Problem 138 - Introductory Algebra for College Students

Question

Explain how to divide fractions and give an example.

Step-by-Step Solution

Answer

The result of dividing \( \frac{1}{3} \) by \( \frac{2}{5} \) is \( \frac{5}{6} \).

Step 1: Understand Fraction Division

Dividing fractions isn't as straightforward as dividing integers, but the process is simple once you remember one key rule: 'Flip and Multiply'. In other words, instead of actually dividing, you can find the reciprocal of the second fraction (flip it upside down) and change the operation from division to multiplication.

Step 2: Find the Reciprocal

The reciprocal of a fraction is obtained by swapping the numerator and the denominator. For example, the reciprocal of \( \frac{3}{4} \) is \( \frac{4}{3} \). Note: The reciprocal of any number cannot be zero as we cannot divide by zero.

Step 3: Implement 'Flip and Multiply'

Let's take an example of dividing two fractions: \( \frac{1}{3} \div \frac{2}{5} \). The reciprocal of \( \frac{2}{5} \) is \( \frac{5}{2} \). Now change the division operation to multiplication: \( \frac{1}{3} \times \frac{5}{2} \).

Step 4: Perform Multiplication

To multiply fractions, simply multiply the numerators together and the denominators together. Applying multiplication for the example \( \frac{1}{3} \times \frac{5}{2} \), we end up with \( \frac{1*5}{3*2} = \frac{5}{6} \). Note: Always simplify the fraction if possible.