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Fraction, Decimal, & Percent Equivalencies Coach Lesson 4 Also see textbook pages 108 โ 110, & 202 โ 205. Jeff Rhodus 6th Grade Elsanor Elementary Getting the Idea! Fractions, decimals, and percents can all be used to show parts of a whole. The word percent means โof 100.โ That is why percents can be written as fractions with denominators of 100. The symbol for percent is %. This chart shows some common fraction-decimal-percent equivalencies. Fraction Decimal 1 100 1 10 1 8 1 5 Percent Fraction Decimal Percent 0.01 1% 0.1 10% 1 4 1 2 3 4 0.125 12.5% 0.2 20% 1 1 or 1 0.25 25% 0.5 50% 0.75 75% 1.0 100% To convert a fraction or mixed number to a decimal, find an equivalent fraction or improper fraction that has a denominator of 10 or 100, then write the decimal. Example 1: Convert the fraction 3/5 to a decimal. Strategy: Find the equivalent fraction with a denominator of 10. Step 1: Multiply the numerator and denominator by 2 to find the equivalent fraction with a denominator of 10. 3 3x5 6 = = 5 5 x 2 10 Step 2: Write the decimal. 6 = 0.6 10 Solution: The decimal equivalent of 3/5 is 0.6 Example 2: Convert the decimal 1.44 to a mixed number. Strategy: Write the decimal as an improper with a denominator of 100, then simplify. Step 1: Since the decimal goes to the hundredths place, remove the decimal point and write the digits as the numerator and 100 as the denominator. 1.44 = 144 100 Step 2: Change the improper fraction to a mixed number. Then simply the fraction part by dividing the numerator and denominator by 4. 144 44 44 : 4 11 =1 = 100 100 100 : 4 25 144 11 =1 100 25 11 Solution: The mixed number equivalent of 1.44 is 1 25 Example 3: Write 23/100 as a percent. Strategy: Look at the denominator of the fraction. It is 100. Since the denominator of 23/100 is 100, the percent is the same as the numerator. Solution: 23/100 = 23% Example 4: Convert the fraction 9/20 to a percent. Strategy: Find an equivalent fraction with a denominator of 100, then write the percent. Step 1: Multiply the numerator and denominator by 5 to find the equivalent fraction with a denominator of 100. 9 = 9 x 5 = 45 20 20 x 5 100 Step 2: Change the fraction to a percent. Since the denominator is 100, the percent is the same as the numerator. 45 = 45% 100 Solution: 9/20 = 45% To convert a percent to a fraction, first convert the percent to a decimal. Then convert the decimal to a fraction. Remember that percents over 100% will be written as mixed numbers since they are greater than a whole. Example 5: Convert 140% to a mixed number. Strategy: Write the percent as an improper fraction with a denominator of 100, then simplify. Step 1: Remove the percent symbol and write the digits as the numerator and 100 as the denominator. 140 140 = 100 Step 2: Change the improper fraction to a mixed number. Then simply the fraction part by dividing the numerator and denominator by 20. 140 = 100 40 1100 40 : 20 2 = 100 : 20 5 140 = 2 1 100 5 Solution: 140% = 1 2 5 To convert a decimal to a percent, move the decimal point two places to the right and insert a percent symbol(%) after the number. Insert zeros as placeholders when necessary. Example 6: Convert the decimal 0.7 to a percent. Strategy: Move the decimal point two places to the right. Step 1: Think of place value. 0.7 = 0.70 Move the decimal point in 0.70 two places to the right. 0.70. Step 2: Insert a percent symbol at the end of the number. 70% Solution: 0.7 = 70%