Skill 29
Use Fractions and Decimals
Fractions. Up to now, we have dealt only with whole numbers. Now we will move on to fractions and decimals, which are parts of a whole. Let’s tackle fractions first. A fraction is like one piece of your favorite pie, not the whole pie. If you took 1 of 8 equal slices, your slice would be 
of the pie. The remaining slices would be 
of the pie. If you took 1 of 4 equal slices, your part would be 
of the pie. In a fraction, the number on the top is called the numerator. The number on the bottom is called the denominator.
Reducing Fractions to Lowest Terms. Let’s work with 
for a moment. There are many other fractions that have the same value: 
and so on. In fact, every fraction in which the bottom number is 4 times larger than the top number is equal to 
. The numbers 1 and 4 are the smallest numbers that represent this 1-to-4 relationship, so for all of these fractions, is said to be in “lowest terms.” A fraction is in lowest terms when the numerator and denominator have no common factors other than 1. In ASVAB math problems involving fractions, you are usually asked to express your answer in lowest terms. So it is important to be able to “reduce” fractions by finding the greatest common factor (GCF) of the numerator and denominator and then dividing both terms by their GCF. For example, if the answer to a problem is 
, you need to see that the GCF of 5 and 20 is 5. Dividing both terms by 5 results in the fraction 
Decimals. Another way to represent parts of a whole is through decimals. In the decimal system, 0.50 is 5 tenths or 50 hundredths. The decimal 0.25 is 25 hundredths, 0.78 is 78 hundredths, and 0.250 is 250 thousandths. (Go back to Skill 27 for a review of place value if you need it.)
Because fractions and decimals both represent parts of a whole, they are just two ways to represent the same thing. You should know how to convert each one to the other.
• To convert a fraction to a decimal, divide the numerator by the denominator.
Here is a simple example. Take the fraction Divide the numerator, 1, by the denominator, 4, to get 0.25. For the fraction 
divide 1 by 8 to get 0.125.
• To convert a decimal to a fraction, express the number in terms of tenths, hundredths, thousandths, or a similar fraction based on the number of places in the decimal. Then write the fraction in lowest terms. For example, 0.25 can be converted to 
reduced to its lowest terms, it is Or take 0.125, which can be converted to 
reduced to its lowest terms, it is 
Test Yourself!
List these fractions in their lowest terms.
Change these fractions into decimals.
Change these decimals into fractions.
