What operation is performed when dividing fractions?

What operation is performed when dividing fractions?

• A. You add the denominators
• B. You find the common denominator
• C. You multiply by the reciprocal
• D. You subtract the numerators

Answer: (C)

When dividing fractions, the operation performed is to multiply by the reciprocal of the second fraction. This means that you take the second fraction (the divisor), flip it over (the reciprocal), and then multiply it by the first fraction (the dividend). This method simplifies the process because dividing by a fraction is equivalent to multiplying by its reciprocal. For example, if you have \( \frac{a}{b} \div \frac{c}{d} \), you would rewrite this as \( \frac{a}{b} \times \frac{d}{c} \). This approach not only leads to a straightforward solution but also reinforces the concept that division is essentially the inverse of multiplication. Thus, the correct answer emphasizes this fundamental property of fractions in arithmetic operations.

When dividing fractions, the operation performed is to multiply by the reciprocal of the second fraction. This means that you take the second fraction (the divisor), flip it over (the reciprocal), and then multiply it by the first fraction (the dividend). This method simplifies the process because dividing by a fraction is equivalent to multiplying by its reciprocal.

For example, if you have ( \frac{a}{b} \div \frac{c}{d} ), you would rewrite this as ( \frac{a}{b} \times \frac{d}{c} ). This approach not only leads to a straightforward solution but also reinforces the concept that division is essentially the inverse of multiplication. Thus, the correct answer emphasizes this fundamental property of fractions in arithmetic operations.