Fraction Calculator Formula

Understand the math behind the fraction calculator. Each variable explained with a worked example.

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Formulas Used

Sum Numerator

sum_numerator = a * d + b * c

Sum Denominator

sum_denominator = b * d

Sum Decimal

sum_decimal = a / b + c / d

Difference Numerator

difference_numerator = a * d - b * c

Difference Denominator

difference_denominator = b * d

Difference Decimal

difference_decimal = a / b - c / d

Product Numerator

product_numerator = a * c

Product Denominator

product_denominator = b * d

Product Decimal

product_decimal = (a * c) / (b * d)

Quotient Numerator

quotient_numerator = a * d

Quotient Denominator

quotient_denominator = b * c

Quotient Decimal

quotient_decimal = (a / b) / (c / d)

Variables

VariableDescriptionDefault
aNumerator 11
bDenominator 13
cNumerator 21
dDenominator 24

How It Works

How to Calculate with Fractions

Addition

a/b + c/d = (a×d + b×c) / (b×d)

Subtraction

a/b - c/d = (a×d - b×c) / (b×d)

Multiplication

a/b × c/d = (a×c) / (b×d)

Division

a/b ÷ c/d = (a×d) / (b×c)

Results may need to be simplified by dividing both numerator and denominator by their greatest common factor.

Worked Example

Calculate 1/3 + 1/4, 1/3 - 1/4, 1/3 × 1/4, and 1/3 ÷ 1/4.

a = 1b = 3c = 1d = 4
  1. 01Sum: (1×4 + 3×1) / (3×4) = 7/12 ≈ 0.583333
  2. 02Difference: (1×4 - 3×1) / (3×4) = 1/12 ≈ 0.083333
  3. 03Product: (1×1) / (3×4) = 1/12 ≈ 0.083333
  4. 04Quotient: (1×4) / (3×1) = 4/3 ≈ 1.333333

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