Problem 47 - Introductory Algebra for College Students

Question

Perform the indicated operation. Where possible, reduce the answer to its lowest terms. $$\frac{1}{10} \cdot \frac{5}{6}$$

Step-by-Step Solution

Answer

The solution to the operation \( \frac{1}{10} \cdot \frac{5}{6} = \frac{1}{12} \)

Step 1: Multiply the Numerators

Multiply the numerator of the first fraction by the numerator of the second fraction. In this case, multiply \(1\) and \(5\) to get \(5\).

Step 2: Multiply the Denominators

Multiply the denominator of the first fraction by the denominator of the second fraction. In this case, multiply \(10\) and \(6\) to get \(60\). This results in the fraction \(\frac{5}{60}\).

Step 3: Reduce to Lowest Terms

Now, simplify this fraction to its lowest terms by finding the greatest common divisor (GCD) of both the numerator and the denominator and dividing both by it. The GCD of \(5\) and \(60\) is \(5\). So, divide \(5\) by \(5\) to get \(1\) and divide \(60\) by \(5\) to get \(12\). So, the fraction reduces to \(\frac{1}{12}\).