Fractions Study Guide: GED Math
Practice problems for these concepts can be found at:
Writing and Recognizing Fractions
What exactly is a fraction? Imagine that you and a friend order a whole pizza for yourselves. The pizza is cut into nine slices.
If one of you eats the whole pizza and doesn't share with the other one, then you would eat nine of the nine slices, or . But what if you ate two slices and your friend ate three slices? Then you ate of the pizza, your friend ate of the pizza, and of the pizza is left over. The numbers , , and are all fractions.
Notice that fractions are two numbers that represent a part of a whole. The two numbers are separated by a bar. The bar means to divide the top number by the bottom number.
The top number is called the numerator. The numerator tells you how many parts of the whole are being talked about. For example, of the pizza refers to two slices of a pizza that has been cut into nine slices.
The bottom number in a fraction is called the denominator. The denominator tells you how many equal parts the whole has been divided into. The pizza has been divided into nine slices, so the denominator is 9. What if you cut the pizza into eight slices? Then the denominator would be 8.
Think about some other common fractions.
- You use fractions to talk about money. For example, a quarter is 25 cents, or of a dollar. Four quarters, or , equal one dollar.
- You also use fractions to talk about time. An hour is a fraction of a day. One hour is of a whole day. One day is a fraction of a week: . What fraction of a year is one month?
- Sometimes you'll see fractions in ads. A department store might have a sale of "one-half off" last season's styles. That means that you pay only of the whole original price.
Reducing Fractions to Lowest Terms
The numerator and the denominator of a fraction are called terms. On the GED, the directions might ask you to reduce fractions to lowest terms. This is the standard and usual way to write fractions.
To reduce a fraction to lowest terms, you need to find a fraction that is equal to the one you have but has a smaller numerator and denominator. Divide both the numerator and the denominator by the same whole number. The whole number must divide evenly into both numbers. Continue to divide the numerator and denominator until there is no number other than 1 that can divide evenly into both numbers. If only 1 can divide into both numbers evenly, then the fraction is said to be reduced to lowest terms.
- Reduce to lowest terms.
- Reduce to lowest terms. Both numbers are even, so you can begin by dividing by 2:
Begin by thinking of a number that will divide evenly into both the numerator and the denominator. You know that 4 × 7 = 28, so you can divide both numbers by 7.
The fraction is equal to . No number other than 1 can divide into both 1 and 4 evenly; so is reduced to lowest terms.
Often when you begin reducing a fraction by dividing by a small number, you will have to divide more than one time. If you can find the largest number that divides into both numbers, you can reduce the fraction faster—often in only one step.
Reduce to lowest terms.
If you begin by dividing by 2, you will have to divide again by 4:
- First, divide by 2:
- Then divide by 4:
If you begin by dividing by 8, you can reduce the fraction in only one step:
Notice that you get the same answer either way.
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