# Division of Fractions

## Understanding Reciprocals

The reciprocal of a fraction (where ) is . In other words, the numerator and denominator switch places.

• The reciprocal of is .
• The reciprocal of is .

To find the reciprocal of a mixed number, first convert it to an improper fraction:

• The reciprocal of is , since .

For whole numbers and negative fractions:

• The reciprocal of is , as .
• The reciprocal of is .
• The reciprocal of is .

## Fraction Division

When dividing one fraction by another, convert the second fraction to its reciprocal form, then change the division operation to multiplication.

For example, given , rewrite this as .

### Examples

Example 1: Find .

The reciprocal of is , and the division becomes multiplication.

Example 2: Find .

Convert the mixed numbers to improper fractions: and .

Rewrite the division as multiplication by taking the reciprocal of the second fraction: .

Multiply the fractions: .

So, .

Example 3: Evaluate .

Convert mixed numbers to improper fractions: and .

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