**1**

^{st}fraction**2**

^{nd}fraction# Adding Fractions Calculator

This adding fractions calculator helps you evaluate **the sum of up to five fractions** in the blink of an eye. If you're looking to convert a fraction to a percent, this calculator can help. In the article below, you'll not only find how to add fractions, but also how to deal with subtraction. Are you struggling with **adding fractions with unlike denominators**? Read on to never have that problem again! After you're done here, the addition of fractions will never be a horror again!

## How to add fractions?

A fraction is a number formed from the ratio of two numbers (`A`

and `B`

). These numbers are typically integers (whole numbers), so that:

`fraction = `

.^{A}/_{B}

It turns out you can convert any decimal to a fraction. As a result, you can add as many decimals as you like together by treating them as if they were fractions. Whenever we want to add two fractions with a common denominator, let's say

and ^{2}/_{7}

, we need to ^{3}/_{7}**add numerators, while the denominator remains the same**:

.^{2}/_{7} + ^{3}/_{7} = ^{(2+3)}/_{7} = ^{5}/_{7}

But how to add fractions with **different denominators**?

## Adding fractions with unlike denominators

When the numbers have different denominators, the addition of fractions is a bit more challenging, as you can't just add the numerators like before. The trick is to use **common denominators**. Let's see how it works. Let's say we want to add

and ^{1}/_{2}

:^{1}/_{3}

^{1}/_{2}+^{1}/_{3}= …- Find the common denominator. To do so, we can estimate the least common multiple (LCM) of
`2`

and`3`

.`LCM(2,3) = 6`

- Expand each fraction so that the denominator is this LCM, in this case
`6`

:

,^{1}/_{2}=^{3}/_{6}^{1}/_{3}=^{2}/_{6} - As we know how to add fractions with the same denominator, you can just add these fractions normally:
`… =`

^{3}/_{6}+^{2}/_{6}=^{5}/_{6}

There are also other equivalent fractions to this result, such as

, ^{10}/_{12}

, to name a few. However, it's convenient to present the result ^{15}/_{18}**in its simplest form**.

## Adding and subtracting fractions

Now we know how the addition of fractions works, even when adding fractions with unlike denominators - cool! But what about subtraction? Is it that simple too?

You can use this adding fractions calculator for subtracting fractions as well. We just need to remember that **the subtraction of a fraction is just like addition**. For example, what is

?^{3}/_{9} - ^{2}/_{8}

- Change the subtraction to an addition:
^{3}/_{9}-^{2}/_{8}=^{3}/_{9}+ (^{-2}/_{8}) - To make your life easier,
**simplify the fractions as much as possible**. Find the greatest common factor for each pair of numerators and denominators:`GCF(3,9) = 3`

,`GCF(2,8) = 2`

- Rewrite the expression as:
^{1}/_{3}+ (^{-1}/_{4}) - The rest is the same as standard addition:
- Work out the common denominator:
`LCM(3,4) = 12`

- Expand the fractions and add them:
^{4}/_{12}+ (^{-3}/_{12}) =^{1}/_{12} - Which is the same as:
^{1}/_{3}-^{1}/_{4}=^{1}/_{12}

Additionally, in our calculator there is no difference between

or ^{-1}/_{4}

- our adding fractions calculator will treat these expressions the same!^{1}/_{-4}

## Addition of fractions in practice - how to use adding fractions calculator?

Imagine a story - you are at a party with some of your friends. And there it comes - the hunger! What's even worse, you've just realized there is nothing left in the fridge.

A solution is simple - you are going to order a pizza, or two, or even more. You have to decide! The point is your favorite pizzeria sells pizzas as a whole, but you have an innovative method that can cut pizzas into 6, 8, or 12 slices. Everyone wants a certain fraction of a pizza: five of you want 4 of 6-slice pizzas, four of you prefer 3 of the 8-slice pizzas, and the remaining three will be happy with 6 of 12-slice ones. The main question is: *How many pizzas should we order?*

You can always evaluate it by hand, but why don't you try our adding fractions calculator and saving your time! Input the following values:

`5*4`

and`6`

for the first number`4*3`

and`8`

for the second number`3*6`

and`12`

for the third one

The outcome is , or

^{19}/

_{3}

**, as a mixed number. It means that six pizzas won't be enough, so you'd better order seven! Moreover, you can choose the**

`6 `^{1}/_{3}

**step by step solution**to see all the calculations with explanations. You are all welcome to read it while enjoying your delicious meal!