➗ ➗ Fraction Calculator: How to Add, Subtract, Multiply, Divide Fractions

Fractions appear throughout everyday life — recipes call for ¾ cup of flour, construction lumber comes in fractional sizes, stock prices move in eighths, and probability calculations rely on fractions. Mastering fraction arithmetic is a foundational skill, and understanding the underlying logic (not just the procedures) makes it stick permanently.

Fraction Basics

A fraction has two parts: the numerator (top number) and the denominator (bottom number). The denominator tells you how many equal parts the whole is divided into; the numerator tells you how many of those parts you have.

• Proper fraction: numerator < denominator (e.g., 3/4)
• Improper fraction: numerator ≥ denominator (e.g., 7/4)
• Mixed number: whole number + proper fraction (e.g., 1¾)

Adding and Subtracting Fractions

Same Denominator (Easy Case)

When denominators match, simply add or subtract the numerators:

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

7/9 − 4/9 = (7−4)/9 = 3/9 = 1/3 (simplified)

Different Denominators (General Case)

Step 1: Find the Least Common Denominator (LCD) — the smallest number both denominators divide into evenly.

Step 2: Convert each fraction to the LCD.

Step 3: Add or subtract the numerators.

Step 4: Simplify if possible.

Worked Example: 2/3 + 3/4

• LCD of 3 and 4 = 12
• Convert: 2/3 = 8/12 and 3/4 = 9/12
• Add: 8/12 + 9/12 = 17/12
• Simplify: 17/12 = 1 5/12

Worked Example: 5/6 − 1/4

• LCD of 6 and 4 = 12
• Convert: 5/6 = 10/12 and 1/4 = 3/12
• Subtract: 10/12 − 3/12 = 7/12

Multiplying Fractions

Multiply straight across — numerator × numerator, denominator × denominator. No common denominator needed.

a/b × c/d = (a×c)/(b×d)

Example: 2/3 × 4/5 = (2×4)/(3×5) = 8/15

Example: 3/4 × 8/9 = 24/36 = 2/3 (simplified by dividing both by 12)

Cross-Canceling (Simplifying Before Multiplying)

To keep numbers small, cancel common factors between any numerator and any denominator before multiplying:

3/4 × 8/9: Notice 3 and 9 share factor 3 (3÷3=1, 9÷3=3), and 8 and 4 share factor 4 (8÷4=2, 4÷4=1):

= 1/1 × 2/3 = 2/3 ✓ (much easier than simplifying 24/36)

Dividing Fractions

To divide by a fraction, multiply by its reciprocal (flip the second fraction)

a/b ÷ c/d = a/b × d/c = (a×d)/(b×c)

Example: 3/4 ÷ 2/5 = 3/4 × 5/2 = 15/8 = 1 7/8

Example: 5/6 ÷ 5/3 = 5/6 × 3/5 = 15/30 = 1/2

The memory trick: "Keep, Change, Flip" — keep the first fraction, change ÷ to ×, flip the second fraction.

Mixed Numbers

Converting Mixed Numbers to Improper Fractions

(Whole × Denominator + Numerator) ÷ Denominator

2 3/4 = (2×4 + 3)/4 = 11/4

3 1/2 = (3×2 + 1)/2 = 7/2

Adding Mixed Numbers

Convert to improper fractions, find LCD, add, then convert back:

2 1/3 + 1 3/4:

• Convert: 7/3 + 7/4
• LCD = 12: 28/12 + 21/12 = 49/12
• Convert back: 4 1/12

Simplifying Fractions

Divide both numerator and denominator by their Greatest Common Divisor (GCD).

Simplify 18/24: GCD(18,24) = 6 → 18/6 = 3, 24/6 = 4 → 3/4

Quick test: if both are even, divide by 2. If both end in 0 or 5, divide by 5. Continue until no common factor remains.

Fraction to Decimal Conversion

Divide numerator by denominator: 3/4 = 3 ÷ 4 = 0.75

Some fractions produce repeating decimals: 1/3 = 0.333... = 0.3̄

Common fraction-decimal equivalents:

• 1/2 = 0.5 | 1/3 ≈ 0.333 | 1/4 = 0.25 | 1/5 = 0.2
• 3/4 = 0.75 | 2/3 ≈ 0.667 | 3/8 = 0.375 | 5/8 = 0.625