This free online add subtract fractions calculator will add one fraction to another, or subtract one fraction from another -- regardless if the two fractions have the same or different denominators -- and give the result fraction in simplest form.
Plus, unlike other online fraction calculators, this calculator will show its work and give a detailed step-by-step explanation as to how it arrived at the answer.
The answer to that question depends on whether you are adding fractions with like denominators or adding fractions with unlike denominators.
Adding fractions with like denominators is easy. All you do is add the numerators together and keep the denominator the same, like this:
|Adding with Like Denominators|
Adding fractions with unlike denominators requires a little more work (unless you use the calculator on this page), because in order to add the fractions you must first turn their unlike denominators into like denominators. You do that by finding the lowest common multiple (LCM) of the denominators.
To illustrate how you use LCM to turn unlike denominators into like denominators, let's suppose you want to add the fraction 1/3 to the fraction 2/5.
The first step is to find the lowest number that both 3 and 5 will divide into evenly (the LCM). According to my calculations, the LCM of the two denominators (3 & 5) is 15.
Once we have found the LCM for the two denominators, the next step is to multiply the top and bottom of each fraction by the number of times each fraction's denominator goes into the LCM.
Since 3 goes into 15 a total of 5 times, you would multiply the top and bottom of 1/3 by 5, which results in 5/15.
Next, since 5 goes into 15 a total of 3 times, you would multiply the top and bottom of 2/5 by 3, which results in 6/15.
Finally, since both denominators are now the same, you simply add the numerators (5 + 6) while keeping the denominator (15) the same -- giving you a result of 11/15. Here is how our example of adding fractions with unlike denominators might appear on paper:
|Adding with Unlike Denominators|
|1 x 5||+||2 x 3||=||5||+||6||=||11|
|3 x 5||5 x 3||15||15||15|
The steps to subtract fractions are the same as the steps to add fractions.
If you are subtracting fractions with like denominators, you simply subtract the second numerator from the first numerator and keep the denominator the same.
|Subtracting with Like Denominators|
If you are subtracting fractions with unlike denominators, you go through the same process as when adding fractions with unlike denominators.
|Subtracting with Unlike Denominators|
|2 x 5||-||1 x 3||=||10||-||3||=||7|
|3 x 5||5 x 3||15||15||15|
With that, let's use the Adding Subtracting Fractions Calculator to add one fraction to another, or to subtract one fraction from another.
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Least Common Multiple (LCM): The process of finding the smallest number that the denominators of two or more fractions will all divide into evenly. This process is necessary for adding or subtracting fractions with different denominators.
Numerators: Enter the top numbers for each of the fractions you are adding or subtracting. If you would like one of the fractions to be whole number, simply enter the desired whole number in the numerator field and enter a 1 in the denominator field (4/1 = 4). If you want to add or subtract a mixed number, simply convert the mixed number to an improper fraction (1 1/3 = 4/3) before entering.
Denominators: Enter the bottom numbers for each of the fractions you are adding or subtracting. Note that the Adding Subtracting Fractions Calculator requires the denominators to be greater than zero.
Answer: This is the result of addition or subtraction of the two fractions. After calculating fractions, the Adding Subtracting Fractions Calculator will show its work and give a detailed explanation of each step it took to arrive at the answer.