In this part of the lesson, you will focus on the relationships between fractions and decimals and how to generate one form of a rational number from the other. Fractions and decimals are two ways that you can represent a quantity that is a part of a whole. For example, the model below shows a square that represents one whole. The square is broken into ten equal parts, three of which are shaded.

Lone Star General Store uses both fractions and decimals to represent information about pricing. Shortly after opening their website, the managers decided to have a sale on online e-book downloads.

Prices of the e-books are given with decimal numbers. Some of the prices are shown below.

Before you can calculate the discounted price of an e-book, you need to convert the fractional discount to a decimal number, or convert the decimal number price to a fraction.

Click through the interactive below to see how Damian used equivalent fractions to rewrite 2 over 5 2 5 as a fraction with a denominator of 10.

Pause and Reflect

Damian wants to write the fraction 11 over 20 11 20 as a decimal number. He knows to generate an equivalent fraction with a denominator of 100. What scale factor does Damian need to use? What will be the resulting equivalent fraction and decimal number?

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Check Your Answer

Damian should use a scale factor of 5 to change the denominator from 20 to 100 since 20 × 5 = 100.

11 over 20 11 20 = 11 x 5 over 20 x 5 11 × 5 20 × 5 = 55 over 100 55 100 = 0.55

Damian wants to write the fraction 7 over 8 7 8 as a decimal number. He knows to generate an equivalent fraction with a denominator of 1000. What scale factor does Damian need to use? What will be the resulting equivalent fraction and decimal number?

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Check Your Answer

Damian should use a scale factor of 125 to change the denominator from 8 to 1000 since 8 × 125 = 1000.

7 over 8 7 8 = 7 x 125 over 8 x 125 7 × 125 8 × 125 = 875 over 1000 875 1000 = 0.875

Not all fractions can be rewritten as equivalent fractions with a denominator of 10, 100, or 1000. For those fractions, you need an alternate method.

In the interactive below, match each fraction with a division problem that you would use to generate an equivalent decimal number by dragging the division problem next to the fraction. Then, match each fraction and division problem with the correct equivalent decimal number by dragging the decimal number next to the division problem.

Pause and Reflect

In general, what are two ways that you can generate a decimal number from a fraction?

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Check Your Answer

One way is to generate an equivalent fraction with a denominator that is a power of 10 (10, 100, or 1,000), then use the numerator to write a decimal number. Another way is to divide the numerator by the denominator (numerator becomes the dividend and denominator becomes the divisor).

If you know a decimal, how can you use place value to write an equivalent fraction? For example, how could you write 0.78 as a fraction?

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Check Your Answer

Write the decimal number as a fraction with a denominator that is a power of 10 (10, 100, or 1,000). Simplify the fraction using common factors between the numerator and denominator.

0.78 = 78 over 100 78 100 = 78 divided by 2 over 100 divided by 2 78 ÷ 2 100 ÷ 2 = 39 over 50 39 50

Practice

1. Lone Star General Store is discounting their e-books by 2 over 5 2 5 . A young adult book normally sells for $6.75. To calculate the discount, what decimal number should you multiply by the normal price of the book?

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   Need a hint?

   Change 2 over 5 2 5 to a decimal number. Either use equivalent fractions with a denominator of 10 or 100, or divide the numerator by the denominator.
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   Check Your Answer

   2 over 5 2 5 = 2 x 2 over 5 x 2 2 × 2 5 × 2 = 4 over 10 4 10 = 0.4
2. A recent survey showed that 110 out of 150 sixth graders prefer the mascot Eagles to the mascot Mustangs. What decimal represents the part of the sixth graders surveyed who prefer the mascot Eagles?

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   Need a hint?

   Write the ratio of sixth graders who prefer the mascot Eagles as a fraction, and then generate an equivalent decimal number.
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   Check Your Answer

   
3. A pickup truck can haul 0.64 tons of cargo. What fraction of a ton can the pickup truck haul?

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   Need a hint?

   Use place value to write the decimal number 0.64 (sixty-four hundredths) as a fraction with a denominator of 100. Simplify the fraction using common factors.
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   Check Your Answer

   0.64 = 64 over 100 64 100 = 64 divided by 4 over 100 divided by 4 64 ÷ 4 100 ÷ 4 = 16 over 25 16 25 of a ton
4. On a recent day, there were 14.76 Mexican pesos to 1 US dollar. What mixed number represents the number of Mexican pesos to 1 US dollar?

   Interactive popup. Assistance may be required.

   Need a hint?

   Use place value to write the decimal number 14.76 (fourteen and seventy-six hundredths) as a mixed number that includes a fraction with a denominator of 100. Simplify the fraction using common factors.
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   Check Your Answer

   14.76 = 1476 over 100 76 100 = 1476 divided by 4 over 100 divided by 4 76 ÷ 4 100 ÷ 4 = 1419 over 25 19 25 Mexican pesos to 1 US dollar