When adding and subtracting fractions, the numerator and denominator are checked. Accordingly, we can add or subtract fractions by examining some rules and things to do. It is possible to add and subtract fractions by various methods. When performing addition and subtraction over fractions, the equality of the numerator and denominator is checked.

##### Adding and Subtracting Fractions with the Same Denominator

Adding and subtracting fractions with equal denominators is quite easy. Because the denominators are the same, we can directly add and subtract.

Example: 3/5 + 4/5 = 7/5

When we examine the example, we understand that their denominator is 5 and they are equal. Therefore, when adding these two fractions, their numerators are added together, while their denominators remain the same. So here we add the numbers 3 and 4 and write 7 in the numerator. Then we write 5 in the same way in the denominator part. So we get 7/5 as a result.

Example: 4/7 – 2/7 = 2/7

This time we did subtraction and subtracted the fractions with the same denominator from each other. In the same way, we subtract 2 from 4, which are the numerator parts, and write 2. Then we wrote 7 in the same way because the denominators are the same. Thus, we found the fraction 2/7.

##### Adding and Subtracting Fractions with the Unlike Denominator

When adding and subtracting fractions with unequal denominators, we first need to make the denominators equal to each other. If the denominators of the fractions are not equal, then subtraction or addition cannot be performed.

Example: 4/9 – 2/5 = ?

4/9 – 2/5 = (Here, the denominators are multiplied with each other and their common multiples are found. While doing this, the numerators are also multiplied by the number written in the denominator.)

4/9 x 5 – 2/ 5 x 9 = 20/45 – 18/45 = 2/45

We multiply the numbers whose denominators are 9 and 5 with each other to find the common multiple of 45.  We completed the process by multiplying the numerators over the number written in the denominator while doing this.

##### Adding and Subtracting a Natural Number and a Fraction

Fractions can also be added together with a natural number. In such cases, a fraction is written under the natural number after writing the fraction in the same way. It will be the number 1. Then again, the denominators are multiplied with each other and their common multiples are found.

Example: 2/5 + 4 = ?

2/5 + 4/1 = (Here again, since the denominators are different, we multiply the denominators with each other and find their common multiple. While doing this, we also multiply the numerators.)

2/5 x 1 + 4/1 x 5 = 2/5 + 20/5 = 22/5

This time, we added a fraction and an integer and completed this operation easily. In our operation, we created a fraction by adding the number 1 to the bottom of a natural number. Then we brought the denominators to the same number and then added. You can do the same with subtraction.