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Fraction, Decimal, & Percent Equivalencies

Fraction, Decimal, & Percent Equivalencies. Coach Lesson 4 Also see textbook pages 108 – 110, & 202 – 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 “of 100.”

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Fraction, Decimal, & Percent Equivalencies

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  1. Fraction, Decimal, & PercentEquivalencies • Coach Lesson 4 • Also see textbook pages 108 – 110, & 202 – 205. • Jeff Rhodus • 6th Grade • Elsanor Elementary

  2. Getting the Idea! Fractions, decimals, and percents can all be used to show parts of a whole. The word percent means “of 100.” That is why percents can be written as fractions with denominators of 100. The symbol for percent is %.

  3. This chart shows some common fraction-decimal-percent equivalencies. Fraction Percent Fraction Decimal Percent Decimal 1 1 1% 0.01 0.25 25% 100 4 1 1 50% 0.5 0.1 10% 10 2 1 3 0.125 12.5% 0.75 75% 8 4 1 1 1 1.0 100% or 0.2 20% 5 1 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.

  4. 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. Step 2: Write the decimal. Solution: The decimal equivalent of 3/5 is 0.6 3 3 x 5 6 = = 5 5 x 2 10 6 = 0.6 10

  5. 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. Step 2: Change the improper fraction to a mixed number. Then simply the fraction part by dividing the numerator and denominator by 4. Solution: The mixed number equivalent of 1.44 is 1 144 1.44 = 100 144 44 44 : 4 11 144 11 1 1 = = = 100 100 100 : 4 25 100 25 11 25

  6. 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%

  7. 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. Step 2: Change the fraction to a percent. Since the denominator is 100, the percent is the same as the numerator. 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. 9 9 x 5 45 = = 20 20 x 5 100 45 45% = 100

  8. 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. Step 2: Change the improper fraction to a mixed number. Then simply the fraction part by dividing the numerator and denominator by 20. Solution: 140% = 1 140 140 = 100 140 40 40 : 20 2 2 140 1 = 1 = = 100 100 100 : 20 5 100 5 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.

  9. 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%

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