Adding Fraction Calculator

How to Add Fractions

Step 1: Find a Common Denominator

Fractions must have the same denominator before you can add them. If they already have the same denominator, skip to step 2.

If the denominators are different, find the least common denominator (LCD), which is the smallest multiple that both denominators share.

Step 2: Convert the Fractions

Rewrite each fraction so they have the common denominator. Multiply both the numerator and denominator of each fraction to match the LCD.

Step 3: Add the Numerators

Once the fractions have the same denominator, add the numerators together and keep the denominator the same.

Step 4: Simplify the Fraction

If possible, simplify the fraction by dividing the numerator and denominator by their Greatest Common Divisor (GCD).

Examples:

Example 1 (Same Denominator):

Fraction 1: 2/5

Fraction 2: 1/5

Add numerators: (2 + 1) / 5 = 3/5

Example 2 (Different Denominators):

Fraction 1: 1/4

Fraction 2: 1/6

LCD of 4 and 6 = 12

Convert: (1×3)/(4×3) = 3/12, (1×2)/(6×2) = 2/12

Add: (3 + 2) / 12 = 5/12

Example 3 (Simplification Required):

Fraction 1: 3/8

Fraction 2: 1/4

LCD of 8 and 4 = 8

Convert: (3/8) stays the same, (1×2)/(4×2) = 2/8

Add: (3 + 2) / 8 = 5/8

Conclusion

Adding fractions is simple: find the common denominator, convert fractions if needed, add the numerators, and simplify if possible.