Math

Fraction Calculator: How to Add, Subtract, Multiply and Divide Fractions

What is a Fraction?


A fraction represents a part of a whole. It consists of a numerator (top number) and denominator (bottom number). Example: 3/4 means 3 parts out of 4.


Types of Fractions


  • Proper fraction: Numerator < Denominator (3/4)
  • Improper fraction: Numerator > Denominator (7/4)
  • Mixed number: Whole number + fraction (1 3/4)

    • Adding Fractions


    Same denominator: Add numerators, keep denominator

  • 2/5 + 1/5 = 3/5

    • Different denominators: Find LCD, convert, then add

  • 1/3 + 1/4 = 4/12 + 3/12 = 7/12

    • Subtracting Fractions


    Same process as addition but subtract numerators:

  • 3/4 - 1/4 = 2/4 = 1/2
  • 2/3 - 1/5 = 10/15 - 3/15 = 7/15

    • Multiplying Fractions


    Multiply numerators together, multiply denominators together:

  • 2/3 x 3/4 = 6/12 = 1/2
  • No need to find common denominator!

    • Dividing Fractions


    Flip the second fraction and multiply:

  • 2/3 / 4/5 = 2/3 x 5/4 = 10/12 = 5/6

    • Simplifying Fractions


    Divide both numerator and denominator by their GCD:

  • 6/8: GCD = 2, so 6/8 = 3/4
  • 12/18: GCD = 6, so 12/18 = 2/3

    • Converting Between Fractions and Decimals


    Fraction to decimal: Divide numerator by denominator

  • 3/4 = 0.75

    • Decimal to fraction: Write as fraction of power of 10, simplify

  • 0.75 = 75/100 = 3/4

    • Try Our Fraction Calculator


    Use our free fraction calculator to perform any fraction operation instantly.

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    Put this knowledge to use with our free online calculator.

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