Ratios
LEARNING OBJECTIVES
On completion of the materials provided in this chapter, you will be able to perform computations accurately by mastering the following mathematical concepts:
1 Changing a proper fraction, decimal fraction, and percent to a ratio reduced to lowest terms
2 Changing a ratio to a proper fraction, a decimal fraction, and a percent
Study the introductory material on ratios. The processes for the calculation of ratio problems are listed in steps. Memorize the steps for each calculation before beginning the work sheet. Review previous chapters on fractions, decimals, and percents as necessary. Complete the work sheet at the end of this chapter, which provides for extensive practice in the manipulation of ratios. Check your answers. If you have difficulties, go back and review the steps for that type of calculation. When you feel ready to evaluate your learning, take the first posttest. Check your answers. An acceptable score as indicated on the posttest signifies that you are ready for the next chapter. An unacceptable score signifies a need for further study before taking the second posttest.
A ratio is another way of indicating a relationship between two numbers. In other words, it is another way to express a fraction. A ratio indicates division. The numerator is the first number listed.
EXAMPLE 1: ¾ written as a ratio is 3 : 4
In reading a ratio, one reads the colon as “is to.” The example would then be read as “three is to four.”
EXAMPLE 2: 7 written as a ratio is 7 : 1
To express any whole number as a ratio, the number following the colon is always 1. The example would be read as “seven is to one.”
CHANGING A PROPER FRACTION TO A RATIO REDUCED TO LOWEST TERMS
1. Reduce the fraction to lowest terms.
2. Write the numerator of the fraction as the first number of the ratio.
3. Place a colon after the first number.
4. Write the denominator of the fraction as the second number of the ratio.
CHANGING A DECIMAL FRACTION TO A RATIO REDUCED TO LOWEST TERMS
1. Express the decimal fraction as a proper fraction reduced to lowest terms.
2. Write the numerator of the fraction as the first number of the ratio.
3. Place a colon after the first number.
4. Write the denominator of the fraction as the second number of the ratio.
CHANGING A PERCENT TO A RATIO REDUCED TO LOWEST TERMS
1. Express the percent as a proper fraction reduced to lowest terms.
2. Write the numerator of the fraction as the first number of the ratio.
3. Place a colon after the first number.
4. Write the denominator of the fraction as the second number of the ratio.