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Home/Formula Library/Fraction arithmetic

Fraction arithmetic

Operate on fractions and reduce the result to lowest terms.

General

  • Percentage proportion
  • Percent error
  • Ratio and proportion
  • Rounding
  • Exponentiation
  • Nth root
  • Fraction arithmetic
  • Long division
  • Order of operations (PEMDAS)

Formula

a/b ± × ÷ c/d → reduced form

Explanation

Addition/subtraction need a common denominator. Multiplication multiplies numerators and denominators. Division multiplies by the reciprocal. Always reduce by dividing numerator and denominator by their GCD. Denominators cannot be zero.

Variables

  • a/bfirst fraction
  • c/dsecond fraction
  • operator+, −, ×, or ÷

When to use

Cooking, measurements, probability, and any exact rational arithmetic.

Use this formula

Calculators

  • Fraction Calculator→

Related formulas

  • Ratio and proportionA:B = C:D → A×D = B×C
  • Long divisiondividend = quotient × divisor + remainder
  • Order of operations (PEMDAS)PEMDAS: ( ) then × ÷ then + −

Other categories

  • Statistics
  • Cooking & apparel
  • Data & digital
  • Electricity & magnetism
  • Encodings & numbers
  • Date & time
Formula Library→

Popular

  • Percentage proportion
  • Arithmetic and weighted mean
  • Exponentiation
  • Number base conversion
Formula Library→