6-3 Finding Percents Warm Up Warm Up California Standards California Standards Lesson Presentation Lesson PresentationPreview

6-3 Finding Percents Warm Up Rewrite each value as indicated. 1. as a percent 2. 25% as a fraction (reduced) 3. as a decimal as a fraction (reduced) 48%

6-3 Finding Percents NS1.3 Convert fractions to decimals and percents and use these representations in estimations, computations, and applications. California Standards

6-3 Finding Percents What percent of 92 is 69? Additional Example 1: Finding the Percent One Number Is of Another (Read) Think: What number is to 100 as 69 is to 92? = number 100 part whole Set up a proportion. Substitute. n = n  92 = 100  69 92n = 6900 Find the cross products. Method 1: Set up a proportion to find the percent. Simplify.

6-3 Finding Percents Additional Example 1 Continued n = 75 Divide both sides by is 75% of 92. Simplify. 92n =

6-3 Finding Percents What percent of 92 is 69? Method 2: Set up an equation. p  92 = 69 Let p represent the percent. Divide both sides by 92. p = 0.75 Simplify. 69 is 75% of p 92 = Additional Example 1 Continued percent  whole = part Set up an equation.

6-3 Finding Percents Additional Example 1 Continued Check 69 = 69 75% of 92 is %  92 = 69 Substitute 75% for p. ? 0.75  92 = 69 Write as a decimal and multiply. ?

6-3 Finding Percents Method 3: Show as a fraction. Convert the fraction to a percent by dividing. What percent of 92 is 69? 69 / 92 Set up fraction. Part over whole. 69 / 92 = 0.75 Divide numerator by denominator 0.75 x 100 = 75% Multiply by 100 to get percent.

6-3 Finding Percents What percent of 140 is 21? (Notes) Think: What number is to 100 as 21 is to 140? = number 100 part whole Set up a proportion. Let n represent the percent. n = n  140 = 100  n = 2100 Find the cross products. Check It Out! Example 1 Method 1: Set up a proportion. Simplify.

6-3 Finding Percents n = 15 Divide both sides by is 15% of 140. Check It Out! Example 1 Continued Simplify. 140n =

6-3 Finding Percents Check It Out! Example 1 Continued What percent of 140 is 21? Method 2: Set up an equation. p  140 = 21 Let p represent the percent. Divide both sides by 140. p = 0.15 Simplify. 21 is 15% of p 140 = percent  whole = part Set up an equation.

6-3 Finding Percents Check It Out! Example 1 Continued 21 = 21 15% of 140 is approximately %  140 = 21 Substitute 15% for p. ? 0.15  140 = 21 Write as a decimal and multiply. ? Check

6-3 Finding Percents Check It Out! Example 1 Continued What percent of 140 is 21? Method 3: Show as a fraction. Convert the fraction to a percent by dividing. 21 / 140 Set up fraction. Part over whole. 21 / 140 = 0.15 Divide numerator by denominator 0.15 x 100 = 15% Multiply by 100 to get percent.

6-3 Finding Percents Additional Example 2A: Recreation Application First, change Aimee and Ken’s amounts to percents. = 20% and 0.31 = 31% Four friends volunteered to cut the grass around their neighbor’s house. Jay cut 23% of the grass, Aimee cut of the grass, Ken cut 0.31 of the grass, and Bryn cut the rest. What percent of the grass did Bryn cut? 1515 Next - since the whole lawn is 100% - subtract the percents you know from 100% to find the remaining percent. 100% – 23% – 20% – 31% = 26%. Bryn cut 26% of the grass.

6-3 Finding Percents When solving a problem when the percent is greater than 100, the number you are looking for will be greater than the number given. Helpful Hint

6-3 Finding Percents Check It Out! Example 3B Ms. Marvin has a savings account with approximately $210,000 in it. Mr. Parson has 30% of the amount of Ms. Marvin’s savings account. What is the amount of Mr. Parson’s savings account? Choose a method: Set up a proportion. = x 210,000 Set up a proportion. 30  210,000 = 100  x Find the cross products. Think: 30% = 30/100 is proportionate to what part of $210,000? = percent 100 part (is) whole (of)

6-3 Finding Percents Check It Out! Example 3B Continued Mr. Parson has $63,000 in his savings account. 6,300,000 = 100x Simplify. = 6,300, x 100 Divide both sides by ,000 = xSimplify.

6-3 Finding Percents Lesson Quiz: Part I Find each percent. 1. What percent of 33 is 22? 2. Of Earth’s 197 million mi 2 of surface area, about 139 million mi 2 is water. Find the percent of Earth’s surface that is covered by water. 3. The Ramirez family bought a large bag of oranges during their trip to Florida. Jorge ate of the oranges, Ann ate 0.18 of the oranges, Mrs. Ramirez ate 22% of the oranges, and Mr. Ramirez ate the rest. What percent of the oranges did Mr. Ramirez eat? 70.6% 20% 66 %

6-3 Finding Percents Lesson Quiz: Part II 4. Rada is 170% as tall as her brother Raj. Raj is 0.82 m tall. To the nearest tenth of a meter, how tall is Rada? 5. 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? 1.4 m 4%