Fraction Calculator

Add, subtract, multiply, and divide fractions with step-by-step solutions

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Result

7
12

1/4 + 1/3 = 7/12

≈ 0.5833

Step-by-Step Solution

  1. Find common denominator: 12
  2. Convert fractions: 1/4 = 3/12, 1/3 = 4/12
  3. Add numerators: 3 + 4 = 7
  4. Result: 7/12 (already simplified)

HOW IT WORKS

This fraction calculator performs addition, subtraction, multiplication, and division of fractions. It automatically finds the common denominator, simplifies the result, and shows step-by-step solutions to help you understand the calculation process.

FRACTION BASICS

Numerator/Denominator: In 3/4, the 3 is the numerator (parts you have), 4 is the denominator (total parts). The fraction represents 3 out of 4 equal parts.

Proper vs Improper: Proper fractions (3/4) have numerator < denominator. Improper fractions (5/4) have numerator ≥ denominator and can be converted to mixed numbers (1 1/4).

Equivalent Fractions: 1/2 = 2/4 = 3/6 = 4/8. Multiplying or dividing both parts by the same number creates equivalent fractions.

Common Uses: Cooking (1/2 cup flour), construction (3/8 inch bolt), time (1/4 hour = 15 minutes), music (1/4 note), and division problems.

FRACTION OPERATIONS EXPLAINED

Adding/Subtracting: Find common denominator first. Example: 1/4 + 1/2 = 1/4 + 2/4 = 3/4. You can't add fractions with different denominators directly.

Multiplying: Multiply numerators together, multiply denominators together. Example: 2/3 × 3/4 = (2×3)/(3×4) = 6/12 = 1/2 (simplified).

Dividing: Flip the second fraction (reciprocal) and multiply. Example: 1/2 ÷ 1/4 = 1/2 × 4/1 = 4/2 = 2.

Simplifying: Divide both numerator and denominator by their greatest common divisor. Example: 6/8 = 3/4 (both divided by 2).

WHY FRACTIONS MATTER

Fractions represent precise portions that decimals sometimes can't express cleanly. In cooking, recipes use fractions (1/3 cup) because they're easier to measure than decimals (0.333... cup). In construction, imperial measurements use fractions (7/16 inch) for precision. Understanding fractions is essential for: following recipes accurately, woodworking and construction, understanding percentages (3/4 = 75%), and splitting resources fairly.