How to add and simplify fractions with prime factors and GCD

Read the fraction before calculating

A fraction represents division: in 3/4, the numerator is 3 and the denominator is 4. To add two fractions, both must describe parts of the same size. Adding numerators and denominators separately does not perform that addition. Before entering values, identify the relationship you need to calculate and retain every sign.

The calculator accepts integers and expressions such as -3/4. Enter 3 for an integer or 3/1 to show its denominator. Mixed numbers and decimals are not accepted: convert 1 1/2 to 3/2 and 0.5 to 1/2 first. A zero denominator is invalid. Each component accepts up to thirty digits. Spaces around a slash do not change the fraction, but extra words or measurement symbols are not operands.

Use LCM to find parts of the same size

For 1/3 + 1/6, enter 3 and 6 separated by a space in the GCD and LCM calculator. The results are GCD 3 and LCM 6. The least common multiple lets you choose 6 as the common denominator: one third equals two sixths, so 2/6 + 1/6 gives 3/6.

GCD answers a different question: what is the largest integer dividing both values without a remainder? Reduce 3/6 by dividing numerator and denominator by their GCD, which is 3. The result is 1/2. Multiplying the original denominators also provides a common denominator, but can create unnecessarily large numbers. Keep the common denominator separate from the divisor used for reduction.

1/3 = 2/6
1/6 = 1/6
2/6 + 1/6 = 3/6 = 1/2

1. Find the LCM of denominators 3 and 6.
2. Enter 1/3 and 1/6 in the fraction calculator.
3. Select addition and calculate.
4. Check that the exact result is 1/2.

Understand what prime factors contribute

The prime factorization of 360 is 2 × 2 × 2 × 3 × 3 × 5. Each factor must appear as many times as needed; writing only 2 × 3 × 5 drops repeated factors and gives a different product. Multiply all factors to recover 360. If the output contains only the original number, that integer is prime.

Factors explain why a common divisor exists. For 24 and 36, shared factors form a GCD of 12, and the LCM is 72. The factorization tool accepts integers from 2 to 1000000000000. One is not prime and is outside this decomposition format. Enter digits without thousands separators or scientific notation; do not confuse a displayed multiplication sign with part of the numeric input.

Multiply, divide and retain the sign

To multiply fractions, multiply their numerators and their denominators. For example, 3/4 × 2/3 gives 6/12, reduced to 1/2. To divide, multiply by the reciprocal of the second operand: 3/4 ÷ 2/3 gives 9/8. Division by a fraction whose value is zero is not defined.

Signs are part of the data too: 3/4 ÷ -2/3 gives -9/8. The calculator displays a positive final denominator and places any negative sign in the numerator. A fraction reduced to denominator one is displayed as an integer, and zero is displayed as 0. Calculations use arbitrary-precision integers instead of replacing an exact fraction with a rounded decimal.

Check before copying the result

Try the inverse operation with the same values. If 1/3 + 1/6 produces 1/2, then 1/2 - 1/6 should return 1/3. For multiplication, divide the result by the second factor when it is nonzero. This check can reveal a changed sign or selection of the wrong operation.

Data is processed in your browser. Calculating prepares the output; downloading a text file is a separate action. Changing an operand invalidates the earlier result. Retain the original problem and selected operation with the answer if you need to review it later: a file containing 1/2 does not explain how it was obtained. The tool solves the calculation entered, rather than interpreting a written word problem automatically.