math

Fractions

A number representing a part of a whole, written as a numerator over a denominator.

Last updated: · Reviewed by Marcus Webb

A fraction consists of a numerator (top number, the parts you have) and a denominator (bottom number, total equal parts).

Operations

  • Adding/Subtracting: Find a common denominator first. 1/3 + 1/4 = 4/12 + 3/12 = 7/12
  • Multiplying: Multiply numerators and denominators. 2/3 × 3/5 = 6/15 = 2/5
  • Dividing: Flip the second fraction and multiply. 3/4 ÷ 2/5 = 3/4 × 5/2 = 15/8

Converting

  • Fraction → Decimal: Divide numerator by denominator (3/8 = 0.375)
  • Fraction → Percentage: Convert to decimal, multiply by 100 (3/8 = 37.5%)

Simplifying Fractions

A fraction is in simplest form when the numerator and denominator share no common factor other than 1. To simplify, divide both by their greatest common divisor (GCD): 12/18 → GCD is 6 → simplifies to 2/3. Calculators and most math problems expect answers in simplest form.

Mixed Numbers vs. Improper Fractions

A mixed number (like 2¾) combines a whole number and a fraction; an improper fraction (like 11/4) has a numerator larger than its denominator — they represent the same value. To convert a mixed number to improper form: multiply the whole number by the denominator, add the numerator, and keep the same denominator.

Related Calculators

📊 Fraction Calculator📊 Percentage Calculator

Related Articles

📝 Fraction Operations Guide

Related Terms

Percentage

A number expressed as a fraction of 100, used to describe proportions and rates of change.

Standard Deviation

A measure of the spread or dispersion of a data set from its mean (average).

Mean, Median, and Mode

Three measures of central tendency used to describe the center of a data set.

Pythagorean Theorem

A fundamental relation in geometry: the square of the hypotenuse equals the sum of squares of the other two sides.

Area and Perimeter

Area measures the surface inside a shape (in square units); perimeter measures the distance around it.

Logarithm

The inverse of exponentiation — the logarithm of a number tells you the exponent needed to produce that number from a given base.

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Marcus Webb

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Engineering & Applied Mathematics Specialist

Marcus specializes in structural analysis, fluid mechanics, and construction calculations, verifying every formula against ASCE standards, ACI codes, and published engineering handbooks. Content lead at CalculatorApp.me.

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