How to Calculate Fractions (Add, Subtract, Multiply)

Fractions trip up a lot of people because each operation follows a different rule: you need a common denominator to add but not to multiply. This guide lays out the rules clearly and walks you through the Fraction Calculator, which adds, subtracts, multiplies and divides fractions and shows the answer reduced to lowest terms with its decimal value. It is free and runs in your browser, perfect for homework, recipes and everyday math.

The rules for each operation

Each operation has its own method:

• Adding and subtracting: find a common denominator, convert both fractions, then add or subtract the numerators. For example, 1/2 + 1/3 becomes 3/6 + 2/6 = 5/6.
• Multiplying: multiply the numerators together and the denominators together. So 2/3 x 4/5 = 8/15.
• Dividing: flip the second fraction and multiply. So 1/2 / 3/4 = 1/2 x 4/3 = 4/6 = 2/3.

Then reduce to lowest terms by dividing the top and bottom by their greatest common divisor (GCD). The calculator does each step automatically.

How to use the Fraction Calculator

Solve a fraction problem in seconds:

1. Open the Fraction Calculator.
2. Enter the first fraction (numerator and denominator).
3. Choose the operation: add, subtract, multiply or divide.
4. Enter the second fraction.
5. Read the answer, automatically reduced to lowest terms, along with its decimal equivalent.

It handles whole numbers too: just enter a 1 as the denominator. Mixed numbers can be entered as improper fractions, for example 1 and 1/2 as 3/2.

A worked example

Add 3/4 and 5/6.

• Common denominator of 4 and 6 is 12.
• Convert: 3/4 = 9/12 and 5/6 = 10/12.
• Add numerators: 9/12 + 10/12 = 19/12.
• 19/12 is already in lowest terms (GCD is 1).
• As a decimal that is about 1.583, or the mixed number 1 and 7/12.

The calculator returns 19/12 and 1.5833 at once, so you can use whichever form your work needs.

Common fraction-to-decimal values

It helps to recognise common conversions at a glance:

The calculator shows the decimal for any fraction you enter, so you never have to memorise these.

Where fractions come up

Fraction math is everywhere outside the classroom:

• Cooking: doubling or halving a recipe (1/3 cup x 2)
• DIY and woodworking: adding measurements in inches
• Time: working in quarter and half hours
• Finance: shares and proportions
• School and exams: the core of arithmetic and algebra

For converting a fraction to a percentage, the Percentage Calculator pairs well with this tool. Browse more in calculators.

How reducing to lowest terms works

A fraction is in lowest terms when the numerator and denominator share no common factor other than 1. To reduce one by hand, find the greatest common divisor (GCD) of the top and bottom, then divide both by it. Take 18/24. The factors of 18 are 1, 2, 3, 6, 9, 18 and the factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24, so the largest factor they share is 6. Dividing both by 6 gives 3/4, which cannot be reduced further. Reducing matters because 3/4 is far easier to read and compare than 18/24, even though they are exactly equal. A quick way to spot a reducible fraction is to check whether both numbers are even, both end in 0 or 5, or both are divisible by 3 (their digits sum to a multiple of 3). The calculator finds the GCD and reduces every answer for you, but knowing the method helps you check the result and simplify fractions on paper during an exam.

A worked multiplication and division example

Multiplication and division do not need a common denominator, which surprises many learners. To multiply 2/3 by 9/10, multiply straight across: 2 x 9 = 18 on top and 3 x 10 = 30 on the bottom, giving 18/30, which reduces to 3/5. You can also cancel before multiplying: the 9 and 3 share a factor of 3, and the 2 and 10 share a factor of 2, leaving (1/1) x (3/5) = 3/5 with smaller numbers to handle.

Division flips the second fraction, then multiplies. To divide 3/5 by 2/7, rewrite it as 3/5 x 7/2 = 21/10, which is 2 and 1/10 as a mixed number, or 2.1 as a decimal. Here is each operation on the same pair, 1/2 and 1/4, so you can see how different the rules are:

Notice that dividing by a fraction smaller than 1 gives a result larger than you started with, which catches people out. The reason is that dividing asks how many of the second fraction fit into the first, and a small piece fits many times. Cancelling common factors before you multiply, as shown above, keeps the numbers small and makes the final reducing step easier, which is well worth the habit on harder problems.

Tips, mistakes and privacy

Avoid the classic errors:

• Do not add denominators when adding fractions. 1/2 + 1/2 is 1, not 2/4.
• Do not forget to flip the second fraction when dividing.
• Always reduce the final answer to lowest terms.

The Fraction Calculator runs entirely in your browser, so nothing you enter is uploaded or stored. It is free with no sign-up. Keep the Fraction Calculator open while you work through problems. See all tools for more.