1.14 Subtracting Fractions

### Subtracting Fractions

Similar to adding fractions, fractions must have a common denominator (the bottom numbers must be the same) before being subtracted.

There are three steps to subtracting fractions:

1. Ensure that the bottom numbers (denominators) are the same. If they are not, change them so that they are the same (they have a common denominator).
2. Once the denominators are the same, subtract the top numbers (numerators) and place the result over the common denominator.
3. Simplify the fraction (if possible).

### Example 1

Now, let's work through the example below. The questions below will guide you through the process.

 Subtract and simplify

First, both numbers must be put in fraction form. In the simplifying fractions section we learned that .

Thus, we are subtracting

Step 1. Are the denominators the same?

The denominators are not the same.

Is one of the denominators multiple of the other?

The denominators are not multiple of each other.

Select the common denominator?

6 is the common denominator and it is obtained by multipling the two denominators: 3x2=6.

Next we need to expand both fractions to have a denominator of 6. Expand both fractions by multiplying them and click done when you are ready. Enter your results in the appropriate boxes.

 5 x = 2 x

 2 x = 3 x

The expanded fractions are and

Now subtract the expanded fractions

 =

Can be simplified?

Because the top number is larger than the bottom number, the fraction can be simplified to a whole number with a fraction remainder.

can be simplified to

### Practice

Subtract and simplify