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 find not only 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, adding fractions will never be a horror again!
🔎 Do you want to multiply fractions? Try our multiplying fractions calculator and learn it in a minute!
How to add fractions?
A fraction is a number formed from the ratio of two numbers (
B). These numbers are typically integers (whole numbers), so that:
fraction = A/B.
It turns out you can convert any decimal to a fraction. If you're unsure how - our decimal to fraction calculator will help!
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 2/7 and 3/7, we need to 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 1/2 and 1/3:
- →1/2 + 1/3 = …
- Find the common denominator. To do so, we can estimate the least common multiple (LCM) of
LCM(2,3) = 6. In case of a more complex example, feel free to use Omni's LCM calculator.
- 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, 15/18, to name a few. However, it's convenient to present the result 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. Do it by hand or use GCF calculator:
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.
- Work out the common denominator:
Additionally, in our calculator, there is no difference between -1/4 or 1/-4 - our adding fractions calculator will treat these expressions the same!
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.
The 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 save your time! Input the following values:
6for the first number;
8for the second number;
12for the third one.
The outcome is 19/3, or 61/3, as a mixed number. It means that six pizzas won't be enough, so you'd better order seven!
Moreover, you can choose the step by step solution to see all the calculations with explanations. You are all welcome to read it while enjoying your delicious meal!