How do you perform division with fractions?

How do you perform division with fractions?

• A. By multiplying the fractions directly
• B. By multiplying by the reciprocal of the second fraction
• C. By adding the fractions
• D. By finding a common denominator

Answer: (B)

When dividing by a fraction, the operation is simplified by multiplying by the reciprocal of that fraction. The reciprocal of a fraction is obtained by flipping its numerator and denominator. For example, if you are dividing by the fraction 2/3, you would multiply by its reciprocal, which is 3/2. This process works because division can be thought of as multiplying by an inverse. So, when you have an expression like \( \frac{a}{b} \div \frac{c}{d} \), you transform it into \( \frac{a}{b} \times \frac{d}{c} \). This makes it easier to carry out the multiplication, allowing for straightforward computation of the product. Utilizing the reciprocal ensures that you are performing the correct operation, which is crucial for arriving at the right answer when dealing with fractions in division.

When dividing by a fraction, the operation is simplified by multiplying by the reciprocal of that fraction. The reciprocal of a fraction is obtained by flipping its numerator and denominator. For example, if you are dividing by the fraction 2/3, you would multiply by its reciprocal, which is 3/2.

This process works because division can be thought of as multiplying by an inverse. So, when you have an expression like ( \frac{a}{b} \div \frac{c}{d} ), you transform it into ( \frac{a}{b} \times \frac{d}{c} ). This makes it easier to carry out the multiplication, allowing for straightforward computation of the product.

Utilizing the reciprocal ensures that you are performing the correct operation, which is crucial for arriving at the right answer when dealing with fractions in division.