🔢

Fraction Calculator — Add, Subtract, Multiply & Divide Fractions

Add, subtract, multiply, and divide up to 5 fractions with ease

0

Fraction 1

/= 0.0000

Fraction 2

/= 0.0000
BK
By Ben Konna, PhD

Fraction Calculator: Add, Subtract, Multiply, and Divide Fractions

Table of Contents - Fraction

Fractions in Modern Applications 2026

Fractions remain fundamental across industries despite the prevalence of decimal calculations. Certain fields continue to rely on fractional representation for precision and practical reasons.

Financial Markets and Investment

Stock Splits and Fractional Shares:

| Company | 2024-2025 Split | Pre-Split Share | Post-Split | |---------|-----------------|-----------------|------------| | Nvidia | 10-for-1 | 1 share | 10 shares | | Broadcom | 10-for-1 | 1 share | 10 shares | | Chipotle | 50-for-1 | 1 share | 50 shares | | Walmart | 3-for-1 | 1 share | 3 shares |

Fractional Share Ownership (UK Platforms 2026):

| Platform | Minimum Investment | Fraction of Share | |----------|-------------------|-------------------| | Trading 212 | £1 | 1/635 of Nvidia | | Freetrade | £2 | 1/85 of Apple | | eToro | £10 | 1/7 of Tesla | | Interactive Investor | £25 | 1/3 of Microsoft |

Engineering and Construction

UK Building Regulations 2026 - Fractional Specifications:

| Element | Specification | Fractional Form | |---------|---------------|-----------------| | Stair rise | Maximum 220mm | 22/100 metres | | Door width | Minimum 838mm | 33/40 of a metre | | Ceiling height | Minimum 2.4m | 12/5 metres | | Insulation U-value | 0.18 W/m²K | 9/50 |

Culinary Measurements

British Baking Conversions:

| Recipe Calls For | Metric | Imperial | |------------------|--------|----------| | 1/4 cup butter | 57g | 2 oz | | 1/3 cup flour | 42g | 1.5 oz | | 1/2 cup sugar | 100g | 3.5 oz | | 2/3 cup milk | 160ml | 5.4 fl oz | | 3/4 cup cream | 180ml | 6 fl oz |

The Core Principle: Fraction Arithmetic

Fractions represent parts of a whole. The numerator (top) tells how many parts exist; the denominator (bottom) tells how many parts make a whole.

Addition and subtraction require common denominators because only like parts can be combined. Adding 1/3 and 1/4 directly is not possible because thirds and fourths are different sizes.

Multiplication is straightforward: multiply numerators together and denominators together. No common denominator is needed because the operation finds a fraction of a fraction.

Division by a fraction means multiplying by its reciprocal. Dividing by 1/2 is the same as multiplying by 2/1.

Simplification uses the greatest common divisor (GCD) to reduce fractions to lowest terms. 4/8 simplifies to 1/2 because both 4 and 8 are divisible by 4.

How to Use This Calculator

Enter fractions using the numerator and denominator fields. The calculator supports multiple fractions (up to 5) for chain calculations.

For each fraction, enter the Numerator (top number) and Denominator (bottom number).

Select the Operation between fractions: + (add), - (subtract), × (multiply), or ÷ (divide).

Use "Add Fraction" to include additional fractions in the calculation. Use the remove button to delete fractions (minimum 2 required).

Click "Calculate" to see results. The output displays:

  • The complete expression (e.g., "3/4 + 1/2 = 5/4")
  • The answer in simplified form
  • The decimal equivalent
  • Step-by-step solution showing how the answer was derived

A "Clear" button resets all fields.

How to Calculate with Fractions Manually

Addition (finding common denominator): 3/4 + 1/6

Step 1: Find LCD of 4 and 6 = 12 Step 2: Convert fractions: 3/4 = 9/12, 1/6 = 2/12 Step 3: Add numerators: 9/12 + 2/12 = 11/12

Subtraction: 5/8 - 1/3

Step 1: Find LCD of 8 and 3 = 24 Step 2: Convert: 5/8 = 15/24, 1/3 = 8/24 Step 3: Subtract: 15/24 - 8/24 = 7/24

Multiplication: 2/3 × 4/5

Step 1: Multiply numerators: 2 × 4 = 8 Step 2: Multiply denominators: 3 × 5 = 15 Step 3: Result: 8/15 (already simplified)

Division: 3/4 ÷ 2/5

Step 1: Flip the second fraction: 2/5 → 5/2 Step 2: Multiply: 3/4 × 5/2 = 15/8 Step 3: Convert if needed: 15/8 = 1 7/8

Simplification: Find GCD of numerator and denominator, divide both.

12/18: GCD(12, 18) = 6 12 ÷ 6 = 2, 18 ÷ 6 = 3 Simplified: 2/3

Real-World Applications

Cooking and recipes. A recipe calls for 2/3 cup of flour but is being doubled: 2/3 × 2 = 4/3 = 1 1/3 cups. Or halving: 2/3 × 1/2 = 2/6 = 1/3 cup.

Construction and woodworking. A board is 5 3/4 inches wide. Removing 1/2 inch from each side: 5 3/4 - 1/2 - 1/2 = 5 3/4 - 1 = 4 3/4 inches remaining.

Financial calculations. Ownership of 3/8 of a property exists. A sibling owns 2/8 (1/4). Together: 3/8 + 2/8 = 5/8. The remaining 3/8 belongs to the parents.

Time calculations. Working 2 1/2 hours Monday and 3 1/4 hours Tuesday: 2 1/2 + 3 1/4 = 5/2 + 13/4 = 10/4 + 13/4 = 23/4 = 5 3/4 hours.

Probability. The chance of event A is 1/4. The chance of event B is 1/3. If independent, probability of both: 1/4 × 1/3 = 1/12.

Worked Calculations and Scenarios

Scenario 1: Pizza Division Problem

Context: 3/4 of a pizza remains. A friend takes 1/3 of what remains.

Amount taken: 3/4 × 1/3 = 3/12 = 1/4 of the whole pizza
Remaining: 3/4 - 1/4 = 2/4 = 1/2 of the whole pizza

Scenario 2: Investment Portfolio Rebalancing

Context: Portfolio allocation adjustment for 2026.

Current allocation:

  • UK Equities: 3/8 of portfolio
  • US Equities: 1/4 of portfolio
  • Bonds: 1/8 of portfolio
  • Cash: remainder
Invested portion: 3/8 + 1/4 + 1/8
Convert to common denominator (8):
= 3/8 + 2/8 + 1/8
= 6/8 = 3/4

Cash allocation: 1 - 3/4 = 1/4

For £80,000 portfolio:

  • UK Equities: £80,000 × 3/8 = £30,000
  • US Equities: £80,000 × 1/4 = £20,000
  • Bonds: £80,000 × 1/8 = £10,000
  • Cash: £80,000 × 1/4 = £20,000

Scenario 3: Recipe Scaling for Dinner Party

Context: Original recipe serves 4, scaling to serve 6.

Scaling factor: 6/4 = 3/2 = 1.5

| Ingredient | Original | × 3/2 | Scaled | |------------|----------|-------|--------| | Flour (2/3 cup) | 2/3 | 2/3 × 3/2 = 6/6 = 1 | 1 cup | | Sugar (1/4 cup) | 1/4 | 1/4 × 3/2 = 3/8 | 3/8 cup | | Butter (3/8 cup) | 3/8 | 3/8 × 3/2 = 9/16 | 9/16 cup | | Eggs (1) | 1 | 1 × 3/2 = 3/2 | 1 1/2 eggs |

Scenario 4: Cryptocurrency Holdings Calculation

Context: Splitting cryptocurrency holdings among wallets.

Total: 2 1/4 BTC (= 9/4 BTC)

Distribution:

  • Cold storage: 2/3 of total
  • Exchange: 1/4 of total
  • Hardware wallet: remainder
Cold storage: 9/4 × 2/3 = 18/12 = 3/2 = 1.5 BTC
Exchange: 9/4 × 1/4 = 9/16 BTC
Hardware: 9/4 - 3/2 - 9/16

Convert to sixteenths:
9/4 = 36/16
3/2 = 24/16
Hardware: 36/16 - 24/16 - 9/16 = 3/16 BTC

Scenario 5: Construction Material Calculation

Context: Cutting timber for shelving project.

Board length: 8 feet Need pieces of: 2 1/4 feet each

Pieces per board: 8 ÷ 2 1/4
= 8 ÷ 9/4
= 8 × 4/9
= 32/9
= 3 5/9

Whole pieces: 3 per board
Waste: 5/9 × 2 1/4 = 5/9 × 9/4 = 45/36 = 1 1/4 feet

Scenario 6: Time Zone Meeting Coordination

Context: Scheduling meeting across time zones.

Meeting duration: 1 3/4 hours Preparation time: 1/2 hour Buffer: 1/4 hour

Total time block: 1 3/4 + 1/2 + 1/4
= 7/4 + 2/4 + 1/4
= 10/4
= 2 1/2 hours

Common Mistakes and How to Recover

Adding denominators. 1/4 + 1/3 ≠ 2/7. A common denominator must be found: 3/12 + 4/12 = 7/12.

Forgetting to simplify. 6/8 is correct but incomplete. Always reduce: 6/8 = 3/4.

Flipping the wrong fraction when dividing. In a ÷ b, flip b, not a. 3/4 ÷ 1/2 = 3/4 × 2/1 = 6/4 = 3/2.

Mixed number arithmetic errors. Convert to improper fractions first. 2 1/3 + 1 1/2: convert to 7/3 + 3/2 = 14/6 + 9/6 = 23/6 = 3 5/6.

LCD mistakes. The least common denominator of 6 and 8 is 24, not 48. Using larger common denominators works but creates bigger numbers to simplify later.

Sources

FAQs

Why do I need a common denominator for addition but not multiplication?

Addition combines like quantities. Only thirds can be added to thirds. Multiplication finds a portion of a portion—3/4 of 1/2 means a different operation entirely.

How do I convert a decimal to a fraction?

0.75 = 75/100 = 3/4. For repeating decimals: 0.333... = 1/3. Some decimals (like π) cannot be expressed as fractions.

What is an improper fraction versus a mixed number?

Improper fraction: numerator is greater than or equal to denominator (7/4). Mixed number: whole plus fraction (1 3/4). They represent the same value.

How do I compare fractions?

Find a common denominator, then compare numerators. Or convert to decimals. 3/8 vs 2/5: 15/40 vs 16/40, so 2/5 is greater than 3/8.

What if my answer has a larger denominator than the inputs?

This is normal for addition and subtraction before simplification. 1/4 + 1/6 = 6/24 + 4/24 = 10/24, which simplifies to 5/12.

Can fractions have negative numbers?

Yes. -3/4 and 3/-4 both equal -0.75. Convention places the negative sign with the numerator or in front of the fraction.

What is a unit fraction?

A fraction with numerator 1, like 1/2, 1/3, 1/4. Ancient Egyptians used only unit fractions, expressing other fractions as sums.

How do I handle zero in fractions?

0/n = 0 for any n. n/0 is undefined (division by zero is not allowed).

What are equivalent fractions?

Fractions that represent the same value: 1/2 = 2/4 = 3/6 = 50/100. Multiplying or dividing both numerator and denominator by the same number creates equivalent fractions.

How do I add mixed numbers?

Convert to improper fractions first, add, then convert back if desired. 2 1/3 + 1 1/2 = 7/3 + 3/2 = 14/6 + 9/6 = 23/6 = 3 5/6.

What is the difference between proper and improper fractions?

Proper fractions have numerator less than denominator (3/4, 2/5). Improper fractions have numerator greater than or equal to denominator (5/3, 7/4). Both are valid representations.

When should I use fractions versus decimals?

Fractions preserve exactness (1/3 stays exact; 0.333... is approximate). Decimals are easier for some calculations and comparisons. Use fractions when precision matters; decimals for quick estimation.

How do I convert between fractions and percentages?

Multiply the fraction by 100 to get percentage: 3/4 × 100 = 75%. Divide percentage by 100 to get decimal, then convert: 75% = 0.75 = 3/4.

What are complex fractions and how do I simplify them?

Complex fractions have fractions in the numerator, denominator, or both. Simplify by multiplying numerator and denominator by the LCD of all internal fractions, or by rewriting as division: (1/2)/(3/4) = 1/2 ÷ 3/4 = 1/2 × 4/3 = 4/6 = 2/3.

What is a reciprocal and when do I use it?

The reciprocal of a/b is b/a. Reciprocals are used in division (dividing by a fraction equals multiplying by its reciprocal) and solving equations where a variable is in the denominator.