Problem 42 - Introductory Algebra for College Students

Question

Perform the indicated operation. Where possible, reduce the answer to its lowest terms. $$\frac{3}{7} \cdot \frac{1}{4}$$

Step-by-Step Solution

Answer

The result of the operation \(\frac{3}{7} \cdot \frac{1}{4}\) is \(\frac{3}{28}\)

Step 1: Multiplication of the Numerators

The first step in multiplying fractions is to multiply the numerators (the numbers on top of each fraction). In our case, multiply \(3\) from the first fraction and \(1\) from the second fraction. So, \(3 \cdot 1 = 3\).

Step 2: Multiplication of the Denominators

Next, multiply the denominators (the numbers at the bottom of each fraction), which are \(7\) in the first fraction and \(4\) in the second fraction. So, \(7 \cdot 4 = 28\).

Step 3: Form the Resulting Fraction

After the multiplication of both the numerators and denominators, form a new fraction with the results. This will give the fraction \(\frac{3}{28}\).

Step 4: Reducing To Lowest Terms

The final step is to check if the resulting fraction can be simplified or reduced to its lowest terms. This means finding a number that can divide both the numerator and denominator without leaving any remainder. However, the fraction \(\frac{3}{28}\) is already in its lowest terms, because there is no number save for \(1\) that can divide both \(3\) and \(28\), leaving no remainder.