How do I add fractions with different denominators?

Find the LCD (lowest common denominator), rewrite both fractions over it, then add the numerators. Example: 1/2 + 1/3 → LCD of 2 and 3 is 6 → 3/6 + 2/6 = 5/6. Same denominators: just add the numerators directly. This calculator does it automatically and simplifies the result.

How do I multiply and divide fractions?

To multiply, multiply numerators together and denominators together: 2/3 × 3/5 = 6/15 = 2/5. To divide, flip (take the reciprocal of) the second fraction and multiply: 5/6 ÷ 5/4 = 5/6 × 4/5 = 20/30 = 2/3. No common denominator is needed for either.

What does simplifying to lowest terms mean?

Divide the numerator and denominator by their GCF (greatest common factor, also called HCF in Indian textbooks). 6/8 ÷ 2 = 3/4. A fraction is in lowest terms when the GCF of its numerator and denominator is 1, so it cannot be reduced further.

How do I convert a fraction to a decimal or percentage?

Divide the numerator by the denominator for the decimal: 3/4 = 3 ÷ 4 = 0.75. Multiply that by 100 for the percentage: 0.75 × 100 = 75%. This is the same step used to turn marks like 18/20 into 90%.

Can this calculator handle negative or improper fractions?

Yes. Enter a negative fraction as -1/3, and improper fractions like 7/4 work directly (the result also shows the mixed-number form 1 3/4). The sign is tracked correctly through addition, subtraction, multiplication, and division.

What is the LCD and how is it different from the GCF?

The LCD (lowest common denominator) is the smallest number both denominators divide into — you need it to add or subtract fractions. The GCF (greatest common factor) is the largest number that divides both the numerator and denominator — you use it to simplify the answer. For 2 and 3 the LCD is 6; for 6 and 8 the GCF is 2.

Fraction Calculator — Add, Subtract, Multiply & Divide

Fraction

📐 Math

Fraction Calculator

Add, subtract, multiply, and divide fractions and mixed numbers with step-by-step solution.

Reviewed by the CalculatorKosh Editorial TeamUpdated June 2026Free · No sign-up

Quick examples

First fraction

Operation

Second fraction

Answer

= 0.833333 (decimal)

Step-by-step solution

Step 1LCD of 2 and 3 = 6

Step 2Convert: 1/2 = 3/6 | 1/3 = 2/6

Step 3Add numerators: 3 + 2 = 5

FinalSimplify by GCF(5,6) = 5/6

How It Works

A fraction is a way of writing a part of a whole — the top number (numerator) tells you how many parts you have, and the bottom number (denominator) tells you how many equal parts make the whole. This calculator adds, subtracts, multiplies, and divides fractions and automatically reduces the answer to lowest terms, showing every step of the working so you can learn the method, not just copy the answer. It handles simple fractions (3/4), negative fractions (−1/2), mixed numbers (2 3/4), improper fractions (7/4), and whole numbers, and it also returns the decimal and mixed-number forms of the result.

Who this calculator is for

Fractions show up constantly in school maths from Class 5 onwards, so this tool is heavily used by CBSE, ICSE and state-board students and the parents helping them check homework. Beyond the classroom, fractions appear in recipe scaling (half of 3/4 cup of atta), in carpentry, tailoring and home-improvement measurements where lengths are written in fractions, in stitching patterns, and whenever you split a bill, a pizza or a box of sweets into unequal shares. Anyone who wants a fast, reliable answer with the steps spelled out — rather than reaching for long-hand arithmetic — will find it useful.

How to enter fractions

Simple fraction: 3/4 · Mixed number: 2 3/4 (with a space) · Whole number: 5 · Negative: -1/3 · Improper: 7/4. A mixed number is converted internally to an improper fraction first — for 2 3/4, multiply the whole number by the denominator and add the numerator (2 × 4 + 3 = 11) to get 11/4 — and the calculator does this for you automatically.

The four fraction formulas

Add / Subtract: a/b ± c/d = (a×d ± c×b) / (b×d) — put both fractions over a common denominator, then add or subtract the numerators while keeping the denominator the same. You can always use the product of the denominators (b×d) as a common denominator, but using the lowest common denominator (LCD) keeps the numbers smaller and the final simplification shorter.

Multiply: a/b × c/d = (a×c) / (b×d) — multiply straight across, numerator times numerator and denominator times denominator; no common denominator is needed. “Of” means multiply, so half of 3/4 is 1/2 × 3/4 = 3/8.

Divide: a/b ÷ c/d = (a×d) / (b×c) — flip the second fraction to its reciprocal and multiply. Dividing by a number and multiplying by its reciprocal always give the same result.

Simplifying with the GCD (HCF)

Every answer is reduced to lowest terms by dividing the numerator and denominator by their greatest common divisor (GCD), called the highest common factor (HCF) in Indian textbooks. A fraction is in lowest terms when that GCD is 1, meaning it cannot be reduced any further. For example, 18/24 has a GCD of 6, so it simplifies to 3/4; 8/12 has a GCD of 4, giving 2/3. The calculator finds the GCD with the Euclidean algorithm and applies it automatically, and it also tracks the sign correctly so that a result like −6/8 is shown cleanly as −3/4.

Worked example

Add 1/2 + 1/3. The denominators 2 and 3 have a lowest common denominator (LCD) of 6. Rewrite each fraction over 6: 1/2 = 3/6 and 1/3 = 2/6. Now add the numerators: 3/6 + 2/6 = 5/6. Since the GCD of 5 and 6 is 1, the fraction is already in lowest terms, so the answer is 5/6 (about 0.833 as a decimal). A division example: 5/6 ÷ 5/4 means flip the second fraction and multiply, 5/6 × 4/5 = 20/30, and dividing top and bottom by their GCD of 10 gives 2/3.

Converting fractions to decimals and percentages

To turn a fraction into a decimal, divide the numerator by the denominator: 3/4 = 3 ÷ 4 = 0.75. Multiply that decimal by 100 to get a percentage: 0.75 × 100 = 75%. This is exactly the step used to turn exam marks like 18/20 into 90%, which is why the result panel above always shows the decimal form alongside the fraction.

Tips and common mistakes

You only need a common denominator for addition and subtraction — never for multiplication or division.
Do not add denominators. 1/2 + 1/3 is not 2/5; you must convert to a common denominator first.
Always simplify at the end by dividing the top and bottom by their GCD (HCF). 6/8 becomes 3/4.
To divide by a fraction, multiply by its reciprocal — “flip the second one”. Dividing by 1/2 is the same as multiplying by 2.
A whole number is just a fraction over 1: 5 = 5/1. That makes it easy to add a whole number to a fraction.
Watch the signs. Subtracting a larger fraction from a smaller one gives a negative answer, and two negatives multiplied give a positive.

Frequently Asked Questions

Find the LCD (lowest common denominator), rewrite both fractions over it, then add the numerators. Example: 1/2 + 1/3 → the LCD of 2 and 3 is 6 → 3/6 + 2/6 = 5/6. If the denominators are already the same, just add the numerators directly. This calculator finds the LCD, converts, adds, and simplifies for you.

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