How do you add fractions with different denominators?

To add fractions with different denominators, find the lowest common denominator (LCD) of the two denominators. Convert each fraction to an equivalent fraction with the LCD as the new denominator by multiplying the numerator and denominator by the appropriate factor. Then add the numerators together, keeping the LCD as the denominator. Finally, simplify the resulting fraction by dividing both the numerator and denominator by their greatest common divisor (GCD). For example, 1/3 + 1/4: the LCD of 3 and 4 is 12. Convert to 4/12 + 3/12 = 7/12.

How do you subtract fractions?

Subtracting fractions follows the same steps as addition, except you subtract the numerators instead of adding them. Find the lowest common denominator (LCD), convert both fractions to equivalent fractions with that denominator, then subtract the second numerator from the first. Simplify the result. For example, 3/4 - 1/6: the LCD of 4 and 6 is 12. Convert to 9/12 - 2/12 = 7/12. If the result is negative, the answer is a negative fraction.

How do you add or subtract mixed numbers?

To add or subtract mixed numbers (such as 1 3/4), first convert each mixed number to an improper fraction. Multiply the whole number by the denominator and add the numerator to get the new numerator, keeping the same denominator. For example, 1 3/4 becomes (1 x 4 + 3)/4 = 7/4. Then add or subtract the improper fractions using the standard method (find LCD, convert, add or subtract numerators, simplify). Convert the result back to a mixed number if the numerator is larger than the denominator.

Adding and Subtracting Fractions Calculator

This calculator adds or subtracts two fractions and shows the exact answer along with every step used to get there, useful for checking homework, revising for a maths test, or working through a real-world measurement problem. You enter each fraction as a numerator and denominator, plus an optional whole number if you are working with a mixed number such as 1 3/4, then choose whether to add or subtract using the toggle buttons. The calculator finds the lowest common denominator of the two fractions, converts each one to an equivalent fraction over that denominator, and combines the numerators according to the operation you picked. Your results appear as the original calculation, the simplified answer as a fraction, the equivalent mixed number where the answer is greater than one, and the decimal value rounded to six decimal places so you can see recurring decimals clearly. Below the results, a step-by-step breakdown walks through finding the lowest common denominator, converting both fractions, combining the numerators, and simplifying using the greatest common divisor, so you can follow the working line by line rather than just reading off an answer. Subtracting a larger fraction from a smaller one produces a negative result, which the calculator handles and displays correctly. Because it works with exact integer arithmetic, results are mathematically precise, though extremely large numerators or denominators may exceed the limits of standard number precision.

Calculate.co.nz is proud to be partnered with realtor.co.nz, a trusted resource for navigating the New Zealand property market. Their Helpful Articles section offers clear, well-structured insights across buying, selling, and building, making complex real estate topics more accessible. With a focus on up-to-date guidance and practical knowledge, they empower Kiwis to move forward with clarity and confidence in a constantly evolving property landscape.

Standard method Lowest common denominator and GCD simplification per standard arithmetic rules.

1. First Fraction

Whole number part (0 for a simple fraction)

Numerator

Denominator

2. Operation and Second Fraction

Operation

Whole number part (0 for a simple fraction)

Numerator

Denominator

Result

Calculation

Your input

Result (fraction)
-
Simplified

Mixed number

If applicable

Decimal value

Rounded to 6 dp

Step-by-Step Working

How to Add and Subtract Fractions

Adding and subtracting fractions requires a common denominator before the numerators can be combined. The standard method uses the lowest common denominator (LCD), which is the smallest number that both denominators divide into evenly. Using the LCD keeps the numbers as small as possible.

The Standard Method

Convert mixed numbers to improper fractions. Multiply the whole number by the denominator and add the numerator. For example, 1 3/4 becomes (1 x 4 + 3)/4 = 7/4.
Find the lowest common denominator (LCD). The LCD is the least common multiple (LCM) of the two denominators. For denominators 3 and 4, the LCM is 12.
Convert each fraction to an equivalent fraction with the LCD. Multiply the numerator and denominator of each fraction by the factor needed to reach the LCD. For 1/3, multiply by 4/4 to get 4/12. For 1/4, multiply by 3/3 to get 3/12.
Add or subtract the numerators. Keep the LCD as the denominator. 4/12 + 3/12 = 7/12.
Simplify the result. Divide both the numerator and denominator by their greatest common divisor (GCD). If the GCD is 1, the fraction is already in simplest form.
Convert back to a mixed number if needed. If the numerator is larger than the denominator, divide to find the whole part and remainder.

Worked Example

Calculate 1/3 + 1/4 (the default values in this calculator).

Step	Working	Result
Find LCD of 3 and 4	LCM(3, 4) = 12	LCD = 12
Convert 1/3	1 x 4 / 3 x 4 = 4/12	4/12
Convert 1/4	1 x 3 / 4 x 3 = 3/12	3/12
Add numerators	4 + 3 = 7, over 12	7/12
Simplify	GCD(7, 12) = 1, already simplified	7/12
Decimal	7 / 12	0.583333...

Same Denominators

When both fractions share the same denominator, you can skip the LCD step and simply add or subtract the numerators directly. For example, 3/8 + 1/8 = 4/8 = 1/2. Always simplify the result afterwards.

Negative Results

When subtracting fractions, the result can be negative if the second fraction is larger than the first. For example, 1/4 - 3/4 = -2/4 = -1/2. The same rules apply: find the LCD, subtract numerators, and simplify.

Related Calculators

Maths and Stats Calculators: browse all maths tools.
Fraction Calculator: multiply and divide fractions as well as add and subtract.
Simplify Fractions Calculator: reduce any fraction to its lowest terms.
Fraction to Decimal Calculator: convert a fraction to its decimal equivalent.
Decimal to Fraction Calculator: convert a decimal back to a fraction.

Method: Lowest common denominator via least common multiple (LCM). Simplification via greatest common divisor (GCD) using the Euclidean algorithm. Standard arithmetic rules for fractions.

This calculator is for general educational use. Results are mathematically exact for integer inputs. Very large numerators or denominators may exceed JavaScript integer precision.