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Percents, Proportionality and Similarity Warm – up Making Choices Power point Pleasing Proportions Guided Percents, Proportionality and Similarity Warm – up Making Choices Power point Pleasing Proportions Guided Practice Make It A Match

Making Choices Warm Up The table shows the size and cost of two different Making Choices Warm Up The table shows the size and cost of two different boxes of Nutty Wafer Chews. Box Cost Size of Bags Large-sized $4. 89 13 ounce Regular-size $2. 59 6. 5 ounce 1. Which package costs less per ounce? small-size, costs $0. 398 ≈ $0. 40 per ounce rounded to the nearest cent large-size, costs $0. 376 ≈ $0. 38 per ounce rounded to the nearest cent 2. Would it make sense to buy one large package or two regular size packages? Explain. One large 13 -ounce box cost $4. 89 and two regular boxes is 2(6. 5 ounces)=13 -ounces but the cost 2($2. 59)=$5. 18 which is more than the large size box. It makes more sense to buy one large-size box.

Ratio and Proportions Equal Ratios Proportions Unit Rates Ratio and Proportions Equal Ratios Proportions Unit Rates

Look at the two examples. Do they represent equal ratios? Explain how you decided Look at the two examples. Do they represent equal ratios? Explain how you decided if they were equal or not equal ratios. 120 x 5 300 You can find equal ratios by multiplying or dividing the numerator and denominator by the same number or use cross products. Equal ratios are like equivalent fractions. They name the same quantity. 300 ÷ 25

Why are these two fractions equivalent? How can you verify their equivalence? 3 x Why are these two fractions equivalent? How can you verify their equivalence? 3 x 10 = 6 x 5 30 = 30 If the cross products are equal then it is a proportion. Proportions Two equal ratios form a proportion.

Are these proportions? Discuss how to determine if these are proportions. 1) 5 = Are these proportions? Discuss how to determine if these are proportions. 1) 5 = 60 3 36 3 x 60 = 5 x 36 2) 8 4 15 = 8 8 x 8 = 15 x 4 180 = 180 64 = 60 The cross products are equal so these are proportional. The cross products are not equal so these are not proportional.

Let’s Solve A Proportion Problem Luis passes out 84 flyers over a 3 -hour Let’s Solve A Proportion Problem Luis passes out 84 flyers over a 3 -hour period. If the number of flyers he passes out remains the same per hour , how many flyers can he pass out in 5 hours? flyers hours 84 = f 3 5 3(f) = 84(5) Set the proportion up with the numerical descriptions. Cross products 3 f =420 Multiply 3 f 3 =420 3 Divide f = 140 flyers in 5 hours

Using Proportions to Solve Problems Camp Dallas USA plans to hire 2 counselors for Using Proportions to Solve Problems Camp Dallas USA plans to hire 2 counselors for every 15 campers. They are expecting 120 campers the first two week, so how many counselors will be needed? What’s being compared? Counselors and campers What word describe each number? 2 counselors, 15 campers, 120 campers What’s missing? The number of counselors for 120 campers Can you set up the two ratios to form the proportion. Always label the numbers. Are all of these proportion correct? Explain why or why not? They are all correct because the cross products for each are the same 15 n and 2 x 120. When solved they will all have the same answer. There will be more than one way to set up any proportion if you keep the comparisons the same on each side of the equal sign.

When the corresponding items are set up correctly on both sides of the equal When the corresponding items are set up correctly on both sides of the equal sign the result will be the same,

Make It A Match Guided Practice 1. An airplane travels at 560 km in Make It A Match Guided Practice 1. An airplane travels at 560 km in 40 minutes. How long will it take to travel 1600 km? Circle all proportions that cannot be used to solve this problem. Be prepared to explain why. a d b c e f

Make It A Match Guided Practice 2. 3. Jogging 5 miles burns 500 calories. Make It A Match Guided Practice 2. 3. Jogging 5 miles burns 500 calories. How many miles will Tanisha need to jog to burn off the 1200 -calorie lunch she ate? Mr. Strange needs 150 graphing calculators for his math class. His budget allows $5, 000 for calculators. He needs to know if he can buy what he needs at the discount store where they are on sale at 8 for $284.

Make It A Match Guided Practice An airplane travels at 560 km in 40 Make It A Match Guided Practice An airplane travels at 560 km in 40 minutes. How long will it take to travel 1600 km? 1. Circle all the proportions that cannot be use to solve this problem. Be prepared to explain why. c a b d e f The cross products are 560(x) and 1600(40).

Make It A Match Guided Practice 2. Jogging 5 miles burns 500 Calories. How Make It A Match Guided Practice 2. Jogging 5 miles burns 500 Calories. How many miles will Tanisha need to jog to burn off the 1200 -Calorie lunch she ate? 3. Mr. Strange needs 150 graphing calculators for his math class. His budget allows $5, 000 for calculators. He needs to know if he can buy what he needs at the discount store where they are on sale at 8 for $284. miles No, he can only buy 140 calculators.