# Equal Fractions

When you have finished the pages below, try the Equal Fractions Quiz.

Other equal fractions page:

Finding the relationships between equal fractions is very important for many operations such as adding, subtracting and reducing or simplifying fractions.

To begin with, any fraction with the same numerator and denominator is equal to one whole. This makes sense - when one divides a cake evenly in fourths, the four fourths of the cake equal one whole cake. This is shown in the graphic below. Although the individual pieces may get smaller as the numerator and denominator increase when the lines are drawn, they altogether equal one whole.

# 64 64

By multiplying the numerator and denominator by the same number, one can create an infinite number of equal fractions. Also by dividing the numerator and denominator by the same number, one can also create equal fractions. It is considered proper form to reduce fractions when possible when an answer to a problem is obtained with fractions. This is referred to as expressing an answer in lowest terms.

Greatest Common Factor:

When one is reducing fractions, there are often several numbers one can divide into the numerator and denominator to reduce the fraction. To simplify matters, one should try to pick the greatest common factor. This is the greatest or biggest number that both the numerator and denominator can be divided by.

For example if one wanted to reduce the fraction twenty-five fiftieths. The right hand column lists all the factors of the two numbers. The greatest common factor of the two numbers is twenty-five. Thus if twenty-five is divided into both numbers, one gets one half.

Consult the Factors page for a listing of numbers up to one hundred and their factors to help in finding the greatest common factor if stuck.

### 1, 5, 25 1, 2, 5, 25, 50

Least Common Multiple:

When one is trying to find a common denominator for two fractions to add or subtract them, one way to do so is to multiply the denominators. However, sometimes the number that one gets is very big and thus more reducing becomes necessary for the final answer. Sometimes this can't be helped, but in many cases it can be avoided by getting the least common multiple for two denominators.

To find the least common multiple, start multiplying the bigger denominator by 2, 3, 4, etc.. and do the same with the smaller denominator. As soon as you have a common or same number, that is your least common multiple.

The factor chart can be helpful in another way. Look at some of the multiples of the bigger denominator. If both denominators are listed as factors of that number, that number can be used as a common denominator.

To convert the fractions to equal fractions with a common denominator:

1. Find the least common multiple
2. Divide the denominator of one of the fractions into the least common multiple.
3. Multiply the numerator of that fraction by the quotient or answer you got when dividing the denominator into the least common multiple.
4. Repeat the process for the second fraction. You should have two fractions with common denominators that are equivalent to the original fractions with uncommon denominators.

### 4, 8, 12, 16, 20, 24

Equal Fractions Videos

 Fractions Main Page Types of Fractions Equal Fractions Adding Fractions Subtracting Fractions Multiplying Fractions Dividing Fractions Factors