Lesson 6-4 Warm-Up

Fractions, Decimals, and Percents (6-4) What is “percent”? How do you write a percent as a fraction or a decimal? percent: a ratio that compares a number to 100 To write a percent as a fraction, make the numerator the percent and the denominator 100 (“out of 100”). Then, simplify the fraction. To write a percent as a decimal: turn it into a fraction first (then you can turn the fraction into a decimal by dividing) or simply move the decimal two places to the left. Example: The following model shows 41 out of 100 squares shaded, or 41% of the big square shaded. Example: Write 125% each percent as a fraction and a decimal. Write as a fraction with a denominator of 100. Then, simplify the fraction. Write the improper fraction as a mixed number. Divide the numerator by the denominator to change a fraction into a decimal. 125 100 25 5 4 = 5 4 = 1 1 4 5  4 = 1.25

Write each percent as a fraction or a mixed number. Fractions, Decimals, and Percents LESSON 6-4 Additional Examples Write each percent as a fraction or a mixed number. a. 30% Write as a fraction with a denominator of 100. 30 100 Simplify. 3 10 b. 175% Write as a fraction with a denominator of 100. 175 100 Simplify. 7 4 1 Write as a mixed number. 3 4

7.3% = Write as a fraction with a denominator of 100. Fractions, Decimals, and Percents LESSON 6-4 Additional Examples Express 7.3% as a decimal. 7.3% = Write as a fraction with a denominator of 100. 7.3 100 = 007.3   Divide by moving the decimal point left two places. You may need to write one or more zeros. = 0.073

Fractions, Decimals, and Percents (6-4) (7-1) How do you write a fraction as a percent? To write a fraction as a percent, find an equal fraction with a denominator of 100 (if the denominator is 100, the numerator will always be the percent, since percent means “out of 100”) or make a proportion and use cross products. Example: According to the school cafeteria, 6 out of 25 students bring their lunch to school. What percent of the students bring their lunches to school? Method 1: Proportion # % Known (Part) 6 x Unknown (Whole) 25 100 = Proportion . 6 25 x 100 25 • x = 6 • 100 Cross products are equal. 25x = 600 Simplify. 1 24 = Divide both sides by 25. . 25x 25 600 1 1 x = 24 Simplify. 24% of the students bring their lunches..

Fractions, Decimals, and Percents (6-4) How do you write a fraction as a percent? Method 2: Equal Fractions = Write an equal fraction with a denominator of 100 (since percents have 100 in the denominator. 6 25 100 = Multiply the numerator by the same number that you multiply the denominator by to find the equivalent fraction with a denominator of 100. 6 25 24 100 4 24% of the students bring their lunches..

= Write a proportion. Percents have 100 in the denominator. Fractions, Decimals, and Percents LESSON 6-4 Additional Examples 7 20 Write as a percent. 7 20 = Write a proportion. Percents have 100 in the denominator. p 100 = Find the fraction with denominator 100 that is equal to . 7 20 35 100 5 7 20 = = 35% Write using a percent symbol. 35 100

0.5714 Divide the numerator by the denominator. Fractions, Decimals, and Percents LESSON 6-4 Additional Examples Four out of seven members of the chess club won a game at the district tournament. What percent of the chess club members won a game? Write a fraction. 4 7 0.5714 Divide the numerator by the denominator. 57.14%   Write as a percent. About 57% of the chess club members won a game.

“Fractions, Decimals, and Percents” (6-4) (7-1) How do you write a decimal as a percent? To write a decimal as a percent, write the decimal as a fraction and change the fraction into a percent using proportions or equal fractions or move the decimal two places to the right. Method 1: Change the decimal to a fraction Example: Write 0.076 as a percent. Method 2: Move the decimal 2 places to the right. 0.076 = Write the decimal as a fraction the way you read it. 76 1000 = Divide the numerator by the same number that you divide the denominator by to find the equivalent fraction with a denominator of 100. 76 1000 7.6 100 10 0.076 = 7.6% 0. 0 7 6 Jump the decimal two places to the right. = 7 . 6 %

Write each decimal as a percent. Fractions, Decimals, and Percents LESSON 6-4 Additional Examples Write each decimal as a percent. a. 0.16 0.16 = 16 100 Write the decimal as a fraction. = 16% Write as a percent. b. 0.03 0.03 = 3 100 Write the decimal as a fraction. = 3% Write as a percent.

Method 1 Rewrite as a fraction. Fractions, Decimals, and Percents LESSON 6-4 Additional Examples Express 0.412 as a percent. Method 1 Rewrite as a fraction. 0.412 = 412 1,000 = 412 ÷ 10 1,000 ÷ 10 = 41.2 100 = 41.2% Method 2 Move the decimal point. 0.412 = 41.2%

Write each percent as a fraction or mixed number, and as a decimal. Fractions, Decimals, and Percents LESSON 6-4 Lesson Quiz Write each percent as a fraction or mixed number, and as a decimal. 1. 325% 2. 1.1% Write each as a percent. 3. 2.01 4. 5. Six out of fifteen students own skateboards. What percent of students own skateboards? 13 4 , or 3 ; 3.25 1 11 1,000 ; or 0.011 3 5 201% 60% 40%