Fraction Calculator

Fraction Calculator With Steps Shown

This fraction calculator will show you the working out for each answer it’s totally free, and there’s no need to register. Add, subtract, multiply, or divide fractions and mixed numbers and see exactly how the fraction calculator got there, not just a final figure dropped on the screen. Helping with homework, working out measurements on a job site, or double-checking your own arithmetic, the steps below go through each operation in the order most people actually need them, with worked examples that are computed fresh for this page rather than copied from anywhere else. There is also a separate section on a more sophisticated topic, partial fraction decomposition, for those dealing with calculus or engineering courses, maintained separate from the main portions so it doesn’t interfere with ordinary homework aid.

Adding Fractions

To add two fractions, you first need a common denominator, a common bottom number that both of the fractions may be written over. If the denominators are the same, all you have to do is add the numerators (the number on top) and keep the numerator the same.

Let us do one-fourth plus two-thirds.

The denominator values are 4 and 3. So the least common denominator (LCD) is the smallest number that both 4 and 3 divide evenly into. (12)

Change both denominators to 12ths:

1/4 = 3/12 (multiply numerator and denominator by 3) 2/3 = 8/12 (multiply numerator and denominator by 4)

Now, let’s add the numerators:

3/12 + 8/12 = 11/12 

There are no common factors of 11 and 12 on the fraction calculator; hence, we have a fraction in lowest terms here. Then that’s the whole trick: find the LCD, switch both fractions, add the numerators, then reduce if you can. This identical LCD, convert, combine, and simplify 4-step approach will work for all addition problems you’ll run into, no matter how the variables look at first glance.

Subtracting Fractions

The initial step in subtracting fractions is precisely the same as adding: establish a common denominator before you touch the numerators.

So we want to find 5/6 – 1/4.

The LCD of 6 and 4 is 12.

Simplify the two fractions:

5/6 = 10/12 (multiply top and bottom by 2). 1/4 = 3/12 (multiply top and bottom by 3)

Now take away:

10/12 − 3/12 = 7/12 

Since 7 and 12 have no common factors, 7/12 is already in simplest form. The only actual difference between adding and subtracting fractions is the last operation performed on the numerators. Everything else about finding a common denominator works exactly the same.

Multiplying Fractions (The Easy One)

The good news is multiplying fractions is actually easier than adding or subtracting them because you don’t have to find a common denominator at all. All you have to do is multiply straight across top by top and bottom by bottom, then simplify.

Now let us see 2/3 x 3/5.

Multiply the top numbers. 2 × 3 = 6 Multiply the denominators as follows: 3 x 5 = 15

That’s 6/15. (Both numbers divide by 3, so we can reduce to 2/5.)

This is honestly the operation students most commonly overthink, looking for a common denominator that is not at all needed here. If you are looking for one before multiplying two fractions, then you should stop and just multiply straight across.

Dividing Fractions

Dividing fractions is just one step more complicated than multiplying. Simply turn over the second fraction (get its reciprocal) and then multiply as normal.

Let’s do 3/4 divided by 2/5.

Change the second fraction to 5/2.

Now multiply instead of divide:

3/4 × 5/2 = 15/8 

Change to the mixed number 15/8 equals 1 7/8.

So, here is why flipping works and is not just something you have to memorize. When you divide by a fraction, it is the same thing as saying “How many of this fraction fit in that one?” Well when you multiply by the reciprocal you are answering the identical question in a mathematically equivalent way. Dividing by 2/5 is the same thing as multiplying by 5/2 because a number divided by a fraction and the number times the reciprocal of the fraction are always equal, always, no matter what fraction you choose.

Mixed Fraction Calculator: Working With Whole Numbers

Most of the errors on fraction calculator homework are with mixed numbers, which are a full number and a fraction, like 2 3/4. They’re worth the added effort to become used to converting them.

To convert a mixed number to an improper fraction (a fraction where the numerator is larger than its denominator), do the following: multiply the entire number by its denominator, then add the numerator, and put that answer over the original denominator.

2 3/4 becomes 2.75

(2 × 4) + 3 = 8 + 3 = 11 

So 2 3/4 = 11/4.

Now let’s apply that to solve a complete mixed-number addition problem: 2 3/4 + 1 1/2.

Change both mixed numbers to improper fractions:

2 3/4 = 11/4 1 1/2 = 3/2 

Find the LCD of 4 and 2, which is 4, and convert:

11/4 stays as 11/4. 3/2 = 6/4 (multiply top and bottom by 2)

Add the top numbers:

11/4 + 6/4 = 17/4 

Mixed number convert: 17 ÷ 4 = 4 remainder 1 So the solution is 4 1/4.

The step people most typically skip is to first convert to an incorrect fraction. Adding the totals and the fractional parts separately is one method to do this, but it is so much easier to make a mistake that way than by converting everything to a single incorrect fraction up front, as demonstrated below. This one habit corrects most mixed-number errors observed in homework: change first, add second.

How to calculate fraction to decimal

One easy rule can be used to turn a fraction into a decimal: divide the numerator by the denominator.

3/8 is equal to 3 times 8, which is 0.375. This is a terminating decimal, which means that the division works out perfectly, with no digits that are repeated.

1/3 = 1/3 x 3 = 0.333, and the 3s keep coming back over and over. The number 0.33 is an example of a repeating decimal. For ease of use, it is usually written with a bar over the repeating digit or rounded to that number.

This table shows common fraction-to-decimal conversions. It can help students and people who need to understand imperial measurements on the job, like a tape measure marked in sixteenths:

People in trades who are reading a tape measure marked in sixteenths and students who are turning a test score into a decimal both use the same method shown above. For imperial measurements, there is no special “trick”; it’s just the same process of going from fractions to decimals, but in a different situation.

Advanced: Partial Fraction Decomposition

A partial fraction decomposition calculator transforms a complicated algebraic fraction into a sum of simpler fractions. This is mostly beneficial as simpler fraction calculators are considerably easier to integrate in calculus. A complex statement that seems impossible to integrate directly often becomes trivial when split out like this. This is a technique you’ll see in calculus courses and some engineering applications, way beyond the daily arithmetic described above, which is precisely why it gets its own clearly distinct part here rather than being jumbled in with the main operations.

Let’s look at a full example with distinct linear factors: (5x − 4) ÷ ((x − 1)(x + 2)).

Rewrite the decomposition as a sum of two simpler fractions with an unknown numerator:

(5x − 4) ÷ (x − 1)(x + 2) = A ÷ (x − 1) + B ÷ (x + 2)

Multiply both sides by (x − 1)(x + 2) to clear the denominator:

5x – 4 = A(x + 2) + B(x – 1)

Now replace x with the values that make one of the terms disappear. First let x = 1, cancelling out the B term:

5(1) − 4 = A(1 + 2) + B(0) 1 = 3A, A = 1/3

Now let x = -2, which zeros out the A term:

5(−2) − 4 = A(0) + B(−2 − 1) −14 = −3B B = 14/3

The last breakdown is

(5x − 4)/((x − 1)(x + 2)) = (1/3)/(x − 1) + (14/3)/(x + 2)

You can check this result by choosing any test value of $x$ and verifying that both sides agree. For x = 0: original expression produces -4 / (-1 * 2) = 2; deconstructed, it gives (1/3) / (-1) + (14/3) / 2 = -1/3 + 7/3 = 2. The correct answers are A and B. They both agree.

This example works with different linear components, the simplest scenario. In practice, there are two other situations: repeated factors, such as (x − 1)², which require an additional term for each power of the repeated factor, and irreducible quadratic factors, which cannot be broken down into linear pieces and instead require a numerator of the form (Cx + D) rather than a single constant. Both situations employ the same fundamental substitution strategy as discussed before, but with more words to resolve for.

Conclusion

All worked examples on this fraction calculator, from the core operations through to the partial fractions section, have been separately computed for this page and checked before posting, including checking the partial fractions result by substituting a test value back into the original expression. This fraction calculator deals with normal, settled curriculum mathematics, from simple fraction arithmetic to a truly more sophisticated calculus-adjacent issue, clearly split so each audience discovers what they came for without wading through stuff meant for someone else. If you don’t get the answer you anticipate, go through the numbers again slowly. Mistakes with fractions usually come down to a missed common denominator step or not converting a mixed number first.

FAQs

Q1. How do you add fractions with different denominators?

Find the lowest common denominator (LCD), change the fractional values to the LCD, then add the numerators. For example 1/4 + 2/3 has an LCD of 12 therefore that is 3/12 + 8/12 = 11/12.

Q2. Why do you flip the second fraction when dividing?

Always dividing by a fraction calculator and multiplying by the reciprocal of that fraction (the opposite of it) gives the same answer. This is not an arbitrary rule, but flipping and multiplying is a mathematically equivalent way of posing the same division question and is just easier to compute.

Q3. How do I turn a mixed number into an improper fraction?

Multiply the entire amount by the bottom number and add the top number. Place that over the bottom number. For 2 3/4: (2 x 4) plus 3 = 11; therefore, 11/4.

Q4. How do I convert a fraction to a decimal?

Divide the numerator by its denominator. 3/8 = 0.375, a terminating decimal. 1/3 = 0.333… (a repeating decimal) since the division never works out perfectly.

Q5. Do I need a common denominator to multiply fractions?

Nope. This is one of the most frequent mistakes in fraction arithmetic. To multiply merely cross multiply, numerator to numerator, denominator to denominator, then cancel. common denominator is only used for adding and subtracting

Q6. What is partial fraction decomposition used for?

It is typically used to split a difficult algebraic fraction into simpler parts to be integrated in calculus. In this method, a fraction that appears complex or impossible to integrate directly typically becomes doable when it is broken down into basic fractions.