1. Chapter 4
Ratios
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2. Lesson 4.1 Converting to and from Ratios
Changing a proper fraction, decimal fraction, and percent to a ratio reduced to lowest terms
Changing a ratio to a proper fraction, a decimal fraction, and a percent
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3. Ratios A ratio indicates a relationship between two numbers.
For example: 4 :7
What relationship does a ratio indicate?
A ratio indicates division. It is another way of expressing a fraction.
How is a ratio read?
In reading a ratio, the colon is read as “is to.” The example would be read as “4 is to 7.”
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4. Changing a Proper Fraction to a Ratio
Reduce to lowest terms.
Write the numerator of the fraction as the first number of the ratio.
Place a colon after the first number.
Write the denominator of the fraction as the second number of the ratio.
For example: 9 12
What does “reduce to lowest terms” mean?
A fraction often can be expressed in smaller numbers without any change in its real value. The reduction is accomplished by dividing both the numerator and the denominator by the same number.
Copyright © 2020 by Mosby, an imprint of Elsevier Inc. All rights reserved.

5. Changing a Decimal Fraction to a Ratio
Express the decimal fraction as a proper fraction reduced to lowest terms.
Write the numerator of the fraction as the first number of the ratio.
Place a colon after the first number.
Write the denominator of the fraction as the second number of the ratio.
For example: 0.65
How is a decimal fraction expressed as a proper fraction?
Converting a decimal fraction to a proper fraction is done by removing the decimal point and the zero preceding it and then using the numerals as the numerator. The placement of the decimal point indicates what the denominator will be. Reduce the proper fraction to lowest terms.
Copyright © 2020 by Mosby, an imprint of Elsevier Inc. All rights reserved.

6. Changing a Percent to a Ratio
Express the percent as a proper fraction reduced to lowest terms.
Write the numerator of the fraction as the first number of the ratio.
Place a colon after the first number.
Write the denominator of the fraction as the second number of the ratio.
For example: 35%
How is a percent expressed as a proper fraction?
First, convert the percent to a decimal fraction by dropping the percent sign and dividing the remaining number by 100. Convert the decimal fraction to a proper fraction by removing the decimal point and the zero preceding it and then using the numerals as the numerator. The placement of the decimal point indicates what the denominator will be. Reduce the proper fraction to lowest terms.
Copyright © 2020 by Mosby, an imprint of Elsevier Inc. All rights reserved.

7. Changing a Ratio to a Proper Fraction
Write the first number of the ratio as the numerator.
Write the second number of the ratio as the denominator.
Reduce to lowest terms.
For example: 4 :16
Remember to always reduce to lowest terms in order to meet the requirement to be a proper fraction.
Change 4 : 16 to a proper fraction.
Write the first number of the ratio as the numerator and the second number as the denominator and then reduce the fraction to lowest terms. In this example, 4/16 is reduced to 1/4.
Copyright © 2020 by Mosby, an imprint of Elsevier Inc. All rights reserved.

8. Changing a Ratio to a Decimal Fraction
Divide the first number of the ratio by the second number of the ratio.
For example: 9 :10
Change 9 : 10 to a decimal fraction.
Divide the first number of the ratio by the second number of the ratio using long division. In this example, 9 divided by 10 is 0.9.
Copyright © 2020 by Mosby, an imprint of Elsevier Inc. All rights reserved.

9. Changing a Ratio to a Percent
Express the ratio as a proper fraction or a decimal fraction.
Multiply by 100.
Add the percent sign (%).
For example: 6 :75
Copyright © 2020 by Mosby, an imprint of Elsevier Inc. All rights reserved.