Problem 52 - Introductory Algebra for College Students

Question

Perform the indicated operation. Where possible, reduce the answer to its lowest terms. $$\left(2 \frac{4}{5}\right)\left(1 \frac{1}{4}\right)$$

Step-by-Step Solution

Answer

The result of the operation is \(3 \frac{1}{2}\)

Step 1: Convert Mixed Numbers to Improper Fractions

To convert \(2 \frac{4}{5}\) to an improper fraction, take the whole number 2, multiply it by the denominator 5, and then add the numerator 4 to get a numerator of 14. The denominator is the same as in the mixed number, 5. Same operation applies for \(1 \frac{1}{4}\), so our fractions are now \(\frac{14}{5}\) and \(\frac{5}{4}\).

Step 2: Multiply the Fractions

Multiply the numerators with each other and the denominators with each other. So, we have \(\frac{14}{5} * \frac{5}{4} = \frac{14*5}{5*4} = \frac{70}{20}\)

Step 3: Simplify the Product

Simplify the fraction \(\frac{70}{20}\) by dividing the numerator and the denominator by their greatest common factor, which is 10. So, \(\frac{70}{20} = \frac{70÷10}{20÷10} = \frac{7}{2}\)

Step 4: Convert to Mixed Number

Since the problem started with mixed numbers, it might be best to finish with a mixed number. To convert the improper fraction \(\frac{7}{2}\) to a mixed number, divide 7 by 2 to get a quotient of 3 and a remainder of 1, which gives us \(3 \frac{1}{2}\)