In the previous sections, you used models to generate equivalent fractions from decimals (and vice versa) and to generate equivalent percents from decimals (and vice versa). In this part of the lesson, you will focus on equivalent forms of fractions and percents.
Lone Star General Store uses both percents and fractions to advertise discounts on their merchandise. Look at one part of this week’s sales flyer.
Because Lone Star General Store uses both percents and fractions, you need to know how to write a percent as a fraction so that you can compare the discounts. You also need to know how to write a fraction as a percent.
Use the slider in the interactive below to show the relationship between a number written as a percent and the number written as a fraction.
Use the interactive to complete the table below. Copy and paste the table below into a word processing or spreadsheet program or app. Record the equivalent fraction from the interactive in the table. Then, generate an equivalent fraction with a denominator of 100. Use your table to answer the questions that follow.
Percent |
Simplified Fraction |
Fraction with Denominator = 100 |
10% |
||
20% |
||
40% |
||
45% |
||
60% |
||
75% |
||
84% |
||
90% |
Interactive popup. Assistance may be required.
Percent |
Simplified Fraction |
Fraction with Denominator = 100 |
10% |
1 over 10
1
10
|
10 over 100
10
100
|
20% |
1 over 5
1
5
|
20 over 100
20
100
|
40% |
2 over 5
2
5
|
40 over 100
40
100
|
45% |
9 over 20
9
20
|
45 over 100
45
100
|
60% |
3 over 5
3
5
|
60 over 100
60
100
|
75% |
3 over 4
3
4
|
75 over 100
75
100
|
84% |
21 over 25
21
25
|
84 over 100
84
100
|
90% |
9 over 10
9
10
|
90 over 100
90
100
|
Interactive popup. Assistance may be required.
When the fraction has a denominator of 100, the numerator is the same as the original percent.
Interactive popup. Assistance may be required.
The numerator of the fraction with a denominator of 100 is the same as the percent.
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Use a denominator of 100.
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Look for common factors in the numerator and denominator. Divide out common factors until there are no longer any factors in common between the numerator and denominator.
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If possible, look for an equivalent fraction that has a denominator of 100. The numerator of the equivalent fraction is the equivalent percent. Otherwise, you can write the fraction as a decimal number, and then generate an equivalent percent from the decimal number.
A percent is a part of the whole given in terms of the number of parts per 100. How does the definition of a percent appear in the relationship between a percent and its equivalent fraction?
If the percent were greater than 100%, such as 245%, how would you convert the percent to a fraction?
The Lone Star General Store has a new sale coming up for next week. According to their sales flyer, the following discounts will be offered.
Interactive popup. Assistance may be required.
Write an equivalent fraction to 2 over 5 2 5 with a denominator of 100.
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Generate a percent that is equivalent to the discount on the rug, and compare the number to the percent discount on the roller blade skates, which are sports equipment.
Interactive popup. Assistance may be required.
Tennis shoes are being sold at a 35% discount, so the sale price will be 100% - 35% = 65% of the original price. Generate a fraction equivalent to 65%, not 35%.