Dividing Fractions Calculator

Divide fractions instantly using the reciprocal method. Get step-by-step solutions, visual explanations, and handle mixed numbers with our comprehensive calculator.

First Fraction (Dividend)

Whole Number

Numerator

Denominator

3/4

Divided by

Second Fraction (Divisor)

Whole Number

Numerator

Denominator

1/2

Example Problems:

Formula

(a/b) ÷ (c/d) = (a/b) × (d/c) = (a × d)/(b × c)

Understanding Fraction Division

Reciprocal Method: The most common way to divide fractions is to multiply by the reciprocal of the divisor.

Why It Works: Dividing by a fraction is equivalent to multiplying by its reciprocal because division asks "how many groups fit into the dividend."

Mixed Numbers: Convert mixed numbers to improper fractions before dividing, then convert the result back if needed.

Simplification: Always simplify the final result by dividing both numerator and denominator by their GCD.

Division Methods

Reciprocal Method:

Flip the second fraction and multiply (most common)

Cross Multiplication:

Multiply numerator of first by denominator of second, and vice versa

Common Denominator:

Convert to same denominator, then divide numerators (less common)

Frequently Asked Questions

How do you divide fractions?

To divide fractions, use the reciprocal method: multiply the first fraction by the reciprocal (flip) of the second fraction. For example, (a/b) ÷ (c/d) = (a/b) × (d/c) = (a×d)/(b×c).

What is the reciprocal method?

The reciprocal method means 'flip and multiply.' To find the reciprocal of a fraction, switch the numerator and denominator. Then multiply instead of dividing.

How do you divide mixed numbers?

First convert mixed numbers to improper fractions, then apply the reciprocal method. Finally, convert the result back to a mixed number if needed.

Why do we flip and multiply when dividing fractions?

Dividing by a fraction is the same as multiplying by its reciprocal. This works because division asks 'how many groups of the divisor fit into the dividend,' which is equivalent to multiplying by the reciprocal.

Can the calculator handle negative fractions?

Yes, the calculator handles negative fractions. The sign rules for division apply: positive ÷ positive = positive, negative ÷ negative = positive, positive ÷ negative = negative, negative ÷ positive = negative.

Related Calculators

Quick Tips

• Always check if fractions can be simplified
• Convert mixed numbers to improper fractions first
• Remember: dividing by a fraction = multiplying by its reciprocal
• Check your answer by multiplying back

Common Mistakes

• Forgetting to flip the second fraction
• Not simplifying the final answer
• Dividing instead of multiplying after flipping
• Incorrect handling of mixed numbers

Tips

Enter the dimensions in the same unit for consistency.
Results update automatically as you type.
Use the unit selector to convert between different measurement systems.