Fraction Calculator: Add and Subtract Fractions

How to use the fraction calculator: Input the numerator and denominator values, choose the arithmetic operator, and let the calculator do the rest.

Basic Definition of a Fraction

A fraction is a numerical quantity that represents part of a whole number. In mathematical terms, a fraction is expressed as one integer (numerator) divided by another integer (denominator), such as 1⁄3, 1⁄5, 2⁄7, etc.

In everyday language, we can simply say that a fraction is how many parts of a certain size there are, like one eight-fifths.

Simple Methods of Calculating Fractions

Simple addition of fractions

The key thing to carrying out the addition of fractions correctly is to always keep in mind the most important part of the fraction, which is the number under the line, known as the denominator. If we have a situation where the denominators in the fractions involved in the addition process are the same, then we merely add the numbers that are above the separation line, or as a mathematician would put it, "Add the numerators only". We can look at an example of adding two fractions like 3⁄7 and 4⁄7. The expression would look like this: 3⁄7 + 4⁄7 = 7⁄7. In the case when the numerator is equal to the denominator, like in the foregoing example, it can also be equated to 1.

However, this was one of the easiest examples of adding fractions. The process may become slightly more difficult if we face a situation when the denominators of the fractions involved in the calculation are different. Nonetheless, there is a rule that allows us to carry out this type of calculation effectively. Remember the first thing: when adding fractions, the denominators must always be the same, or, to put it in mathematicians' language, the fractions should have a common denominator. To do that, we need to look at the denominator that we have. Here is an example: 2⁄3 + 3⁄5. So, we do not have a common denominator yet. Therefore, we use the multiplication table to find the number that is the product of the multiplication of 5 by 3. This is 15. So, the common denominator for this fraction will be 15. However, this is not the end. If we divide 15 by 3, we get 5. So, now we need to multiply the first fraction's numerator by 5, which gives us 10 (2 x 5). Also, we multiply the second fraction's numerator by 3 because 15⁄5 = 3. We get 9 (3 x 3 = 9). Now we can input all these numbers into the expression: 10⁄15 + 9⁄15 = 19⁄15.

Note: When the numerator is greater than the denominator, we then divide it by the latter.

Simple subtraction of fractions

The key thing to carrying out the subtraction of fractions correctly is to always keep in mind that the most important part of the fraction is the number under the line, known as the denominator. If we have a situation where the denominators in the fractions involved in the subtraction process are the same, then we merely subtract the numbers that are above the separation line or as a mathematician would put it: "Subtracting the numerators only". We can look at an example of subtracting two fractions like 3⁄7 and 4⁄7. The expression would look like this: 4⁄7 - 3⁄7 = 1⁄7.

However, this was one of the easiest examples of subtracting fractions. The process may become slightly more difficult if we face a situation when the denominators of the fractions involved in the calculation are different. Nonetheless, there is a rule that allows us to carry out this type of calculation effectively. Remember the first thing: when subtracting fractions, the denominators must always be the same, or, to put it in mathematicians' language, the fractions should have a common denominator. To do that, we need to look at the denominators that we have. Here is an example: 2⁄3 - 3⁄5. So, we do not have a common denominator yet. Therefore, we use the multiplication table to find the number that is the product of the multiplication of 5 by 3. This is 15. So, the common denominator for these fractions will be 15. However, this is not the end. If we divide 15 by 3, we get 5. So, now we need to multiply the first fraction's numerator by 5 which gives us 10 (2 x 5 = 10). Also, we multiply the second fraction's numerator by 3 because 15⁄5 = 3. We get 9 (3 x 3 = 9). Now we can input all these numbers into the expression: 10⁄15 - 9⁄15 = 1⁄15. Therefore, 2⁄3 - 3⁄5 is equal to 1⁄15.

Note: When the numerator is greater than the denominator, we then divide it by the latter.

You may also be interested in our Egyptian Fraction (EF) Calculator or/and Factoring Calculator