How To Add Fractions Calculator

Fraction Addition Formula:

\[ \frac{a}{b} + \frac{c}{d} = \frac{a \times d + b \times c}{b \times d} \]

Result:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Fraction Addition?

Fraction addition is a mathematical operation that combines two fractions into a single fraction. The key principle is finding a common denominator before adding the numerators.

2. How Does the Calculator Work?

The calculator uses the standard fraction addition formula:

\[ \frac{a}{b} + \frac{c}{d} = \frac{a \times d + b \times c}{b \times d} \]

Where:

\( a \) — Numerator of first fraction
\( b \) — Denominator of first fraction
\( c \) — Numerator of second fraction
\( d \) — Denominator of second fraction

Explanation: The formula finds a common denominator by multiplying the denominators, then combines the numerators accordingly.

3. Importance of Common Denominator

Details: Fractions can only be directly added when they share the same denominator. The calculator automatically finds the least common denominator (LCD) by multiplying the denominators.

4. Using the Calculator

Tips: Enter all four values (two numerators and two denominators). Denominators must be positive integers. The calculator will simplify the result if possible.

5. Frequently Asked Questions (FAQ)

Q1: Can I add fractions with different denominators?
A: Yes, but you must first find a common denominator. This calculator does that automatically.

Q2: How are the results simplified?
A: The calculator finds the greatest common divisor (GCD) to reduce the fraction to its simplest form.

Q3: What if I enter a zero denominator?
A: The calculator requires denominators to be positive integers (≥1).

Q4: Can I add mixed numbers?
A: Convert mixed numbers to improper fractions first (e.g., 1½ = 3/2).

Q5: Why does the result show a decimal?
A: The decimal equivalent is provided for easier interpretation, but the exact fractional result is always shown first.