How do you add fractions with different denominators?

To add fractions with different denominators, first find the least common denominator (LCD) of the two denominators. Convert each fraction to an equivalent fraction with that LCD by multiplying the numerator and denominator by the required factor. Then add the numerators together and keep the LCD as the denominator. Finally, simplify the result by dividing numerator and denominator by their greatest common divisor (GCD). For example, 1/2 + 1/3: the LCD is 6, so convert to 3/6 + 2/6 = 5/6.

How do you add fractions with the same denominator?

When fractions share the same denominator, simply add the numerators together and keep the denominator unchanged. For example, 2/7 + 3/7 = 5/7. If the result can be simplified, divide both numerator and denominator by their greatest common divisor. If the numerator is greater than or equal to the denominator, the result is an improper fraction, which can also be expressed as a mixed number.

How do you add mixed numbers?

To add mixed numbers, first convert each mixed number to an improper fraction. To convert, multiply the whole number by the denominator, add the numerator, and place the result over the original denominator. For example, 1 3/4 becomes (1 x 4 + 3)/4 = 7/4. Then add the two improper fractions using the standard LCD method. Convert the result back to a mixed number if needed by dividing the numerator by the denominator: the quotient is the whole part and the remainder is the numerator of the fractional part.

Adding Fractions Calculator

Add two fractions and get the simplified answer instantly. Enter any numerators and denominators below. The calculator finds the least common denominator (LCD), converts both fractions, adds the numerators, and reduces the result to its lowest terms.

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Standard method Uses the least common denominator (LCD) and GCD reduction. Works for proper fractions, improper fractions, and fractions with the same denominator.

1. First Fraction

Numerator (top number)

Denominator (bottom number)

2. Second Fraction

Numerator (top number)

Denominator (bottom number)

Please enter whole numbers only. Denominators cannot be zero.

Result

Answer (simplified)
5/6

Least Common Denominator

LCD of the two denominators

Before Simplifying

5/6

Sum over LCD

Step-by-Step Working

Fraction Details

First fraction1/2

Second fraction1/3

LCD6

Converted first3/6

Converted second2/6

Sum (simplified)5/6

As Decimal

First fraction0.5000

Second fraction0.3333

Sum (decimal)0.8333

How to Add Fractions

Adding fractions follows a consistent method regardless of whether the denominators are the same or different. The key is always to make sure both fractions share the same denominator before you add the numerators.

The Standard Method

Find the least common denominator (LCD). The LCD is the smallest number that both denominators divide into evenly. For example, the LCD of 2 and 3 is 6.
Convert each fraction. Multiply numerator and denominator of each fraction by the factor needed to reach the LCD. For 1/2: multiply by 3 to get 3/6. For 1/3: multiply by 2 to get 2/6.
Add the numerators. Keep the LCD as the denominator: 3/6 + 2/6 = 5/6.
Simplify the result. Divide both numerator and denominator by their greatest common divisor (GCD). If the GCD is 1, the fraction is already in its simplest form.

Worked Example

Step	Working	Result
Fractions to add	1/2 + 1/3
Find LCD of 2 and 3	LCM(2, 3) = 6	LCD = 6
Convert 1/2	1 x 3 = 3, denominator 2 x 3 = 6	3/6
Convert 1/3	1 x 2 = 2, denominator 3 x 2 = 6	2/6
Add numerators	3 + 2 = 5, denominator stays 6	5/6
Simplify	GCD(5, 6) = 1, already simplified	5/6

Finding the LCD

The LCD is the least common multiple (LCM) of the two denominators. There are two common approaches:

Listing multiples: Write out the multiples of each denominator and find the first one they share. Multiples of 4: 4, 8, 12, 16 ... Multiples of 6: 6, 12, 18 ... LCD = 12.
Using the formula: LCM(a, b) = (a x b) / GCD(a, b). For a = 4 and b = 6: GCD(4, 6) = 2, so LCM = (4 x 6) / 2 = 12.

When denominators are already the same, the LCD is simply that denominator, and you skip straight to adding the numerators.

Simplifying the Result

A fraction is in its lowest terms (simplest form) when the numerator and denominator share no common factor other than 1. To simplify, find the GCD of the numerator and denominator using the Euclidean algorithm, then divide both by it. For example, 6/8 has GCD(6, 8) = 2, so 6/8 = 3/4.

Improper Fractions and Mixed Numbers

If the sum of the numerators is greater than or equal to the denominator, the result is an improper fraction (for example, 7/4). This can be expressed as a mixed number: divide the numerator by the denominator to get the whole number, and the remainder becomes the new numerator over the same denominator. So 7/4 = 1 remainder 3 = 1 and 3/4, written as 1 3/4.

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Method: Least common denominator found using LCM(a, b) = (a x b) / GCD(a, b) via the Euclidean algorithm. Result reduced by dividing by GCD(numerator, denominator).

This calculator works with whole-number numerators and denominators. For mixed number addition, convert each mixed number to an improper fraction first (for example, 1 3/4 becomes 7/4) then enter the numerator and denominator.

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