Fraction Calculator - Calculate with Fractions

Example 1: Adding Fractions with Different Denominators

Problem: 1/4 + 2/3

Step 1: Find the Lowest Common Denominator (LCD)

Multiples of 4: 4, 8, 12, 16...

Multiples of 3: 3, 6, 9, 12, 15...

LCD = 12

Step 2: Convert fractions to common denominator

1/4 = (1×3)/(4×3) = 3/12

2/3 = (2×4)/(3×4) = 8/12

Step 3: Add the numerators

3/12 + 8/12 = (3+8)/12 = 11/12

Answer: 11/12

Example 2: Subtracting Mixed Numbers

Problem: 3 1/2 - 1 1/4

Step 1: Convert to improper fractions

3 1/2 = (3×2 + 1)/2 = 7/2

1 1/4 = (1×4 + 1)/4 = 5/4

Step 2: Find LCD (LCD of 2 and 4 = 4)

Step 3: Convert to common denominator

7/2 = 14/4

5/4 = 5/4

Step 4: Subtract

14/4 - 5/4 = 9/4

Step 5: Convert back to mixed number

9/4 = 2 1/4

Answer: 2 1/4

Example 3: Multiplying Fractions

Problem: 2/3 × 3/4

Step 1: Multiply numerators together

2 × 3 = 6

Step 2: Multiply denominators together

3 × 4 = 12

Step 3: Combine and simplify

6/12 = 1/2 (divide both by 6)

Shortcut: Cancel common factors before multiplying

2/3 × 3/4 → cancel the 3s → 2/1 × 1/4 = 2/4 = 1/2

Answer: 1/2

Example 4: Dividing Fractions (Keep, Change, Flip)

Problem: 3/4 ÷ 2/5

Step 1: KEEP the first fraction

3/4 (stays as is)

Step 2: CHANGE division to multiplication

÷ becomes ×

Step 3: FLIP the second fraction (reciprocal)

2/5 becomes 5/2

Step 4: Multiply

3/4 × 5/2 = (3×5)/(4×2) = 15/8

Step 5: Convert to mixed number

15/8 = 1 7/8

Answer: 1 7/8 or 15/8

Example 5: Simplifying Fractions

Problem: Simplify 24/36

Method 1: Find GCF (Greatest Common Factor)

Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24

Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36

GCF = 12

24÷12 / 36÷12 = 2/3

Method 2: Divide by small primes repeatedly

24/36 → ÷2 → 12/18 → ÷2 → 6/9 → ÷3 → 2/3

Answer: 2/3

Quick Mental Math Tips

• Halving shortcut: To find 1/2 of a fraction, multiply numerator by 1 and denominator by 2. Example: 1/2 of 3/4 = 3/8
• Doubling shortcut: To double a fraction, multiply numerator by 2. Example: 2 × 3/5 = 6/5 = 1 1/5
• Same denominator: When denominators match, just add/subtract numerators. Example: 5/8 + 2/8 = 7/8
• Multiplying by whole numbers: Write whole number as fraction over 1. Example: 4 × 2/3 = 4/1 × 2/3 = 8/3
• Finding equivalent fractions: Multiply OR divide both numerator and denominator by the same number. Example: 2/3 = 4/6 = 6/9 = 8/12

Simplification Quick Checks

• Both even? Divide by 2 (and keep dividing until one is odd)
• Both end in 0 or 5? Divide by 5
• Sum of digits divisible by 3? The number is divisible by 3. Example: 15/21 → 1+5=6, 2+1=3 → both divisible by 3 → 5/7
• Ends in 0? Divisible by 10, 5, and 2
• Last two digits divisible by 4? The whole number is divisible by 4

Memory Aids

• "Keep, Change, Flip" for division: Keep first fraction, Change ÷ to ×, Flip second fraction
• "Butterfly Method" for comparing: Cross-multiply to see which is bigger. For 2/3 vs 3/4: 2×4=8, 3×3=9, so 3/4 is bigger
• Pizza rule: Bigger denominator = smaller pieces (1/8 of pizza is smaller than 1/4)
• Addition/Subtraction: "Find common ground" (common denominator) before combining
• Multiplication: "Straight across" - multiply tops, multiply bottoms

❌ Mistake 1: Adding denominators

WRONG: 1/4 + 1/4 = 2/8

CORRECT: 1/4 + 1/4 = 2/4 = 1/2

Never add or subtract denominators! Only add/subtract numerators when denominators are the same.

❌ Mistake 2: Forgetting to find common denominator

WRONG: 1/3 + 1/4 = 2/7

CORRECT: 1/3 + 1/4 = 4/12 + 3/12 = 7/12

Different denominators? Must find LCD first!

❌ Mistake 3: Dividing fractions incorrectly

WRONG: 1/2 ÷ 1/4 = 1/8

CORRECT: 1/2 ÷ 1/4 = 1/2 × 4/1 = 4/2 = 2

Remember: flip the SECOND fraction only, not the first!

❌ Mistake 4: Not simplifying final answer

INCOMPLETE: 2/3 + 1/6 = 5/6 (not simplified but already simplest)

BUT: 2/4 + 1/4 = 3/4 ✓ NOT 3/4 (wait, this IS simplified!)

BAD EXAMPLE: 1/2 + 1/4 = 3/4 is correct AND simplified

BETTER EXAMPLE: 2/6 + 1/6 = 3/6, but you must simplify to 1/2

Always simplify your final answer to lowest terms unless told otherwise!

❌ Mistake 5: Converting mixed numbers incorrectly

WRONG: 2 1/3 = 3/3 (just adding whole and numerator)

CORRECT: 2 1/3 = (2×3 + 1)/3 = 7/3

Formula: (whole × denominator + numerator) / denominator

❌ Mistake 6: Multiplying fractions like adding them

WRONG: 1/2 × 1/3 = 2/5 (trying to find common denominator)

CORRECT: 1/2 × 1/3 = 1/6 (multiply straight across)

Multiplication doesn't need common denominators!

❌ Mistake 7: Thinking bigger denominator = bigger fraction

WRONG: 1/8 is bigger than 1/4 (because 8 > 4)

CORRECT: 1/4 is bigger than 1/8 (1/4 = 2/8)

Bigger denominator = smaller pieces! Think pizza slices: 1/8 of pizza is smaller than 1/4.

Understanding Fractions

A fraction represents a part of a whole. It consists of two numbers separated by a line: the numerator (top number) shows how many parts you have, and the denominator (bottom number) shows how many equal parts the whole is divided into. For example, in the fraction 3/4, you have 3 parts out of 4 equal parts total.

Types of Fractions

• Proper Fraction: Numerator is less than denominator (e.g., 3/4, 2/5). Value is less than 1.
• Improper Fraction: Numerator is greater than or equal to denominator (e.g., 7/4, 5/5). Value is 1 or more.
• Mixed Number: Whole number combined with a fraction (e.g., 2 1/3, 5 3/4).
• Equivalent Fractions: Different fractions representing the same value (e.g., 1/2 = 2/4 = 3/6).
• Unit Fraction: Numerator is 1 (e.g., 1/2, 1/5, 1/10).

Step-by-Step: Adding and Subtracting Fractions

1. Same denominators: Simply add or subtract the numerators and keep the denominator.
   Example: 3/8 + 2/8 = 5/8
2. Different denominators:
   • Find the Lowest Common Denominator (LCD)
   • Convert each fraction to equivalent fraction with LCD
   • Add or subtract the numerators
   • Simplify if possible
   Example: 1/3 + 1/4 → LCD=12 → 4/12 + 3/12 = 7/12

Step-by-Step: Multiplying Fractions

1. Multiply the numerators together
2. Multiply the denominators together
3. Simplify the result
4. Pro tip: Cancel common factors before multiplying to make calculation easier

Example: 2/3 × 3/5 → Cancel 3s → 2/1 × 1/5 = 2/5

Step-by-Step: Dividing Fractions

1. Keep the first fraction as is
2. Change the division sign to multiplication
3. Flip the second fraction (reciprocal)
4. Multiply the fractions
5. Simplify the result

Example: 2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6

Converting Between Forms

Mixed Number to Improper Fraction:

Formula: (whole × denominator + numerator) / denominator

Example: 3 2/5 = (3×5 + 2)/5 = 17/5

Improper Fraction to Mixed Number:

Divide numerator by denominator: quotient becomes whole number, remainder becomes new numerator

Example: 17/5 → 17÷5 = 3 remainder 2 → 3 2/5

Fraction to Decimal:

Divide numerator by denominator

Example: 3/4 = 3÷4 = 0.75

Real-World Applications

• Cooking: Recipe calls for 2/3 cup but you want to double it: 2/3 × 2 = 4/3 = 1 1/3 cups
• Construction: Board is 7/8 inch thick, need to stack 4 boards: 7/8 × 4 = 28/8 = 3 1/2 inches
• Shopping: Sale is 1/4 off, item costs £40: £40 × 1/4 = £10 discount, pay £30
• Time: 1/4 hour = 15 minutes, 3/4 hour = 45 minutes
• Money: 1/2 of £50 = £25, 2/5 of £100 = £40

How do I add and subtract fractions with different denominators?

Find the Lowest Common Multiple (LCM) of the denominators to get a common denominator. Convert each fraction to an equivalent fraction with this common denominator, then add or subtract the numerators. Finally, simplify the result if possible. For example: 1/4 + 2/3 → LCD=12 → 3/12 + 8/12 = 11/12.

How do I multiply and divide fractions?

To multiply: multiply numerators together and denominators together, then simplify. To divide: use "Keep, Change, Flip" - keep the first fraction, change division to multiplication, flip the second fraction (reciprocal), then multiply. Example: 3/4 ÷ 2/5 = 3/4 × 5/2 = 15/8.

How do I simplify fractions to lowest terms?

Find the Greatest Common Factor (GCF) of the numerator and denominator, then divide both by this number. Alternatively, keep dividing both numbers by small primes (2, 3, 5, etc.) until they share no common factors. Example: 24/36 → GCF=12 → 24÷12 / 36÷12 = 2/3.

What is an improper fraction?

An improper fraction has a numerator greater than or equal to its denominator (e.g., 7/4, 5/5), representing a value of 1 or more. Convert to mixed number by dividing: 7/4 = 1 3/4 (7÷4 = 1 remainder 3).

How do I convert a mixed number to an improper fraction?

Multiply the whole number by the denominator, add the numerator, and place over the original denominator. Formula: (whole × denominator + numerator) / denominator. Example: 2 3/5 = (2×5 + 3) / 5 = 13/5.

Is this calculator accurate for GCSE maths?

Yes! This calculator uses standard mathematical algorithms and is perfect for checking GCSE maths homework. It handles all fraction operations taught in GCSE and A-Level courses.

Can I use this calculator on my phone?

Absolutely! This fraction calculator is fully responsive and works perfectly on mobile phones, tablets, and desktop computers. No app download needed - just use your browser.

Is this calculator free to use?

Yes! Completely free with no signup, no hidden fees, and unlimited calculations. We believe everyone should have access to quality educational tools.

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