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Division Formula:
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Dividing a whole number by a fraction is a fundamental arithmetic operation that can be solved by converting the division into multiplication by the reciprocal of the fraction. This calculator provides step-by-step solutions to help understand the process.
The calculator uses the following formula:
Where:
Explanation: Dividing by a fraction is equivalent to multiplying by its reciprocal. The calculator also simplifies the resulting fraction to its lowest terms.
Details: The formula transforms division by a fraction into multiplication by flipping the numerator and denominator of the fraction. This is mathematically equivalent but often easier to compute.
Tips: Enter positive whole numbers for all values. The calculator will show each step of the calculation, including the multiplication, resulting fraction, and simplification if possible.
Q1: Why does dividing by a fraction equal multiplying by its reciprocal?
A: This is a fundamental property of fractions. Dividing by a/b is the same as multiplying by b/a because division is the inverse of multiplication.
Q2: What if my fraction is improper (numerator > denominator)?
A: The calculator works the same way for proper and improper fractions. The formula applies regardless of the fraction's form.
Q3: Can I use this for mixed numbers?
A: First convert mixed numbers to improper fractions. For example, 2 1/2 becomes 5/2.
Q4: What if I get a fraction that can be simplified?
A: The calculator automatically simplifies fractions by finding the greatest common divisor (GCD) of the numerator and denominator.
Q5: Why does the calculator show both fraction and decimal results?
A: The fraction form is exact while the decimal is approximate. Both forms are useful in different contexts.