Thanks to our free Fraction Calculator You can easily calculate the sum, the difference, the product or the quotient of two fractions. Under the Fraction Calculator, you will also find the rules used for the addition, subtraction, multiplication and division of fractions.
Some information on the use of the Fraction Calculator
1. How does the Fraction Calculator calculate?
Based on the rules of mathematics, of course. The use of the Fraction Calculator is very straightforward, and it works incredibly simply. If you want to learn more about the addition, subtraction, multiplication and division operations of fractions, you will find detailed information below.
2. What are fractions, and what shall I known about them before I start with the calculations?
A fraction is practically something “not whole”; more precisely it is the ratio of two integers. When talking about fractions, it is worth clarifying a few simple terms as these might come in handy when doing the calculations.
A fraction consists of two parts: a numerator displayed above the line and a denominator displayed below the line. Let’s have a specific example:
Here 3 is the numerator and 4 is the denominator. It is important to be familiar with these terms so that we may simply and clearly refer to them when talking about the arithmetic operations (addition, subtraction, multiplication and division) with fractions.
Before you start with real calculations, you should also learn about the concept of “reciprocal”, which will be useful when dividing fractions. To get the reciprocal of a fraction, you simply swap over the numerator and denominator. This means that the reciprocal of the fraction mentioned in the example above is:
Finally, there is one more very important concept: the common denominator. It is important in several types of operations. If we want to do calculations with fractions, sometimes we have to bring them to a common denominator. As a result, the two fractions will have the same denominator (the integer below the line). In order to achieve this, we multiply the denominators. Obviously, without any further steps, the value of the fractions would change. So not only the denominator but also the numerator of the first fraction must be multiplied by the second denominator. Let’s have an example here, as well:
The first fraction: 1/2
The second fraction: 2/3
When using a common denominator, the first fraction will be 3/6 (both the numerator and the denominator are multiplied by the denominator of the second fraction).
When using a common denominator, the second fraction will be 4/6 (just like above, both the numerator and the denominator are multiplied by the denominator of the other fraction).
3. How to add fractions
First, bring them to a common denominator (see above), then simply add the two numerators.
Let’s have an example: 3/4+1/2 = 6/8+4/8 = 12/8
4. How to add fractions with whole numbers
Convert the whole number into a fraction. In the next step you have to add the two fractions in the way explained above. The same thing happens here: you have to bring the two numbers to a common denominator. This will convert the whole number into a fraction.
Let’s have an example: 3/4 + 1 = 3/4 + 4/4 = 7/4
5. How to subtract fractions
First, bring them to a common denominator, and then simply subtract one of the numerators from the other one.
Let’s have an example: 3/4 – 1/2 = 6/8 – 4/8 = 2/8
6. How to subtract fractions from whole numbers
Convert the whole number into a fraction. In the next step you only have to subtract a fraction from another fraction (see the previous example). The same thing happens here: you have to bring the two numbers to a common denominator. This will convert the whole number into a fraction.
Let’s have an example: 1-3/4 = 4/4 – 3/4 = 1/4
7. How to multiply two fractions
It is simple: multiply the first numerator by the second numerator and the first denominator by the second denominator.
Let’s have an example: 3/4 * 1/2 = 3/8
8. How to multiply a fraction by a whole number
Multiply the numerator of the fraction (only the numerator!) by the whole number, and you will instantly get the result. This might be reduced if the numerator and the denominator are both exactly divisible by a given number.
Let’s have an example: 3/4 * 2 = 6/4 (or it reduces to 3/2).
9. How to divide a fraction by another fraction
At the beginning of our article on the Fraction Calculator, we discussed the concept of reciprocal. This is the point where the concept comes in handy. If you want to divide a fraction by another fraction, you use the reciprocal of one of them. After that, you simply use the rules of multiplication.
Let’s have an example: If you want to divide 3/4 by 1/2, you do it as follows: 3/4 * 2/1 = 6/4
10. How to divide a fraction by a whole number
Bring the two fractions to a common denominator, and then multiply the two fractions by using the reciprocal of one of them.
Let’s have an example: You want to divide 3/4 by 2. 2 may also be expressed as a fraction, let’s say 8/4. Use the reciprocal to multiply: 3/4 * 4/8 = 12 / 32 (or it reduces to 6/16, or it further reduces to 3/8).