What is the Least Common Denominator (LCD)?

The LCD is the smallest number that both denominators divide into evenly. It is equal to the Least Common Multiple (LCM) of the two denominators. Using the LCD minimises the size of the numbers you work with and ensures the result is already in a manageable form.

Do I need to simplify after adding fractions?

Yes — after adding, check if the resulting fraction can be reduced. Divide both numerator and denominator by their Greatest Common Factor (GCF) to get the simplest form. For example, 6/8 simplifies to 3/4 because GCF(6,8) = 2.

How do I add mixed numbers?

Convert each mixed number to an improper fraction first: multiply the whole number by the denominator and add the numerator (e.g., 2¾ = (2×4+3)/4 = 11/4). Then add the two improper fractions using the LCD method, and convert the result back to a mixed number if needed.

Can I add more than two fractions at once?

To add three or more fractions, find the LCD of all denominators, convert every fraction to an equivalent fraction with that LCD, then add all the numerators together over the single LCD. Simplify the final result.

Why can't I just add numerators and denominators straight across?

Adding across (e.g., 1/2 + 1/3 = 2/5) is mathematically incorrect — it changes the actual values. The denominator represents the size of each equal part. You must use a common denominator so all pieces are the same size before you count them together.

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IPL 2026

Adding Fractions Calculator

Add fractions with like or unlike denominators, including mixed numbers.

Complete User Guide

Step 1: Enter the numerator and denominator of the first fraction.

Step 2: Enter the numerator and denominator of the second fraction.

Step 3: Click 'Add Fractions'.

The calculator finds the Least Common Denominator (LCD), converts both fractions to equivalent fractions with that denominator, adds the numerators, and simplifies the result automatically using the Greatest Common Factor (GCF).

The Mathematical Formula

(a/b) + (c/d) = (ad + bc) / bd

For fractions with the same denominator: a/b + c/b = (a+c)/b — simply add the numerators and keep the denominator.

For fractions with different denominators, find the Least Common Denominator (LCD) — the smallest positive integer divisible by both denominators. Convert each fraction: multiply numerator and denominator by the factor needed to reach the LCD. Then add the resulting numerators over the LCD.

General formula: a/b + c/d = (a×d + c×b) / (b×d), then simplify by dividing by GCF(numerator, denominator).

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