Problem 109 - Introductory Algebra for College Students

Question

Will help you prepare for the material covered in the next section. In each exercise, use the given formula to perform the indicated operation with the two fractions. $$\frac{a}{b} \cdot \frac{c}{d}=\frac{a \cdot c}{b \cdot d} ; \quad \frac{3}{7} \cdot \frac{2}{5}$$

Step-by-Step Solution

Answer

The result of \(\frac{3}{7} \cdot \frac{2}{5}\) is \(\frac{6}{35}\).

Step 1: Identify Numerator and Denominator

In the equation \(\frac{3}{7} \cdot \frac{2}{5}\), identify the numerators (3 and 2) from both fractions and the denominators (7 and 5).

Step 2: Use the Multiplication Formula for Fractions

Apply the formula \(\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}\), where \(a\) and \(c\) are the numerators and \(b\) and \(d\) are the denominators of the fractions. So the result of \(\frac{3}{7} \cdot \frac{2}{5}\) would be \(\frac{3 \cdot 2}{7 \cdot 5}\)

Step 3: Calculate Resultant Fraction

Calculate the resultant fraction \(\frac{3 \cdot 2}{7 \cdot 5}\) by multiplying numerators together (3*2=6) and denominators together (7*5=35). So, \(\frac{3 \cdot 2}{7 \cdot 5} = \frac{6}{35}\)