Fraction Calculator

Common Fractions Reference

Common Fractions Conversion Table

Fraction	Decimal	Percentage
1/2	0.5	50%
1/3	0.333	33.3%
2/3	0.667	66.7%
1/4	0.25	25%
3/4	0.75	75%
1/5	0.2	20%
2/5	0.4	40%
3/5	0.6	60%
4/5	0.8	80%
1/8	0.125	12.5%
3/8	0.375	37.5%
5/8	0.625	62.5%
7/8	0.875	87.5%

Fraction Types

Proper

Numerator < Denominator

40%

Improper

Numerator ≥ Denominator

25%

Mixed

Whole number + Fraction

20%

Equivalent

Same value, different form

15%

Quick Examples

1/2 = 0.5 = 50% - Half of a whole

1/4 = 0.25 = 25% - Quarter of a whole

3/4 = 0.75 = 75% - Three quarters

Understanding Fractions

A fraction represents a part of a whole or, more generally, any number of equal parts. It consists of a numerator (top number) and a denominator (bottom number), written in the form a/b.

Key Components:

Numerator: The number of parts you have (top number)
Denominator: The total number of equal parts (bottom number)
Mixed Number: A whole number plus a proper fraction (e.g., 2 1/3)
Improper Fraction: Where numerator ≥ denominator (e.g., 7/4)

Fraction Operations Explained

Adding Fractions

Method: Find common denominator, then add numerators

Formula: a/b + c/d = (ad + bc)/bd

Example: 1/2 + 1/4 = 2/4 + 1/4 = 3/4

Subtracting Fractions

Method: Find common denominator, then subtract numerators

Formula: a/b - c/d = (ad - bc)/bd

Example: 3/4 - 1/2 = 3/4 - 2/4 = 1/4

Multiplying Fractions

Method: Multiply numerators and denominators separately

Formula: a/b × c/d = ac/bd

Example: 2/3 × 3/4 = 6/12 = 1/2

Dividing Fractions

Method: Multiply by the reciprocal of the second fraction

Formula: a/b ÷ c/d = a/b × d/c = ad/bc

Example: 3/4 ÷ 1/2 = 3/4 × 2/1 = 6/4 = 1 1/2

Real-World Applications

Cooking & Baking

Adjusting recipe quantities, measuring ingredients, and scaling servings.

Construction

Measuring materials, calculating dimensions, and dividing spaces.

Finance

Calculating interest rates, discounts, and investment returns.

Education

Grade calculations, statistical analysis, and mathematical problem-solving.

Mixed Number Conversions

Common Mixed Numbers & Their Equivalents

Mixed number chart temporarily disabled for troubleshooting

Conversion Rules:

Mixed → Improper:
2¾ = (2 × 4 + 3)/4 = 11/4

Improper → Mixed:
11/4 = 2 remainder 3 = 2¾

Quick Tip:
Divide numerator by denominator

Mixed Number	Improper Fraction	Decimal	Percentage
1½	3/2	1.5	150.0%
2¼	9/4	2.25	225.0%
3¾	15/4	3.75	375.0%
1⅓	4/3	1.333	133.3%
2⅔	8/3	2.667	266.7%

Fraction Simplification Guide

Step-by-Step Simplification Process

Original

12/18

GCD: 6

Find GCD

12/18 ÷ 6

GCD: 6

Divide

2/3

GCD: 1

Common Simplification Methods:

Prime Factorization:

12/18 = (2×2×3)/(2×3×3) = 2/3

Euclidean Algorithm:

Find GCD of 12 and 18 = 6

Divide by Common Factors:

12/18 ÷ 2/2 = 6/9 ÷ 3/3 = 2/3

Quick Recognition Tips:

Even numbers: divide by 2

Numbers ending in 5 or 0: divide by 5

Sum of digits divisible by 3: divide by 3

Both end in even digits: divide by 2, then 2 again

Tips for Working with Fractions

Always simplify fractions - Reducing fractions to their lowest terms makes calculations easier and results clearer.

Find the least common denominator - When adding or subtracting, use the LCD to minimize simplification later.

Convert mixed numbers carefully - Remember: 2 1/3 = 7/3 (2 × 3 + 1 = 7)

Check your work - Convert final answers back to decimals to verify they make sense.

Related Tools

Basic Calculator

Standard arithmetic operations

Percentage Calculator

Calculate percentages and ratios

Scientific Calculator

Advanced mathematical functions

Quick Reference

1/20.5 or 50%

1/30.333 or 33.3%

1/40.25 or 25%

1/50.2 or 20%

2/30.667 or 66.7%

Features

Step-by-step solutions
Mixed number support
Automatic simplification
Decimal conversion
Error checking