Adding and Subtracting Fractions Calculator
Struggling with fractions again, huh... Worry not — Omni is here, saving the day with the adding and subtracting fractions calculator! It provides you with a step-by-step guide to fraction addition/subtraction problems so that you can learn how to add and subtract fractions by using the tool!
In case you want to acquire a solid theoretical background, we've explained all there is about the different cases you may run into in the article below. We've covered the following:
- Adding and subtracting fractions with like denominators;
- Adding and subtracting fractions with different denominators;
- How to simplify adding and subtracting fraction; and
- Adding and subtracting mixed fractions.
We hope that adding and subtracting fractions will never be a struggle again!
Adding and subtracting fractions with like denominators
Fractions are strange creatures. In their crazy world, unlike in the good ol' world of integers, addition and subtraction may be more complicated than multiplication and division. If you want to compare, we suggest you first go through this article and then take a look at Omni's multiplying fractions calculator and dividing fractions calculator. You'll see what we mean.
But don't get discouraged! We'll take you through all the secrets of adding and subtracting fractions! In fact, if you're very lucky, then fraction addition and subtraction are as easy as in the case of integers. Namely, if the fractions you need to add/subtract all have the same denominator, then your task boils down to adding/subtracting the numerators and keeping the denominator unchanged. Easy-peasy!
Let's look at an example and compute 1/8 + 6/8 − 2/8.
All the denominators are 8. Yeah!
Compute the numerators:
1 + 6 − 2 = 5.
The result is 5/8.
That's all there is to adding and subtracting fractions with like denominators! The
problem challenge begins when we have to begin adding and subtracting fractions with unlike denominators. Excited? Let's go!
How do I add and subtract fractions with unlike denominators?
To add or subtract fractions with unlike denominators, follow these easy steps:
Simplify each fraction by dividing its numerator and denominator by their greatest common factor.
Determine the least common multiple (LCM) of the fractions' denominators. This is our least common denominator (LCD).
Expand the fractions: multiply each fraction's numerator and denominator so that the LCD is the new denominator.
Perform addition or subtraction on these new fractions (specifically on their numerators).
🙋 You can discover more about the least common denominators with our LCD calculator. In fact, any common denominator would do (and there are infinitely many of them) — but we use the LCD to have the simplest calculations possible.
Since we're done here, let's move on to adding and subtracting mixed fractions!
How do I add and subtract mixed fractions?
To add or subtract mixed fractions, first convert the mixed fractions to improper fractions. Follow these steps:
For each mixed fraction: multiply the denominator by the whole number and then add the numerator to get the numerator of the improper fraction. The denominator stays the same as in the mixed fraction.
Proceed as usual with subtraction or addition for the improper fractions. If the denominators are different, you'll need to find the least common denominator.
How to use this adding and subtracting fractions calculator
This adding and subtracting fractions calculator is a really simple yet powerful tool! You need to:
- Choose if you want to perform addition or subtraction of fractions.
- Choose the form of your numbers: are they fractions or mixed numbers?
- Input the numbers.
- Enjoy the result!
- Omni's adding and subtracting fractions calculator can display a step-by-step solution as well!
🙋 If you have to deal with a whole number, choose the mixed fraction mode and leave both the numerator and denominator empty. Alternatively, input
0 as the numerator and any (non-zero) number as the denominator.
How do I simplify adding and subtracting fractions?
There are two main ways to simplify the addition or subtraction of fractions:
Dividing the numerator and denominator of each fraction by their greatest common divisor.
Rewrite the fractions with their least common denominator. It is equal to the least common multiple of the two denominators. Remember to expand the numerators accordingly!
What is 5/6 minus 1/4 as a fraction?
The answer is 7/12. To arrive at this result, note that the LCM (least common multiple) of 4 and 6 is 12, so we need to expand both fractions so that their denominators are both 12. So, 5/6 = 10/12 and 1/4 = 3/12.
Now we have to perform the subtraction (dealing in fact only with the numerators): 10/12 − 3/12 = 7/12.