8 2 Finding Percents PreAlgebra HOMEWORK Page 407

8 -2 Finding Percents Pre-Algebra HOMEWORK Page 407 #17 -27 & Spiral Review Pre-Algebra

8 -2 Finding Percents Our Learning Goal Students will be able to determine and construct fractions, decimals, and percents by understanding their relationships, solving for the unknown, solving increase and decrease, solving sales tax/total cost contextual problems and compute simple interest. Pre-Algebra

8 -2 Finding Percents Our Learning Goal Assignments • Learn to relate decimals, fractions, & percents (8 -1) • Learn to find percents (8 -2) • Learn to find a number when the percent is known (8 -3) • Learn to find percent increase and decrease (8 -4) • Learn to estimate with percents (8 -5) • Learn to find commission, sales tax, and withholding tax (8 -6) • Learn to compute simple interest (8 -7) Pre-Algebra

8 -2 Finding Percents Learning Goal Scale Students are able to determine & construct fractions, decimals, & percents: 4 • • • Clear understanding their relationships Able to solve for the unknown Understands how to solve for increase & decrease Calculating solving sales tax/total cost contextual problems Computing simple interest Pre-Algebra 3 • • • Understands their relationships Some solving for the unknown Difficulty solving for increase & decrease 2 • • Understands their relationships Difficulty solving for the unknown 1 • Some • understanding their relationships 0 Even with help, no understanding or skill demonstrated

8 -2 Finding. Percents Warm Up Problem of the Day Lesson Presentation Pre-Algebra

8 -2 Finding Percents Warm Up Rewrite each value as indicated. 1. 24 as a percent 50 2. 25% as a fraction 48% 1 4 3. 3 as a decimal 0. 375 8 4 4. 0. 16 as a fraction 25 Pre-Algebra

8 -2 Finding Percents Problem of the Day A number between 1 and 10 is halved, and the result is squared. This gives an answer that is double the original number. What is the starting number? 8 Pre-Algebra

8 -2 Finding Percents Today’s Learning Goal Assignment Learn to find percents. Pre-Algebra

8 -2 Finding Percents Relative humidity is a measure of the amount of water vapor in the air. When the relative humidity is 100%, the air has the maximum amount of water vapor. At this point, any additional water vapor would cause precipitation. To find the relative humidity on a given day, you would need to find a percent. Pre-Algebra

8 -2 Finding Percents Additional Example 1 A: Finding the Percent One Number Is of Another A. What percent of 220 is 88? Method 1: Set up an equation to find the percent. p 220 = 88 p= 88 220 p = 0. 4 Set up an equation. Solve for p. 0. 4 is 40%. So 88 is 40% of 220. Pre-Algebra

8 -2 Finding Percents Additional Example 1 B: Finding the Percent One Number Is of Another B. Eddie weighs 160 lb, and his bones weigh 24 lb. Find the percent of his weight that his bones are. Think: What number is to 100 as 24 is to 160? part number = 100 whole n = 24 160 100 n 160 = 100 Substitute. 160 n = 2400 Pre-Algebra Set up a proportion. 24 Find the cross products.

8 -2 Finding Percents Additional Example 1 Continued n = 2400 160 n = 15 15 24 = 100 160 Solve for n. The proportion is reasonable. So 15% of Eddie’s weight is bone. Pre-Algebra

8 -2 Finding Percents Try This: Example 1 A A. What percent of 110 is 11? Method 1: Set up an equation to find the percent. p 110 = 11 p= 11 110 p = 0. 1 So 11 is 10% of 110. Pre-Algebra Set up an equation. Solve for p. 0. 1 is 10%.

8 -2 Finding Percents Try This: Example 1 B B. Jamie weighs 140 lb, and his bones weigh 21 lb. Find the percent of his weight that his bones are. Think: What number is to 100 as 21 is to 140? part number = 100 whole n = 21 140 100 n 140 = 100 Substitute. 140 n = 2100 Pre-Algebra Set up a proportion. 21 Find the cross products.

8 -2 Finding Percents n = 2100 140 n = 15 15 21 = 100 140 Solve for n. The proportion is reasonable. So 15% of Jamie’s weight is bone. Pre-Algebra

8 -2 Finding Percents Additional Example 2 A: Finding a Percent of a Number A. After a drought, a reservoir had only 66 2 3 % of the average amount of water. If the average amount of water is 57, 000 gallons, how much water was in the reservoir after the drought? Choose a method: Set up an equation. Think: What number is 66 2 % of 57, 000? 3 w = 66 2% 3 57, 000 w = 2 57, 000 3 Pre-Algebra Set up an equation. 2 2 66 3% is equivalent to 3.

8 -2 Finding Percents Additional Example 2 A Continued 114, 000 w= = 38, 000 3 The reservoir contained 38, 000 gallons of water after the drought. Pre-Algebra

8 -2 Finding Percents Additional Example 2 B: Finding Percents B. Ms. Chang deposited $550 in the bank. Four years later her account held 110% of the original amount. How much money did Ms. Chang have in the bank at the end of the four years? Choose a method: Set up a proportion. 110 a = 100 550 110 550 = 100 Set up a proportion. 60, 500 = 100 a Pre-Algebra a Find the cross products.

8 -2 Finding Percents Additional Example 2 B Continued 605 = a Solve for a. Ms. Chang had $605 in the bank at the end of the four years. Pre-Algebra

8 -2 Finding Percents Try This: Example 2 A A. After a drought, a river had only 50 2 3 % of the average amount of water flow. If the average amount of water flow is 60, 000 gallons per day, how much water was flowing in the river after the drought? Choose a method: Set up an equation. Think: What number is 50 2 % of 60, 000? 3 w = 50 2% 3 60, 000 Set up an equation. w = 0. 506 60, 000 50 Pre-Algebra 2 % is equivalent to 0. 506. 3

8 -2 Finding Percents Try This: Example 2 A w = 30, 400, 000 The water flow in the river was 30, 400, 000 gallons per day after the drought. Pre-Algebra

8 -2 Finding Percents Try This: Example 2 B B. Mr. Downing deposited $770 in the bank. Four years later his account held 120% of the original amount. How much money did Mr. Downing have in the bank at the end of the four years? Choose a method: Set up a proportion. 120 a = 100 770 120 770 = 100 92, 400 = 100 a Pre-Algebra Set up a proportion. a Find the cross products.

8 -2 Finding Percents Try This: Example 2 B Continued 924 = a Solve for a. Mr. Downing had $924 in the bank at the end of the four years. Pre-Algebra

8 -2 Finding Percents Lesson Quiz Find each percent to the nearest tenth. 1. What percent of 33 is 22? 66. 7% 2. What percent of 300 is 120? 40% 3. 18 is what percent of 25? 72% 4. The volume of Lake Superior is 2900 mi 3 and the volume of Lake Erie is 116 mi 3. What percent of the volume of Lake Superior is the volume of Lake Erie? 4% Pre-Algebra