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6-2 Fractions, Decimals, and Percents Warm Up Write each fraction in the simplest form. 1. 4 2 10 5 2. 8 4 50 25 3. 75 3 100 4 1 4. 12 36 3 5. 9 3 15 5 6. 18 3 48 8 6-2 Fractions, Decimals, and Percents Problem of the Day Use the clues to find the mystery percent. 1. The product of its digits is 24. 2. It is greater than 1 . 2 3. The sum of its digits is a prime number. 83% 6-2 Fractions, Decimals, and Percents Learn to write decimals and fractions as percents. 6-2 Fractions, Decimals, and Percents The students at Westview Middle School are collecting cans of food for the local food bank. Their goal is to collect 2,000 cans in one month. After 10 days, they have 800 cans of food. What percent of their goal have they reached? 6-2 Fractions, Decimals, and Percents 0 200 1 5 0 0 0 400 0 600 800 2 5 1,000 1,200 1,400 1,600 3 5 4 5 1,800 2,000 5 5 0.2 0.4 0.6 0.8 1.0 20% 40% 60% 80% 100% 800 2 The model shows that 800 out of 2,000 can be written as , , 2000 5 0.4, or 40%. The students have reached 40% of their goal. 6-2 Fractions, Decimals, and Percents Additional Example 1: Writing Decimals as Percents Write 0.7 as a percent. Method 1: Use pencil and paper. 0.7 = 7 70 = 10 100 = 70% Write the decimal as a fraction with a denominator of 100. Write the numerator with a percent sign. 6-2 Fractions, Decimals, and Percents Additional Example 1 Continued Write 0.7 as a percent. Method 2: Use mental math. 0.70 = 70% = 70% Move the decimal point two places to the right and add a percent sign. 6-2 Fractions, Decimals, and Percents Check It Out: Example 1 Write 0.3 as a percent. Method 1: Use pencil and paper. 0.3 = 3 30 = 10 100 = 30% Write the decimal as a fraction with a denominator of 100. Write the numerator with a percent sign. 6-2 Fractions, Decimals, and Percents Check It Out: Example 1 Continued Write 0.93 as a percent. Method 2: Use mental math. 0.30 = 30% = 30% Move the decimal point two places to the right and add a percent sign. 6-2 Fractions, Decimals, and Percents Example 2: Writing Fractions as Decimals Write 5 as a percent. 8 Use pencil and paper. 5 =5÷8 8 = .625 = 62.5% Use division to write the fraction as a decimal. Write the decimal as a percent. Remember! To divide 5 by 8, use long division and place a decimal point followed by a zero after the 5. .625 8 5.00 6-2 Fractions, Decimals, and Percents Check It Out: Example 2 Write 3 as a percent. 5 Use pencil and paper. 3 =3÷5 5 = 0.60 = 60% Use division to write the fraction as a decimal. Write the decimal as a percent. 6-2 Fractions, Decimals, and Percents Check It Out: Example 2 Continued Write 3 as a percent. 5 Use mental math. 3 5 • • 20 20 = 60 100 Write an equivalent fraction with a denominator of 100. = 60% Write the numerator with a percent sign. 6-2 Fractions, Decimals, and Percents Additional Example 3: Ordering Rational Numbers 4 3 Order 17%, 0.25, , 0.1, 5 , and 20% from 4 least to greatest. Step 1: Write the numbers as decimals with the same number of decimal places. 17% = 0.17 0.25 = 0.25 3 = 0.75 4 0.1 = 0.10 4 = 0.80 5 20% = 0.20 6-2 Fractions, Decimals, and Percents Additional Example 3 Continued 4 Order 17%, 0.25, 3 , 0.1, , and 20% from 5 least to greatest. 4 Step 2: Compare the decimals. 0.10 < 0.17 < 0.20 < 0.25 < 0.75 < 0.80 From least to greatest, the numbers are: 0.1, 17%, 20%, 0.25, 3 , 4 . 4 5 Remember: Put the answer back into original form, do NOT leave them all as decimals!!! 6-2 Fractions, Decimals, and Percents Additional Example 4: Choosing a Method of Computation Decide whether using pencil and paper, mental math, or a calculator is most useful when solving the following problem. Then solve. If 27 out of 50 people have the newspaper delivered to their home, what percent of these people have the newspaper delivered to their home? 27 Think: 27 ÷ 50 divides evenly. 50 Using pencil and paper is the best method. = 0.54 27 out of 50 = Write the decimal as a percent. = 54% 54% of the people have the newspaper delivered to their home. 6-2 Fractions, Decimals, and Percents Lesson Quiz for Student Response Systems 1. Which of the following represents 0.52 as a percent? A. 52% B. 26% C. 13% D. 4% 6-2 Fractions, Decimals, and Percents Lesson Quiz for Student Response Systems 2. Which of the following represents 0.08 as a percent? A. 80% B. 40% C. 28% D. 8% 6-2 Fractions, Decimals, and Percents Lesson Quiz for Student Response Systems 3. Which of the following represents 7 as a 10 percent? A. 7% B. 17% C. 70% D. 77% 6-2 Fractions, Decimals, and Percents Lesson Quiz for Student Response Systems 2 4. Order 0.2, 14%, 0.63, and in order from 5 least to greatest. A. 0.2, 14%, 2 , 0.63 C. 14%, 0.2, 2 , 0.63 5 5 B. 14%, 0.2, 0.63, 2 5 D. 0.63, 2 , 0.2, 14% 5 6-2 Fractions, Decimals, and Percents Lesson Quiz for Student Response Systems 5. Choose the most useful method of computation and then solve. If 45 out of 90 students surveyed prefer Algebra to Geometry, what percent of these students prefer Algebra? A. calculator; 30% B. calculator; 50% C. mental math; 30% D. mental math; 50%