ALGEBRAFractionsMathematics Calculator
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Fraction Operations

Add, subtract, multiply, and divide fractions. Addition and subtraction require LCD; multiplication and division use direct rules.

Concept Fundamentals
Need LCD
Add/Sub
a/b × c/d = (a×c)/(b×d)
Multiply
a/b ÷ c/d = a/b × d/c
Divide
GCD to lowest terms
Simplify

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Multiplication and division do not need LCD—unlike add/subtract. Division by fraction = multiply by reciprocal (Keep-Change-Flip). Always simplify final results to lowest terms.

Key quantities
Need LCD
Add/Sub
Key relation
a/b × c/d = (a×c)/(b×d)
Multiply
Key relation
a/b ÷ c/d = a/b × d/c
Divide
Key relation
GCD to lowest terms
Simplify
Key relation

Ready to run the numbers?

Why: Fraction operations are essential for cooking, construction, finance, and science—anywhere parts of wholes are combined or compared.

How: Add: find LCD, convert, add numerators. Subtract: same. Multiply: multiply numerators and denominators. Divide: multiply by reciprocal.

Multiplication and division do not need LCD—unlike add/subtract.Division by fraction = multiply by reciprocal (Keep-Change-Flip).
Sources:Khan Academy — Fraction ArithmeticMath is Fun — Fractions

Run the calculator when you are ready.

Fraction CalculatorAdd, subtract, multiply, divide

📐 Examples — Click to Load

Fraction 1

Operation

Fraction 2

fraction-calc.sh
CALCULATED
$ calc --expr="1/2 + 1/3"
Expression
1/2 + 1/3
Result
5/6
Decimal
0.833333
Fraction Calculator
1/2 + 1/3 = 5/6
Decimal: 0.833333 · numbervibe.com
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Values Comparison

Proportion

📐 Step-by-Step

INPUT
Fraction 11/2
INPUT
Fraction 21/3
METHOD
LCDLCD(2, 3) = 6
METHOD
Convert 11/2 = 3/6
METHOD
Convert 21/3 = 2/6
METHOD
Add numerators3 + 2 = 5
RESULT
Result5/6

For educational and informational purposes only. Verify with a qualified professional.

🧮 Fascinating Math Facts

🏛️

Ancient Egyptians used unit fractions (1/n) and had sophisticated fraction arithmetic.

🍕

Pizza fractions: 1/2 + 1/4 = 3/4—three quarters of a pizza.

1. Key Takeaways

  • • Addition/Subtraction: Find LCD, convert both fractions, add/subtract numerators.
  • • Multiplication: Multiply numerators and denominators separately, then simplify.
  • • Division: Multiply by the reciprocal of the second fraction (keep, change, flip).
  • • Always simplify the result to lowest terms using GCD.
  • • Same denominator: add/subtract numerators directly (e.g., 3/8 + 5/8 = 8/8 = 1).

2. Did You Know?

LCD for Addition

For 1/2 + 1/3, LCD(2,3)=6. So 3/6 + 2/6 = 5/6.

Reciprocal

To divide by a/b, multiply by b/a. 1/2 ÷ 1/4 = 1/2 × 4/1 = 2.

Cross Multiply

a/b + c/d = (ad+bc)/(bd). No need to find LCD first.

Simplify Before Multiply

2/3 × 3/4: can cancel 3 before multiplying: 2/4 = 1/2.

Mixed Numbers

Convert to improper first: 1½ + 2⅓ = 3/2 + 7/3, then add.

Zero and One

a/b × 0 = 0. a/b × 1 = a/b. a/b ÷ 1 = a/b.

3. How It Works

Fraction operations follow standard rules. For addition and subtraction, fractions must have the same denominator (LCD). Convert each fraction to an equivalent with the LCD, then add or subtract numerators. For multiplication, multiply numerators and denominators. For division, multiply by the reciprocal of the divisor. Always simplify the result.

Inputs

Two fractions (num1/den1, num2/den2) and operation (+, −, ×, ÷)

Outputs

Result as simplified fraction, decimal value, step-by-step solution

4. Expert Tips

Find LCD for add/subtract

LCD of 4 and 6 is 12. 3/4 = 9/12, 1/6 = 2/12.

Keep, change, flip

For division: keep first fraction, change ÷ to ×, flip second fraction.

Simplify at the end

After computing, divide num and den by GCD to get lowest terms.

Check with decimals

1/2 + 1/3 = 0.5 + 0.333 = 0.833. 5/6 ≈ 0.833. Verify!

5. Comparison Table

OperationRuleExample
Adda/b + c/d = (ad+bc)/(bd)1/2 + 1/3 = 5/6
Subtracta/b − c/d = (ad−bc)/(bd)3/4 − 1/6 = 7/12
Multiplya/b × c/d = ac/(bd)2/3 × 3/5 = 6/15 = 2/5
Dividea/b ÷ c/d = (a/b)×(d/c)4/7 ÷ 2/3 = 12/14 = 6/7

6. FAQ

How do I add 1/2 and 1/3?

LCD of 2 and 3 is 6. 1/2 = 3/6, 1/3 = 2/6. 3/6 + 2/6 = 5/6.

How do I multiply fractions?

Multiply numerators: 2×3=6. Multiply denominators: 3×5=15. Result: 6/15 = 2/5 (simplified).

How do I divide fractions?

Use "keep, change, flip": 4/7 ÷ 2/3 = 4/7 × 3/2 = 12/14 = 6/7.

What is the LCD?

Least Common Denominator = LCM of the denominators. For 4 and 6, LCM = 12.

How do I simplify a fraction?

Find GCD of numerator and denominator. Divide both by GCD. E.g., 6/15, GCD=3, so 2/5.

Can I add fractions with different denominators directly?

No. Convert to equivalent fractions with the same denominator (LCD) first, then add numerators.

7. Quick Stats

LCD

Common denominator

a×d + b×c

Add formula

a×c / b×d

Multiply

a×d / b×c

Divide

8. Sources

Wikipedia — FractionsKhan Academy — Fraction ArithmeticMath is Fun — FractionsPurplemath — Fraction HelpWolfram MathWorld — FractionCommon Core Math Standards

9. Disclaimer

⚠️ Warning: This calculator is for educational purposes. Fraction operations use standard mathematical rules. Always verify results for critical applications.

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