Problem 51 - Introductory Algebra for College Students

Question

Perform the indicated operation. Where possible, reduce the answer to its lowest terms. $$\left(3 \frac{3}{4}\right)\left(1 \frac{3}{5}\right)$$

Step-by-Step Solution

Answer

6

Step 1: Convert both mixed fractions into improper fractions

A mixed fraction can be converted to an improper fraction by multiplying the whole number by the denominator and adding the numerator. Then put this value over the denominator. So, \(3 \frac{3}{4}\) can be converted to \(\frac{15}{4}\) and \(1 \frac{3}{5}\) can be converted to \(\frac{8}{5}\).

Step 2: Multiply the improper fractions

To multiply fractions, you multiply the numerators together and the denominators together. So, \(\frac{15}{4} * \(\frac{8}{5}\) results in \(\frac{120}{20}\).

Step 3: Simplify the fraction

Divide both numerator and denominator by their greatest common divisor. In this case, GCD of 120 and 20 is 20. So, the fraction \(\frac{120}{20}\) simplifies to \(\frac{6}{1}\), which is 6.