Problem 43 - Introductory Algebra for College Students

Question

Perform the indicated operation. Where possible, reduce the answer to its lowest terms. $$\frac{3}{8} \cdot \frac{7}{11}$$

Step-by-Step Solution

Answer

The result of \(\frac{3}{8} \cdot \frac{7}{11}\) is \(\frac{21}{88}\).

Step 1: Multiplication of Fractions

When multiplying fractions, you multiply the numerators (the top numbers) to get the new numerator and multiply the denominators (the bottom numbers) to get the new denominator. So for \(\frac{3}{8} \cdot \frac{7}{11}\), multiply 3 and 7 for the numerator and 8 and 11 for the denominator, which will give \(\frac{3*7}{8*11}\).

Step 2: Simplify the Multiplication

After doing the multiplication, the new fraction to simplify is \(\frac{21}{88}\).

Step 3: Reduce to Lowest Terms

To reduce a fraction to its lowest terms, find the Greatest Common Divisor (GCD) of both the numerator and the denominator, and divide them both by it. For 21 and 88, the GCD is 1, so the fraction \(\frac{21}{88}\) is already in its lowest terms.