ratios can be written in three different ways: 7 to 5, 7:5, and Order matters when writing a ratio.

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Ratios, Unit Rate, and Proportions

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  1. Ratios, Unit Rate, and Proportions Constructed Response Assessment October 17th

  2. 7 5 Day 1: Ratios A ratio is a comparison of two quantities using division. Ratios can be written in three different ways: 7 to 5, 7:5, and Order matters when writing a ratio. Find the ratio of boys to girls in Donnelly’s class.

  3. Practice: Write each problem in 3 different ways. Lucky Ladd Farms has: 16 cows, 8 sheep, and 6 pigs • cows to sheep • pigs to total animals • sheep to pigs Always simplify your ratio to the lowest term.

  4. Ratios: • The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak. • For every vote candidate A received, candidate C received nearly three votes. Make a table or model to represent one of the above situations.

  5. Day 2: RATIOS Remember, a ratio makes a comparison. The ratio of green aliens to total aliens is 3 to 7. ****Make sure you write the ratio just like they ask for it!**** The ratio of total aliens to purple aliens is 7 to 4. Not 4 to 7

  6. Use the picture to write the ratios being asked • 1. What is the ratio of blue balloons to red balloons? • 2. What is the ratio of total balloons to orange balloons? • 3. What is the ratio of yellow balloons to total balloons? • 4. What is the ratio of green balloons to purple balloons?

  7. Day 3: Equivalent Ratios Ratios that make the same comparison are equivalent ratios. To check whether two ratios are equivalent, you can write both in simplest form. 20 cars : 30 trucks 80 : 120 10 : 15 2 : 3

  8. shirts jeans 24 ÷ 3 9 ÷ 3 Check It Out! Example 1 Write the ratio 24 shirts to 9 jeans in simplest form. Write the ratio as a fraction. 24 9 = 8 3 Simplify. = = 8 3 The ratio of shirts to jeans is , 8:3, or 8 to 3.

  9. 8 30 30 7 1 2 12 45 Possible answer: , Possible answer: , 4 15 7 21 3. 4. 1 3 14 42 Lesson Quiz: Part I Write each ratio in simplest form. 1. 22 tigers to 44 lions 2. 5 feet to 14 inches Find a ratios that is equivalent to each given ratio.

  10. 12 15 3 27 27 36 2 18 B. A. and and Determining Whether Two Ratios Are Equivalent Simplify to tell whether the ratios are equivalent.

  11. 36 24 16 10 5. 6. 8 64 16 128 and ; yes, both equal 28 18 32 20 8 5 3 2 14 9 8 5 1 8 =  ; yes ; no Lesson Quiz: Part II Simplify to tell whether the ratios are equivalent. and and 7. Kate poured 8 oz of juice from a 64 oz bottle. Brian poured 16 oz of juice from a 128 oz bottle. Are the ratios of poured juice to starting amount of juice equivalent?

  12. Day 4: RATES A rate is a ratio that compares quantities that are measured in different units. This spaceship travels at a certain speed. Speed is an example of a rate. This spaceship can travel 100 miles in 5 seconds is a rate. It can be written 100 miles 5 seconds

  13. RATES A rate is a ratio that compares quantities that are measured in different units. • One key word that often identifies a rate is PER. • Example: Miles per gallon, Points per free throw, • Dollars per pizza, Sticks of gum per pack • What other examples of rates can • your group think of?

  14. Day 5: Unit Rate • Remember: A rate is a ratio that compares two quantities measured in different units (miles, inches, feet, hours, minutes, seconds). • The unit rateis the rate for one unit of a given quantity. Unit rates have a denominator of 1.

  15. UNIT RATES A unit rate compares a quantity to one unit of another quantity. These are all examples of unit rates. 6 tentacles per head 1 tail per body 2 eyes per alien 1 foot per leg 3 windows per spaceship 3 riders per spaceship

  16. Unit Rate 150 heartbeats Rate 2 minutes Unit Rate (divide to get it): 150 ÷ 2 = 75 75 heartbeats to 1minute OR 75 heartbeats per minute

  17. Find the Unit Rate Amy can read 88 pages in 4 hours (rate). What is the unit rate? (How many pages can she read per hour?) 88 pages 22 pages / hour 4 hours

  18. 90 3 The ratio can be simplified by dividing: Try this by yourself! Unit rates are rates in which the second quantity is 1. 90 3 30 1 = 30 miles, 1 hour unit rate: or 30 mi/h

  19. Check It Out! Can you solve? Penelope can type 90 words in 2 minutes. How many words can she type in 1 minute? 90 words 2 minutes Write a rate. Divide to find words per minute. 90 words ÷ 2 2 minutes ÷ 2 45 words 1 minute = Penelope can type 45 words in one minute.

  20. Day 6: Comparing Unit Prices • Unit price is a unit rate used to compare price per item. • Use division to find the unit prices of the two products in question. • The unit rate that is smaller (costs less) is the better value.

  21. Example Juice is sold in two different sizes. A 48-fluid ounce bottle costs $2.07. A 32-fluid ounce bottle costs $1.64. Which is the better buy? $2.07 $0.04 per fl.oz. 0.043125 48 fl.oz. $1.64 $0.05 per fl.oz. 0.05125 32 fl.oz. The 48 fl.oz. bottle is the better value.

  22. Additional Example: Finding Unit Prices to Compare Costs Pens can be purchased in a 5-pack for $1.95 or a 15-pack for $6.20. Which pack has the lower unit price? Divide the price by the number of pens. price for package number of pens $1.95 5 = = $0.39 price for package number of pens $6.20 15 =  $0.41 The 5-pack for $1.95 has the lower unit price.

  23. price for bottle number of ounces price for bottle number of ounces Try this by yourself John can buy a 24 oz bottle of ketchup for $2.19 or a 36 oz bottle for $3.79. Which bottle has the lower unit price? Divide the price by the number of ounces. $2.19 24 =  $0.09 $3.79 36 =  $0.11 The 24 oz jar for $2.19 has the lower unit price.

  24. Day 7: A proportion is an equation stating that two ratios are equal. x 3 Yes, these two ratios DO form a proportion, because the same relationship exists in both the numerators and denominators. 7 21 , 10 30 x 3 ÷ 4 8 2 No, these ratios do NOT form a proportion, because the ratios are not equal. , 9 3 ÷ 3

  25. Proportion • A proportion is an equation stating that two ratios are equal. Example: Example: A piglet can gain 3 pounds in 36 hours. If this rate continues, the pig will reach 18 pounds in _________ hours. Jessica drives 130 miles every two hours. If this rate continues, how long will it take her to drive 1,000 miles?

  26. Proportion Example Joe’s car goes 25 miles per gallon of gasoline. How far can it go on 8 gallons of gasoline? x 8 25 miles = Unit Rate 8 gallons 1 gallon x 8 25 x 8 = 200. Joe’s car can go 200 miles on 8 gallons of gas.

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