Problem 53 - Introductory Algebra for College Students

Question

Perform the indicated operation. Where possible, reduce the answer to its lowest terms. $$\frac{5}{4} \div \frac{4}{3}$$

Step-by-Step Solution

Answer

The answer is \(\frac{15}{16}\).

Step 1: Writing division as multiplication

When dividing by a fraction, it is the same as multiplying by the reciprocal of the fraction. Therefore, we can write \(\frac{5}{4} \div \frac{4}{3}\) as \(\frac{5}{4} * \frac{3}{4}\).

Step 2: Multiply the fractions

We multiply the fractions by multiplying the numerators (the top numbers) to get the new numerator, and multiplying the denominators (the bottom numbers) to get the new denominator. We get \(\frac{5 * 3}{4 * 4}\) which equals \(\frac{15}{16}\).

Step 3: Simplifying the fraction

As 15 and 16 don't share any common factor other than 1, the fraction \(\frac{15}{16}\) is already in its lowest terms and can't be simplified further.