This fraction calculator can help you solve any fraction arithmetic operations such as multiply and add or subtract and divide and learn how to deal with them. Everything there is to know about this topic is presented below.


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What is a fraction?

In mathematics fraction is defined as a part of a certain whole. For instance when using one half (1/2) or three-quarters (3/4) you are actually using them.

A fraction contains an integer numerator which is positioned above the line (or on the left side of a slash) and a non-zero integer denominator positioned below the line. For instance 1/2 consists of the numerator 1 that indicates the fact that in this case is a single equal part and of the denominator 2 that indicates the facts that in this case the whole is made of 2 equal parts.

As the form of the fraction is now clear we should refer a bit to the set of rational numbers represented in mathematics by Q. This is the set of all numbers that can be written in the form of a fraction (numerator/denominator), more specifically as x/y with two condition that x and y are integer numbers AND that y is a non zero number. If one number can be written in this form then it is called a rational number.

Example of numbers and how can they be expressed as fractions:

For instance when you are referring to a decimal number such as 0.05, this is as fractional number even though you do not see its numerator and denominator as it can easily be written as 5/100.

For example when you are using a percentage such as 10%, this can be written as fraction too since any percentage is made of a numerator (in this case the numerator is 10) and a denominator which always 100; which in our case means that the fraction is 10/100.

Even when speaking about integer numbers such as 10, they can be expressed as fraction since every integer number has 1 as denominator, which means 10/1 = 10.

When you are using negative exponents numbers they can also be written as fractions. Let’s take the following negative exponent 10−2 that equals to 1/100.

When you are referring to division such as 2 ÷ 5 this is actually a fraction as it is equal to 2/5.

Also when you use ratios such as ratio 5:6 this is actually the same with 5/6 which is a fraction.

How to multiply fractions?

Even though our fraction calculator allows you perform this calculation let’s answer on how to multiply fractions.

How to multiply a fraction by another fraction?

In order to multiply a fraction by another you have to multiply their numerators and multiply their denominators as shown in this example:

How to multiply a fraction by another fraction

How to multiply a fraction by a whole number?

In case you have to multiply a whole number with a fraction you need to consider that the integer number can be written as a fraction having the denominator 1, and then simply multiply two fractions by following the rule explained above. For instance:

How to multiply a fraction by a whole number

How to multiply mixed numbers?

In order to multiply mixed numbers the best way to do it is by converting the mixed number into a common fraction and then perform the calculation by following the standard multiplication rule. For instance:

- In case of a multiplication between an integer number and a mixed number:

How to multiply mixed numbers

- In case of a multiplication between a simple fraction and a mixed number you only have to convert the mixed number into a common fraction and then apply the standard multiplication rule. For instance:

How to multiply mixed numbers

How to add fractions?

The basic rule on how to add fractions says that you can perform an addition only if the denominator of the two fractions is the same. That is why you first have to ensure that both fractions get the same denominator, which means when they have different denominator you should see which is the closest common denominator and convert them.

How to add fractions having different denominators?

In order to add fractions containing different denominators you need to convert both fractions to the same denominator and the simplest way to do this is to multiply together the two denominators (bottom number). For instance:

How to add fractions having different denominators

How to add an integer number to a fraction?

To add an integer number to a fraction you have to first express the given number as a fraction and then convert it in a fraction having the same denominator as the one you need to add to. For instance:

How to add an integer number to a fraction

How to subtract fractions?

The steps to follow in case of a subtraction between two fractions are similar to the ones as in case of an addition, which means you can subtract fraction only if they have the same denominator. This way the fraction that is obtained after subtraction will have that denominator while its numerator will be the result of subtracting the numerators of the initial fractions.

How to subtract fractions having different denominators?

In order to subtract fractions having different denominators you need to convert both of them to the same denominator and the simplest way to do this is to multiply together the two denominators (bottom number). For instance:

 How to subtract fractions having different denominators

How to subtract an integer number from a fraction?

To subtract an integer number from a fraction you have to first write the given number as a fraction and then convert it in a one having the same denominator as the one you need to subtract from. For example:

How to subtract an integer number from a fraction

How to divide fractions?

■ How to divide a fraction by a whole number?

In order to this calculation there are two approaches: you either choose to divide the numerator by the number only if the given value goes evenly into the numerator (a), or multiply the denominator by the given number (b). For example:

a)

How to divide a fraction by a whole number

b)

How to divide a fraction by a whole number

How to divide a number by a fraction?

In this case the solution is to multiply that number by the reciprocal of the given fraction, for example:

How to divide a number by a fraction

22 Feb, 2015 | 0 comments

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