Fraction Calculator

Do arithmetic with fractions and mixed numbers, every operation simplified, with the steps shown.

How to use this calculator

Enter two fractions, plain (3/4), mixed (1 1/2), or whole numbers, pick the operation, and press Calculate. You get the simplified result three ways: as a fraction, as a mixed number, and as a decimal, with the working shown.

How it works

Each operation has its own rule. Adding and subtracting need a common denominator first. Multiplying is direct: numerator times numerator, denominator times denominator. Dividing means multiplying by the reciprocal (flip the second fraction). Every result is then reduced by its GCF.

+/− : common denominator · × : straight across · ÷ : multiply by reciprocal

Worked example

Example: 1/2 + 1/3

Step 1, Common denominator: the LCM of 2 and 3 is 6, so 1/2 = 3/6 and 1/3 = 2/6.

Step 2, Add numerators: 3/6 + 2/6 = 5/6.

Step 3, Simplify: 5/6 is already in lowest terms. As a decimal: ≈ 0.833.

Common mistakes

Adding straight across: 1/2 + 1/3 is not 2/5. Denominators must match before numerators combine.
Forgetting the reciprocal: 1/2 ÷ 1/4 = 1/2 × 4/1 = 2, not 1/8.
Leaving the answer unsimplified: 2/4 should be reduced to 1/2, the calculator always reduces for you.

When to use it

Fractions run cooking measurements, construction, music rhythm, probabilities, and any US customary units (halves, quarters, eighths of an inch). Fluency here pays off everywhere from middle-school homework to workshop math.

Frequently asked questions

How do you add fractions with different denominators?

Find a common denominator (the LCM of the denominators works best), convert both fractions, then add the numerators. 1/2 + 1/3 = 3/6 + 2/6 = 5/6.

How do you divide fractions?

Flip the second fraction and multiply: a/b ÷ c/d = a/b × d/c. So 1/2 ÷ 1/4 = 1/2 × 4/1 = 2.

What is a mixed number?

A whole number plus a fraction, like 1 1/2 (one and a half). To compute with it, convert first: 1 1/2 = 3/2.

How do you simplify a fraction?

Divide the numerator and denominator by their greatest common factor. For 6/8, the GCF is 2, giving 3/4.

More worked examples: all four operations

The example above covers one addition. Here are five more, one for each operation, all with different numbers. Each one shows the full working, so you can follow the same steps with your own numbers.

Example: 3/4 + 5/6

Step 1, Common denominator: the LCM of 4 and 6 is 12, so 3/4 = 9/12 and 5/6 = 10/12.

Step 2, Add numerators: 9/12 + 10/12 = 19/12.

Step 3, Convert: 19/12 is an improper fraction, so 19 divided by 12 is 1 remainder 7, giving 1 7/12. As a decimal: about 1.5833.

If you use 24 instead of 12 it still works: 18/24 + 20/24 = 38/24, which simplifies to 19/12. The LCM just keeps the numbers smaller.

Example: 7/8 – 3/5

Step 1, Common denominator: the LCM of 8 and 5 is 40, so 7/8 = 35/40 and 3/5 = 24/40.

Step 2, Subtract numerators: 35/40 – 24/40 = 11/40.

Step 3, Simplify: 11 is prime and shares no factor with 40, so 11/40 is already in lowest terms. As a decimal: 0.275.

Check: 7/8 is 0.875 and 3/5 is 0.6, and 0.875 – 0.6 = 0.275, which matches the fraction answer.

Example: 5/6 x 4/7

Step 1, Cancel first: 4 and 6 share a factor of 2, so cancel them to 2 and 3. The problem becomes 5/3 x 2/7. This step is optional, but it keeps the numbers small.

Step 2, Multiply across: numerators 5 x 2 = 10, denominators 3 x 7 = 21, giving 10/21.

Step 3, Simplify: 10 and 21 share no common factor, so 10/21 is final. As a decimal: about 0.4762.

Multiplying straight across without cancelling gives 20/42, which simplifies to the same 10/21.

Example: 9/10 ÷ 3/4

Step 1, Flip the second fraction: 3/4 becomes 4/3, and the problem becomes 9/10 x 4/3.

Step 2, Cancel first: 9 and 3 share a factor of 3, so cancel them to 3 and 1. The problem becomes 3/10 x 4/1.

Step 3, Multiply across: 3 x 4 = 12 and 10 x 1 = 10, giving 12/10, which simplifies to 6/5, or 1 1/5. As a decimal: 1.2.

Check: 6/5 x 3/4 = 18/20 = 9/10, which is the number we started with, so the division is correct.

Example: 2 3/5 + 1 2/3

Step 1, Convert to improper fractions: 2 3/5 = 13/5 and 1 2/3 = 5/3.

Step 2, Common denominator: the LCM of 5 and 3 is 15, so 13/5 = 39/15 and 5/3 = 25/15.

Step 3, Add: 39/15 + 25/15 = 64/15.

Step 4, Convert back: 64 divided by 15 is 4 remainder 4, giving 4 4/15. As a decimal: about 4.2667.

When to add, subtract, multiply or divide

The hardest part of fraction work is often not the arithmetic but choosing the operation. These four questions decide it.

Add or subtract when you combine or compare parts of the same whole. In cooking, you pour 5/8 cup of flour into a bowl that already holds 1/4 cup. Since 1/4 = 2/8, the total is 5/8 + 2/8 = 7/8 cup. In woodworking, a board measures 5 1/4 inches and you cut off 1 1/2 inches. As improper fractions that is 21/4 – 6/4 = 15/4, or 3 3/4 inches left.

Multiply when you take a fraction of a fraction. The word “of” is the signal. Taking 3/4 of 2/5 of a cake means 3/4 x 2/5 = 6/20 = 3/10 of the cake. Scaling a recipe works the same way: half of 2/3 cup is 1/2 x 2/3 = 2/6 = 1/3 cup.

Divide when you split something into equal portions, or ask how many of one amount fit into another. How many 1/4 cup scoops fill 3 cups? 3 ÷ 1/4 = 3 x 4 = 12 scoops. How many 1/6 yard pouches can you cut from 5/6 yard of fabric? 5/6 ÷ 1/6 = 5 pouches.

Quick check: if the answer should be smaller than what you started with, you probably multiplied by a proper fraction, or divided by a number bigger than 1. If the answer should be bigger, you probably added, or divided by a fraction smaller than 1, since dividing by 1/4 is the same as multiplying by 4.

Fractions, decimals and percentages: which form to use

All three forms describe the same value, but each one fits a different job.

Fractions keep exact values. One third is 1/3 exactly, while 0.333 is only an approximation, and 33.33 percent is also rounded. Use fractions when the exact answer matters, for example in homework that asks for exact form, or in a recipe where 1/3 cup is a real measuring mark.

Decimals are easiest when you need to compare sizes quickly or add on a calculator, and money is almost always decimal. A decimal ruler or a digital scale reads in decimals, so convert when the tool you are using speaks decimal.

Percentages are best for comparing parts of different wholes. 68 percent versus 71 percent is clearer than 17/25 versus 71/100, because both percentages are out of the same 100. Test scores, discounts and survey results are usually percentages for this reason.

2/5 = 0.4 = 40% · 3/5 = 0.6 = 60% · 4/5 = 0.8 = 80% · 7/10 = 0.7 = 70% · 9/10 = 0.9 = 90% · 1/10 = 0.1 = 10%

Rule of thumb: keep the fraction while you work, and convert only at the last step, for the answer your reader expects. Converting early invites rounding errors, because a rounded decimal carried through three steps is no longer exact.

How to check your answer

Estimate first. 3/4 is close to 1 and 5/6 is close to 1, so their sum must be close to, but less than, 2. The answer 1 7/12 passes that test. If your exact answer is nowhere near your estimate, recheck the common denominator.

Check the sign. Subtracting a bigger fraction from a smaller one must give a negative answer. If you get a positive answer there, the order is flipped.

Check the simplification. The numerator and denominator of a finished answer should share no common factor other than 1. If both are even, or both end in 5 or 0, you can still divide.

Check by reversing. Multiply your answer by the divisor to get back the first fraction, or add the answer to the fraction you subtracted. If the round trip fails, one step is wrong.