Fraction Calculator

How to Use the Fraction Calculator

This calculator handles five fraction operations: arithmetic (add, subtract, multiply, divide), simplifying to lowest terms, converting mixed numbers to improper fractions, converting between decimals and fractions, and comparing two fractions. All calculations use exact fraction arithmetic via mathjs, so results are precise with no floating-point rounding errors.

Results display in mixed number form when the result is improper (for example, "1 1/2"), or as a simple fraction when it is not. When the mixed and improper forms differ, the improper form appears in parentheses (for example, "1 1/2 (3/2)"). Below the result card, a Calculation Breakdown card shows the step-by-step math rendered with KaTeX. For simplify mode, a Prime Factorization section also appears when reduction is meaningful.

Calculation Modes

Calculate — Add, Subtract, Multiply, or Divide

Enter two fractions and select an operation. The calculator handles the arithmetic and reduces the result to lowest terms automatically.

Addition: Find a common denominator, add the numerators, then simplify.

Example: 3/4 + 1/2

• First Numerator: 3, First Denominator: 4
• Operation: Add
• Second Numerator: 1, Second Denominator: 2
• Result: 1 1/4 (5/4)

$\frac{3}{4} + \frac{1}{2} = \frac{3 \cdot 2 + 1 \cdot 4}{4 \cdot 2}$

$= \frac{10}{8} = \frac{10 \div 2}{8 \div 2} = 1\,\frac{1}{4} \, \left(\frac{5}{4}\right)$

Subtraction: Same as addition, but subtract the second numerator.

Example: 5/6 - 1/3

• First Numerator: 5, First Denominator: 6
• Operation: Subtract
• Second Numerator: 1, Second Denominator: 3
• Result: 1/2

$\frac{5}{6} - \frac{1}{3} = \frac{5 \cdot 3 - 1 \cdot 6}{6 \cdot 3}$

$= \frac{9}{18} = \frac{9 \div 9}{18 \div 9} = \frac{1}{2}$

Multiplication: Multiply numerators together and denominators together.

Example: 2/3 × 3/5

• First Numerator: 2, First Denominator: 3
• Operation: Multiply
• Second Numerator: 3, Second Denominator: 5
• Result: 2/5

$\frac{2}{3} \times \frac{3}{5} = \frac{2 \cdot 3}{3 \cdot 5}$

$= \frac{6}{15} = \frac{6 \div 3}{15 \div 3} = \frac{2}{5}$

Division: Flip the second fraction (reciprocal) and multiply.

Example: 3/4 ÷ 2/5

• First Numerator: 3, First Denominator: 4
• Operation: Divide
• Second Numerator: 2, Second Denominator: 5
• Result: 1 7/8 (15/8)

$\frac{3}{4} \div \frac{2}{5} = \frac{3}{4} \times \frac{5}{2} = \frac{3 \cdot 5}{4 \cdot 2}$

$= \frac{15}{8} = 1\,\frac{7}{8} \, \left(\frac{15}{8}\right)$

Simplify — Reduce to Lowest Terms

Enter a fraction and the calculator reduces it by dividing both numerator and denominator by their greatest common divisor (GCD).

Example: 12/16

• Numerator: 12
• Denominator: 16
• Simplified Result: 3/4

$\frac{12}{16} = \frac{12 \div 4}{16 \div 4} = \frac{3}{4}$

Example: 7/13

• Numerator: 7
• Denominator: 13
• Simplified Result: 7/13 (already in lowest terms)

$\frac{7}{13} = \frac{7}{13}$

When a fraction is already reduced, only a single equality is shown with no factorization section.

Mixed — Convert Mixed Number to Improper Fraction

Enter a whole number, numerator, and denominator to convert a mixed number into an improper fraction.

Example: 2 3/8

• Whole Number: 2
• Numerator: 3
• Denominator: 8
• Improper Fraction: 19/8

$2 \, \frac{3}{8} = \frac{(2 \cdot 8) + 3}{8}$

$= \frac{19}{8}$

Example: -1 2/5

• Whole Number: -1
• Numerator: 2
• Denominator: 5
• Improper Fraction: -7/5

$-1 \, \frac{2}{5} = \frac{(1 \cdot 5) + 2}{5}$

$= -\frac{7}{5}$

Convert — Decimal to Fraction or Fraction to Decimal

Select the conversion direction, then enter the value.

Decimal to Fraction: Enter a decimal number and the calculator finds the exact fraction.

Example: 0.75

• Direction: Decimal to Fraction
• Value: 0.75
• Result: 3/4

$0.75 = \frac{75}{100}$

$= \frac{75 \div 25}{100 \div 25} = \frac{3}{4}$

Example: 2.6

• Direction: Decimal to Fraction
• Value: 2.6
• Result: 2 3/5 (13/5)

$2.6 = \frac{26}{10}$

$= \frac{26 \div 2}{10 \div 2} = 2\,\frac{3}{5} \, \left(\frac{13}{5}\right)$

Fraction to Decimal: Enter a fraction in standard notation and the calculator divides numerator by denominator.

Accepted formats:

• Simple fraction: 3/4
• Mixed number: 1 1/2
• Whole number: 5 or -3

Example: 3/4

• Direction: Fraction to Decimal
• Value: 3/4
• Result: 0.75

$\frac{3}{4} = 3 \div 4 = 0.75$

Example: 1 3/8

• Direction: Fraction to Decimal
• Value: 1 3/8
• Result: 1.375

$\frac{11}{8} = 11 \div 8 = 1.375$

Compare — Which Fraction is Larger?

Enter two fractions to see which is larger, or if they are equal.

Method: Cross-multiplication. The calculator multiplies the first numerator by the second denominator and compares it to the second numerator times the first denominator.

Example: Compare 3/4 and 2/3

• First Numerator: 3, First Denominator: 4
• Second Numerator: 2, Second Denominator: 3
• Result: 3/4 > 2/3

$3 \times 3 = 9 \quad 2 \times 4 = 8$

$\frac{3}{4} > \frac{2}{3}$

Example: Compare 2/5 and 4/10

• First Numerator: 2, First Denominator: 5
• Second Numerator: 4, Second Denominator: 10
• Result: Equal

$2 \times 10 = 20 \quad 4 \times 5 = 20$

$\frac{2}{5} = \frac{4}{10}$

Common Use Cases

Adjusting a Recipe

A recipe calls for 3/4 cup of flour and you want to make half the amount:

1. Switch to Calculate
2. Enter 3/4 as the first fraction
3. Select Multiply
4. Enter 1/2 as the second fraction
5. Result: 3/8 cup

Reducing a Survey Result

28 out of 48 respondents said yes:

1. Switch to Simplify
2. Enter 28 as Numerator
3. Enter 48 as Denominator
4. Result: 7/12

Converting a Cooking Measurement

A recipe says 1.25 cups but your measuring cups are marked in fractions:

1. Switch to Convert
2. Direction: Decimal to Fraction
3. Enter 1.25
4. Result: 1 1/4 (5/4)

Checking if Two Ratios Are Equivalent

Is 6/9 the same as 14/21?

1. Switch to Compare
2. Enter 6/9 and 14/21
3. Result: Equal (both reduce to 2/3)

Splitting a Pizza

You have 3 1/2 pizzas and want to give each person 1/4 pizza. How many people can you serve?

1. Switch to Mixed
2. Convert 3 1/2 to improper fraction: 7/2
3. Switch to Calculate
4. Divide 7/2 by 1/4
5. Result: 14

Tips for Accurate Calculations

1. Denominators must be positive: Move any negative sign to the numerator
2. Mixed number validation: The numerator must be smaller in magnitude than the denominator
3. Division by zero is blocked: Dividing by a fraction whose numerator is 0 triggers a clear error message
4. Fraction-to-decimal accepts three formats: Simple 3/4, mixed 1 1/2, or whole numbers like -5
5. Results are always reduced: Every operation automatically simplifies the result to lowest terms
6. Cross-multiplication for comparison: Compare mode uses cross-multiplication instead of decimal conversion

Troubleshooting

Required

This appears when a field is left empty. Enter a value in all fields before calculating

Must be an integer

Numerators and whole numbers must be valid integers without decimal points. Enter 3, not 3.0

Must be a positive integer

Denominators must be positive whole numbers. Zero and negative denominators are not valid

Numerator magnitude must be less than denominator

In Mixed mode, the fractional part must be a proper fraction. Enter 2 3/8, not 2 9/8

Please select an operation

In Calculate mode, choose Add, Subtract, Multiply, or Divide from the dropdown before calculating

Please select a direction

In Convert mode, choose Decimal to Fraction or Fraction to Decimal from the dropdown

Invalid format

In Convert mode with Fraction to Decimal selected, the value must match fraction notation: 3/4, 1 1/2, or -5

Cannot divide by zero

In Calculate mode, dividing by a fraction whose numerator is 0 is undefined

Invalid fraction

This typically means a denominator of 0 was entered, or the input could not be parsed as a valid fraction

Invalid fraction operation

The entered values could not be processed as a valid fraction arithmetic operation. Check that all numerators and denominators are valid integers

Invalid mixed number

The whole number, numerator, and denominator combination could not be converted. Ensure the denominator is positive and the numerator is smaller in magnitude than the denominator

Invalid input

The conversion could not be completed. For Decimal to Fraction, enter a valid decimal number. For Fraction to Decimal, enter a fraction in 3/4, 1 1/2, or -5 format