# The Craft of Word Problems

## CONTENTS OF CURRICULUM UNIT 04.05.04

## The Art of Interpreting Percent

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## Lesson 3

Goals: Students must appreciate the relationship between fractions, decimals, and percentage. Students will become comfortable with converting fractions and decimals to percentages and vice versa. When one has a fraction and desires to determine the percentage one can do the following. Take the original fraction and make an equivalent fraction with a denominator of 100. Rewrite the numerator and add a percent sign to determine the percentage. (See the left column below) This works because percentage is some number out of 100.

Percents can also be expressed as lowest-term fractions. Simply take the numerical percentage without the percent symbol and use this as the numerator with 100 as the denominator. Then find an equivalent fraction by dividing the numerator and the denominator by the same number. This can be repeated until
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one
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is the only common factor of the numerator and the denominator, resulting in the lowest-term fraction. (See the right column below)

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Fraction to Percent
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Percent to Fraction
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1/2 = 50/100 = 50% 50% = 50/100 = 25/50 = 5/10 = 1/2

1/4 = 25/100 = 25% 25% = 25/100 = 5/20 = 1/4

3/4 = 75/100 = 75% 75% = 75/100 = 15/20 = 3/4

4/4 = 100/100 = 100% 100% = 100/100 = 1

If an equivalent fraction with a denominator of 100 is not easily determined then one may divide the fraction and calculate the decimal. The resulting number is not always an exact whole number percent. Therefore, one must approximate or round the answer. In fact, percentages allow amounts less than 1/100 of a given whole number to be small enough to ignore. When we have a number which would require a fraction of a percent to be expressed, we frequently round it to the nearest whole percent. Once the decimal is calculated and rounded then move the decimal two places to the right and add a percentage sign. (See column below on left) The same answer can be calculated by taking the decimal and multiply by 100 and added a percentage sign to the answer. (See column below on right)

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Fraction to Percent
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Decimal to Percent
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2/3 = 0.67 = 67% 0.67 x 100 = 67%

5/6 = 0.83 = 83% 0.83 x 100 = 83%

7/8 = 0.88 = 88% 0.88 x 100 = 88%

4/7 = 0.57 = 57% 0.57 x 100 = 57%

In addition, when one has a percentage one can remove the percentage sign and move the decimal two places to the left to determine the decimal. This formula works because it is the same outcome as if one took the decimal and multiplied it by 100. (See chart below)

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Percent to Decimal
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Decimal to Percent
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25% = 0.25 0.25 x 100 = 25%

50% = 0.50 0.50 x 100 = 50%

75% = 0.75 0.75 x 100 = 75%

100% = 1.00 1.00 x 100 = 100%

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