Problem 62 - Introductory Algebra for College Students

Question

Perform the indicated operation. Where possible, reduce the answer to its lowest terms. $$\frac{7}{4} \div \frac{3}{8}$$

Step-by-Step Solution

Answer

The result of the operation, in its lowest terms, is \(\frac{14}{3}\)

Step 1: Write the Division as Multiplication

Rewrite the division operation as multiplication by the reciprocal of the divisor. The reciprocal of a fraction is obtained by exchanging its numerator and denominator. Here, the reciprocal of \(\frac{3}{8}\) is \(\frac{8}{3}\). So, write the operation as \(\frac{7}{4} \times \frac{8}{3}\)

Step 2: Perform the Multiplication

To multiply two fractions, multiply their numerators together to get the new numerator, and multiply their denominators together to get the new denominator. So, \(\frac{7}{4} \times \frac{8}{3} = \frac{7 \times 8}{4 \times 3} = \frac{56}{12}\)

Step 3: Reduce to Lowest Terms

To reduce a fraction to its lowest terms, find the greatest common divisor (GCD) of the numerator and denominator, and then divide both by the GCD. The GCD of 56 and 12 is 4. Dividing both by 4, the fraction becomes \(\frac{56}{4} / \frac{12}{4} = \frac{14}{3}\)