Fractions

Law of fractions - Learn about numerators, denominators, and operations on fractions including addition, multiplication, and division.

Fractions

Definition

Fractions consist of two basic parts:

  • Numerator - the top number (a)
  • Denominator - the bottom number (b)

Fraction: a / b

Types of Fractions

  • Proper fraction - the numerator is smaller than the denominator
  • Improper fraction - the numerator is larger than the denominator
  • Reducible fraction - a fraction that can be reduced to lower terms
  • Mixed number - a combination of a whole number and a fraction

Laws of Fractions

  1. Addition: (a / b) + (c / d) = (ad + bc) / (bd)
  2. Multiplication: (a / b) × (c / d) = (ac) / (bd)
  3. Division: (a / b) ÷ (c / d) = (a / b) × (d / c)
  4. Negation: (-a / b) = -(a / b) = a / (-b)
Calculator

Inputs

Results

Result Numerator--
Result Denominator--
Result (Decimal)--
OperationFormulaExample 1Example 2Example 3
Addition(a/b) + (c/d) = (ad + bc)/(bd)(1/4) + (3/16) = 7/16 = 0.4375(1/4) + (7/8) = 9/8 = 1.125(3/4) + (1/8) = 7/8 = 0.875
Multiplication(a/b) × (c/d) = (ac)/(bd)(3/4) × (9/16) = 27/64 ≈ 0.422(1/2) × (3/4) = 3/8 = 0.375(2/3) × (3/5) = 6/15 = 0.4
Division(a/b) ÷ (c/d) = (ad)/(bc)(3/4) ÷ (9/16) = 48/36 = 4/3 ≈ 1.333(1/2) ÷ (1/4) = 2/1 = 2(3/4) ÷ (1/2) = 6/4 = 1.5
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