How do you add fractions with different denominators?

Find the least common denominator (LCD) — the LCM of the two denominators. Convert each fraction to an equivalent fraction with the LCD. Add the numerators, keeping the LCD as the denominator. Simplify if possible. Example: 1/3 + 1/4. LCD = 12. Convert: 4/12 + 3/12 = 7/12. No simplification needed (7 and 12 share no common factors).

How do you multiply fractions?

Multiply numerators together, then multiply denominators together. Simplify the result. Example: 3/5 × 2/7 = 6/35. For 4/9 × 3/8: simplify before multiplying by canceling common factors — 4 and 8 share factor 4, and 3 and 9 share factor 3: (4÷4)/(9÷3) × (3÷3)/(8÷4) = 1/3 × 1/2 = 1/6. This pre-simplification keeps numbers manageable.

How do you divide fractions?

Keep the first fraction, change division to multiplication, and flip (take the reciprocal of) the second fraction. Then multiply as normal. Example: 5/6 ÷ 2/3 = 5/6 × 3/2 = 15/12 = 5/4 = 1 1/4. This works because dividing by a number is the same as multiplying by its multiplicative inverse (reciprocal).

How do you convert a fraction to a decimal?

Divide the numerator by the denominator. 3/4 = 3 ÷ 4 = 0.75. 5/8 = 0.625. 1/3 = 0.333... (repeating). Some fractions produce terminating decimals (denominators with only 2 and 5 as prime factors: 1/4, 3/8, 7/20); others produce repeating decimals (1/3, 2/7, 5/6).

What is a proper vs improper fraction?

A proper fraction has a numerator smaller than the denominator: 3/7, 5/8, 1/100. Its value is between 0 and 1. An improper fraction has a numerator equal to or greater than the denominator: 7/3, 11/4, 5/5. Its value is ≥ 1. Improper fractions can be written as mixed numbers: 7/3 = 2 1/3. Both forms are mathematically equivalent; mixed numbers are easier to interpret intuitively while improper fractions are easier to work with arithmetically.

How do you simplify a fraction?

Find the greatest common factor (GCF) of the numerator and denominator, then divide both by it. Example: 36/48. GCF(36, 48) = 12. 36÷12 = 3, 48÷12 = 4. Simplified: 3/4. Quick check: a fraction is in simplest form when the only common factor of numerator and denominator is 1. If both are even, you can always divide by 2 as a first step; keep simplifying until no common factors remain.

Fraction Calculator — Add, Subtract, Multiply & Divide with Steps

Perform all arithmetic operations on fractions and mixed numbers. See simplified results and step-by-step working.

By HarshFounder, Cloud Calculators App

Verified formula

Updated 2026-06-09

Fraction Calculator

Numerator

Denominator

Numerator

Denominator

Quick Answer

1/3 + 1/4 = 7/12. To add fractions, find the common denominator (12), convert both (4/12 + 3/12), then add (7/12). For multiplication: 2/3 × 3/4 = 6/12 = 1/2. For division: 2/3 ÷ 3/4 = 2/3 × 4/3 = 8/9. This calculator handles all four operations, simplification, and mixed number conversion.

How the Fraction Calculator Works Step by Step

A fraction calculator performs arithmetic operations (addition, subtraction, multiplication, division) on fractions and mixed numbers, and simplifies results to lowest terms. The four operations have distinct procedures: addition and subtraction require a common denominator (usually the least common multiple of the two denominators), while multiplication and division don't require a common denominator.

Step-by-step addition example: 3/8 + 5/6. Find LCM(8, 6) = 24. Convert: 9/24 + 20/24 = 29/24 = 1 and 5/24. For subtraction with different denominators: 7/10 – 1/4. LCM(10, 4) = 20. Convert: 14/20 – 5/20 = 9/20. For multiplication: 5/6 × 4/9 = (5×4)/(6×9) = 20/54 = 10/27 (simplified by dividing both by GCF 2). For division (multiply by reciprocal): 7/8 ÷ 2/5 = 7/8 × 5/2 = 35/16 = 2 and 3/16.

Simplification uses the Greatest Common Factor (GCF) — divide both numerator and denominator by their GCF. 36/48: GCF(36,48) = 12. 36÷12 = 3, 48÷12 = 4. Simplified: 3/4. Mixed numbers are converted to improper fractions for arithmetic (2 and 3/4 = 11/4) then converted back to mixed number form in results.

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Understanding Each Fraction Calculator Input Field

Each field in the Fraction Calculator serves a specific purpose. Here's why each input matters and how to provide the most accurate values:

Numerator

The top number of the fraction — how many parts you have. Can be any integer, including values larger than the denominator (which makes an improper fraction).

Denominator

The bottom number — how many equal parts make the whole. Cannot be zero (division by zero is undefined).

Operation

Select addition (+), subtraction (–), multiplication (×), or division (÷). Each operation follows different procedural rules.

Fraction Calculator Formula and Methodology Explained

The Fraction Calculatoruses the following validated formula. Understanding the math helps you interpret results accurately and trust the calculations you're relying on.

Addition: a/b + c/d = (a×d + c×b) / (b×d) Subtraction: a/b – c/d = (a×d – c×b) / (b×d) Multiplication: a/b × c/d = (a×c) / (b×d) Division: a/b ÷ c/d = a/b × d/c = (a×d) / (b×c) Simplification: divide numerator and denominator by GCF(numerator, denominator) Mixed number: a b/c = (a×c + b) / c

How the Fraction Calculator Formula Works

For addition/subtraction, the shortcut formula (a×d + c×b)/(b×d) always works but may not produce the simplest form — simplify afterward. For large denominators, finding the LCM first produces a smaller intermediate result. Division by a fraction is equivalent to multiplication by its reciprocal — the "Keep, Change, Flip" rule taught in schools.

When to Use the Fraction Calculator

→Cooking and baking with recipe scaling (doubling 3/4 cup, halving 1 1/3 cups)
→Construction and carpentry measurements in fractions of inches
→Academic math problems involving fraction arithmetic
→Finance and statistics calculations requiring exact rational arithmetic

💡 Expert Tips for Using the Fraction Calculator Accurately

Tip 1

For recipe scaling, always convert mixed numbers to improper fractions before multiplying, then simplify: to triple 2 1/3 cups: (7/3) × 3 = 21/3 = 7 cups.

Tip 2

Before adding fractions in your head, check if the denominators are already multiples of each other: 1/4 + 3/8 → 2/8 + 3/8 = 5/8 (multiply the 1/4 by 2/2, not full LCM calculation needed).

Tip 3

The GCF of two numbers can be found quickly using the Euclidean algorithm: GCF(48, 18) = GCF(18, 12) = GCF(12, 6) = GCF(6, 0) = 6.

Tip 4

When dividing fractions, 'Keep Change Flip': keep the first fraction, change ÷ to ×, flip the second fraction to its reciprocal.

⚠️ Common Fraction Calculator Mistakes to Avoid

✗Adding numerators and denominators separately (1/2 + 1/3 ≠ 2/5 — this is wrong; the correct answer is 5/6)
✗Forgetting to simplify the result to lowest terms after performing the operation
✗Converting mixed numbers incorrectly: 3 2/5 = (3×5+2)/5 = 17/5, not 32/5
✗Dividing by multiplying numerator and denominator separately instead of using the reciprocal

Frequently Asked Questions

Everything you need to know about the Fraction Calculator. Can't find your answer? Contact us.

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