Problem 49 - Introductory Algebra for College Students

Question

Perform the indicated operation. Where possible, reduce the answer to its lowest terms. $$\frac{5}{4} \cdot \frac{6}{7}$$

Step-by-Step Solution

Answer

The simplified product of the fractions \(\frac{5}{4}\) and \(\frac{6}{7}\) is \(\frac{15}{14}\).

Step 1: Multiplication of Numerators and Denominators

The first thing to do is to multiply the numerators: 5 and 6 as well as the denominators: 4 and 7. This gives the initial fraction: \( \frac{5 \cdot 6}{4 \cdot 7} \).

Step 2: Performing the Multiplication

Performing the multiplication in both the numerator and the denominator gives us \( \frac{30}{28} \).

Step 3: Simplify to Lowest Terms

The fraction \( \frac{30}{28} \) can be simplified to its lowest terms by dividing both the numerator and denominator by their greatest common divisor, which is 2. Dividing both gives \( \frac{30 \div 2}{28 \div 2} \) which simplifies to \( \frac{15}{14} \).