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Fraction Simplification Formula:
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Fraction simplification is the process of reducing a complex fraction (a fraction divided by another fraction) to its simplest form. The rule states that dividing by a fraction is the same as multiplying by its reciprocal.
The calculator uses the fraction simplification formula:
Where:
Explanation: The calculator first converts the complex fraction into a simple fraction by multiplying the numerator by the reciprocal of the denominator, then simplifies the resulting fraction by dividing both numerator and denominator by their greatest common divisor.
Details: Simplified fractions are easier to work with in calculations and comparisons. They provide the most reduced form of a ratio, making mathematical operations more straightforward and results more interpretable.
Tips: Enter all four values (a, b, c, d) where b and d cannot be zero. The calculator will show the original form, the intermediate step of multiplication, and the final simplified form.
Q1: Why can't denominators be zero?
A: Division by zero is undefined in mathematics, as it leads to impossible results.
Q2: What if my simplified fraction has a denominator of 1?
A: This means your fraction simplifies to a whole number (the numerator).
Q3: Does the order of fractions matter?
A: Yes, (a/b)/(c/d) is different from (c/d)/(a/b) - the first is equivalent to (a×d)/(b×c) while the second would be (c×b)/(d×a).
Q4: Can this handle negative fractions?
A: Yes, the calculator works with negative numbers. The negative sign will be applied to the numerator in the simplified form.
Q5: How is the greatest common divisor found?
A: The calculator uses the Euclidean algorithm to find the GCD of numerator and denominator.