Math & Arithmetic Full 6-Tool Suite

Fraction Calculator

Add, subtract, multiply, and divide fractions, mixed numbers, and decimals with step-by-step reduction, LCD calculation, and visual fraction diagrams.

Standard Fraction Calculator

Perform arithmetic on two fractions: (N₁ / D₁) op (N₂ / D₂)

Common Fractions to Decimals & Percentages Cheatsheet

Fraction	Decimal	Percentage
1/2	0.5	50%
1/3	0.3333...	33.33%
2/3	0.6667...	66.67%
1/4	0.25	25%
3/4	0.75	75%
1/5	0.2	20%
1/8	0.125	12.5%
3/8	0.375	37.5%
5/8	0.625	62.5%
7/8	0.875	87.5%

Comprehensive Guide to Fractions & Arithmetic

Anatomy of a Fraction: Numerator & Denominator

A fraction represents a numerical quantity that is not a whole number. It consists of two essential parts separated by a horizontal fraction bar (vinculum):

Numerator (Top): Indicates how many equal parts of the whole are being considered.
Denominator (Bottom): Represents the total number of equal parts that make up the whole. The denominator can never be zero (D ≠ 0).

3 / 4 = 75% of whole

1. Adding & Subtracting Fractions

Fractions must have a common denominator before adding or subtracting. Find the Least Common Denominator (LCD), convert each fraction, then add or subtract the numerators:

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

2. Multiplying Fractions

Multiply straight across: multiply the numerators together, then multiply the denominators together, and reduce using the GCD:

(a/b) × (c/d) = (a × c) / (b × d)

3. Dividing Fractions (Keep, Change, Flip)

Invert the divisor fraction (reciprocal) and multiply:

(a/b) ÷ (c/d) = (a/b) × (d/c) = (ad) / (bc)

4. Negative Mixed Fractions Rule

A negative sign applies to the entire mixed fraction, not just the whole number:

-2 3/4 = -(2 + 3/4) = -11/4 (NOT -2 + 3/4)

Frequently Asked Questions

Why can a denominator never be zero?

Dividing by zero is mathematically undefined. A fraction a/b answers "how many groups of b are in a?". If b = 0, no number of zeros can ever equal a non-zero numerator, making division impossible.

What is the difference between proper, improper, and mixed fractions?

A proper fraction has a numerator smaller than its denominator (e.g. 3/4 < 1). An improper fraction has a numerator equal to or greater than its denominator (e.g. 7/4 ≥ 1). A mixed number combines an integer and a proper fraction (e.g. 1 3/4).

How does the calculator simplify fractions to lowest terms?

It uses the Euclidean algorithm to calculate the Greatest Common Divisor (GCD) of the numerator and denominator, then divides both numbers by the GCD.

What is the Least Common Denominator (LCD)?

The LCD is the Least Common Multiple (LCM) of the denominators of two or more fractions. Converting fractions to the LCD allows them to be directly added or subtracted.

How does the Big Number calculator avoid precision loss?

Standard JavaScript numbers use 64-bit floating point (IEEE-754) with 53 bits of precision (~15-17 digits). The Big Number calculator uses native arbitrary-precision BigInt integers, allowing calculations on numbers with hundreds of digits without rounding error.