1. PRE-ALGEBRA

2. Lesson 6-5 Warm-Up

3. PRE-ALGEBRA How do you find the percent of a number using a proportion?? You can use a proportion to solve any percent problem. To solve a percent problem using a proportion, first create a proportion table. Instead of using “known” and “unknown” on the side, it is suggested that you use “part” and “whole”. Since percent is always out of 100, the whole percent is always 100. The whole number is always the number after the word “of”. Example: What is 22% of 250? 55 So 22% of 250 is 55 #% Part (Known)x 22 Whole (Unknown)250 100 = Proportion. x 250 22 100 100 x = 250 22 Cross products are equal. 100x = 5500 Simplify. = Divide both sides by 100.. 100x 100 5500 100 1 x = 55 Simplify. Proportions and Percents (6-5) 11

4. PRE-ALGEBRA How can you check the answer to a percent problem?? Proportions and Percents (6-5) To check whether the answer to a percent problem is reasonable, break up the percent into a smaller compatibles percents, like 1% or 10%, and use estimation to see whether multiples of those smaller numbers are close to your answer. Example: Is 22% of 250 equals 55 reasonable? Check: 10% of 250 is 25 (move the decimal over 1 place to the left to find 10%) and 1% of 250 is 2.5 (move the decimal over 2 place to the left to find 1%). 22% = 10% + 10% + 1% + 1% = 25 + 25 + 2.5 + 2.5 = 55. The answer is reasonable.

5. PRE-ALGEBRA Find 23% of 158. 100 n = 158(23)Write cross products. 100n = 3634Simplify. 23% of 158 is 36.34. = Use the table or model to write a proportion. n 158 23 100 = Divide each side by 100. 100n 100 3684 100 Proportions and Percents LESSON 6-5 Additional Examples #% Part (Known) n23 Whole (Unknown) 158100 n = 36.34Simplify. 1 1 Check. Is the answer reasonable? 10% of 158 is 15.8  16 and 1% of 158 is 1.58  2. 23% = 10%+10%+1%+1%+1%  16 + 16 +2 + 2 + 2  38, which is close to 36, so the answer is reasonable. 1 36.34

6. PRE-ALGEBRA 34 p = 100 28Write cross products. 34p = 2800Simplify. Use the table or model to =write a proportion. Hint: The word after “of” is the whole number. 28 34 p 100 = Divide each side by 34. 34p 34 2800 34 Proportions and Percents LESSON 6-5 Additional Examples #% Part (Known) 28p Whole (Unknown) 34100 p  82.35Simplify. 1 1 What percent of 34 is 28? Round to the nearest tenth of a percent. 28 is approximately 82.4% of 34. Check. Is the answer reasonable? 10% of 34 is 3.4, and 80% is 10% 8 = 3.4 8  27, which is close to 28, so the answer is reasonable.

7. PRE-ALGEBRA 72 n = 100 216Write cross products. 72n = 21,600Simplify. Use the table or model to =write a proportion. Hint: The word after “of” is the whole number. 216 n 72 100 = Divide each side by 72. 72n 72 21,600 72 Proportions and Percents LESSON 6-5 Additional Examples #% Part (Known) 21672 Whole (Unknown) n100 n = 300Simplify. 1 1 1 216 216 is 72% of what number? 216 is 72% of 300. Check. Is the answer reasonable? 10% of 300 is 30 and 1% of 300 is 3. 70% = 10% +10%+10%+10%+10%+10%+10%+1%+1% = 30 + 30 + 30 + 30 + 30 + 30 + 30 + 3 + 3 = 216. The answer is reasonable.

8. PRE-ALGEBRA A tile floor has 90 blue tiles, which is 15% of all the tiles in the floor. How many tiles are in the floor in all? 15n = 100(90)Write cross products. x = 600Simplify. The floor has 600 tiles in all. Check. Is the answer reasonable? The problem says the number of blue tiles is 15%. 10% of 600 is 60 and 5% of 600 is 30, so 15% is 60 + 30 = 90. The answer is reasonable. = Write a proportion. 90 n 15 100 = Divide each side by 15. 9000) 15 15n 15 Proportions and Percents LESSON 6-5 Additional Examples #% Part 9015 Whole n100 1 1 600 1 Make a proportion table or a model. Hint: 90 is smaller than the total, so it is the “part” number.

9. PRE-ALGEBRA Solve. 1.Find 47% of 2,400.2.What percent of 700 is 1,498? 3.6 is 3% of what number? 4. On Saturday, 1,150 people ate at a restaurant. The previous day, only 68% of that number ate there. About how many people ate at the restaurant on Friday? 1,128 200 214% 782 Lesson Quiz Proportions and Percents LESSON 6-5