Reducing and Enlarging Fractions

Now that you have looked at multiplying and dividing fractions, we can look at reducing and enlarging fractions.

Reducing Fractions

Reducing a fraction means to use lower numbers in a fraction to express the same number. To illustrate this principle, examine the numberline showing below:

Now look at the numberline showing :

Notice that BOTH fractions represent the same amount! 2 pieces out of four is a half, and one piece out of 2 is a half. So we have two fractions that represent the exact same amount. There are many more fractions that represent one half. A few of them are shown below:

So which fraction is the best fraction to use to represent one half? Usually we use , since it is expressed in lowest terms. For a fraction to be in lowest terms, it CANNOT be reduced. So how do you reduce a fraction?

Let's look at again. Is there a single number that divides into the numerator and the denominator evenly? Yes! The number 2 divides into both the numerator and the denominator evenly. So divide BOTH the numerator and the denominator by 2, as shown below:

So, the common rule for reducing a fraction is:

Divide the numerator and the denominator by a common factor (other than 1), if a factor exists.

Once you cannot reduce a fraction anymore (you cannot find any other common factors) that fraction is said to be in lowest terms. Let's look at a few examples:

Example 1

Reduce the fraction to its lowest terms.

Solution

First, look for a number that divides into both 3 and 6 evenly. 2 does not work (as it only divides into 6 evenly), but 3 does work! Now divide the numerator and the denominator by 3. (3 ÷ 3 = 1 for the numerator, and 6 ÷ 3 = 2 for the denominator). You end up with an answer
of .

Example 2

Reduce the fraction to its lowest terms.

Solution

Again, we must start by looking for a number that divides evenly into both 10 and 30. 2 works, but so does 5, and so does 10! Which number should we use? When possible, use the greatest common factor. That means out of 2, 5 and 10, use 10 since it is the largest. This will keep us from having to reduce AGAIN after the first step. So, divide the numerator by 10 (10 ÷ 10 = 1) and divide the denominator by 10 (30 ÷ 10 = 3). You should get an answer of .

Enlarging Fractions

To enlarge a fraction is the opposite of reducing a fraction! Why would you want to enlarge a fraction, you ask? You may need to enlarge fractions in order to add and subtract them. (You may need to enlarge fractions to give them a common denominator).

To enlarge a fraction, simply multiply the numerator and denominator of the fraction by the same number. You can multiply by any number you wish. For example:

1/2 and 4/8 represent the same amount - namely one half. As long as you multiply by the same number on the top and the bottom, you can enlarge a fraction as large as you would like. A quick example is shown below. To see more enlarging of fractions, see the lesson on adding and subtracting fractions.

Example 1

Enlarge the fraction so that it has a denominator of 18.

Solution

To give the fraction a denominator of 18, we have to multiply the denominator (3) by 6. However, to properly enlarge a fraction, we must multiply both the numerator and the denominator by the same number. So we get:

Now that you have seen examples of reducing and enlarging fractions, you can try the sample questions sheet or you can head back to the fractions main page.