How do you add fractions with different denominators?

Find the Least Common Denominator (LCD), convert both fractions so they share the common denominator, add the numerators together, and simplify to lowest terms.

What is Keep, Change, Flip for dividing fractions?

To divide fractions: Keep the first fraction, Change the division sign to multiplication, and Flip (invert) the second fraction, then multiply the numerators and denominators.

What is 6/7 as a percentage?

6 divided by 7 is approximately 0.8571428. Multiplied by 100%, 6/7 is equal to 85.71%.

Fraction Calculator & Decimal Solver

Perform all four fraction arithmetic operations (+, −, ×, ÷), simplify fractions, and convert between fractions, decimals, and percentages with full step-by-step working.

Comprehensive Guide & Practice

Master the mathematical principles, formulas, and step-by-step methods with worked examples and FAQs.

1. How to Use the CalcSolver Fraction Calculator

This calculator handles all four core fraction operations: addition, subtraction, multiplication, and division. It computes the result in real time, reduces it to its simplest lowest terms using Greatest Common Factor (GCF) factoring, and calculates the exact decimal and percentage values.

Enter Fraction A: Input the numerator in the top box and the denominator in the lower box.
Select Your Operation: Choose + (Addition), − (Subtraction), × (Multiplication), or ÷ (Division).
Enter Fraction B: Input the numerator and denominator for the second fraction.
Click Calculate: View the exact reduced fraction, mixed number representation (if improper), decimal value, and step-by-step arithmetic working.

2. What Fractions Actually Mean: Anatomy & Categories

A fraction represents division and describes equal parts of a whole. In any fraction A / B:

Denominator (Bottom Number): Indicates how many equal parts the whole unit has been divided into.
Numerator (Top Number): Indicates how many of those equal parts are being counted or held.

Example: 3/8 means the object was sliced into 8 equal parts, and you are holding 3 of them.

3. Step-by-Step Walkthroughs for All 4 Operations

A. Adding Fractions (Finding the LCD)

You cannot simply add denominators together. Fractions can only be added when they share a common unit size.

Problem: 3/8 + 5/12
Step 1: Find LCD of 8 and 12 → Multiples of 12: 12, 24. 8 divides into 24 evenly. LCD = 24.
Step 2: Convert fractions → (3 × 3)/(8 × 3) = 9/24; (5 × 2)/(12 × 2) = 10/24.
Step 3: Add numerators → (9 + 10)/24 = 19/24.

4. How to Convert Fractions to Decimals and Percentages

Every fraction represents division. To convert A/B:

Decimal = Numerator ÷ Denominator
Percentage = Decimal × 100%

5. Common Mistakes to Avoid

Adding denominators together: 1/3 + 1/4 ≠ 2/7. You must find the common denominator (12) first (4/12 + 3/12 = 7/12).
Flipping the wrong fraction in division: Always flip the second fraction (the divisor), never the first.
Forgetting to reduce: Always check if the numerator and denominator share a common factor (e.g. 12/16 → 3/4).

6. Real-World Applications of Fraction Math

Fractions are vital across dozens of real-world professions:

Culinary Arts & Baking: Scaling recipes up or down requires exact fractional multiplication (e.g. scaling a 3/4 cup recipe by 1.5).
Carpentry & Engineering: Tape measures use fractional increments (1/16, 1/8, 1/4, 1/2 inch).
Personal Finance: Mortgage rate changes, stock yields, and discount margins are calculated using fractions and basis points.
Music Theory: Time signatures (3/4, 4/4, 6/8) dictate the rhythmic structure of musical compositions.