Problem 6 - Introductory Algebra for College Students

Question

Multiply as indicated. $$\frac{7}{x} \cdot \frac{5 x}{35}$$

Step-by-Step Solution

Answer

The result of multiplying the two fractions is 1.

Step 1: Multiply the Numerators and Denominators

First, we need to multiply the numerator of the first fraction by the numerator of the second, and the denominator of the first fraction by the denominator of the second. This gives us \( \frac{7 \cdot 5x}{x \cdot 35} \).

Step 2: Simplify the Fraction

Next, we simplify the fraction by cancelling common factors. The x in the numerator cancels out with the x in the denominator. Also, 7 and 35 have a common factor of 7. Therefore, once simplified, this gives us \( \frac{5}{5} \).

Step 3: Final Result

Lastly, the fraction \( \frac{5}{5} \) simplifies to 1 because any number divided by itself equals 1.