Questions: Multiply. Write your answer in lowest terms. (8-2z)/49 * 98/(7z-28)

Transcript text: Multiply. Write your answer in lowest terms. \[ \frac{8-2 z}{49} \cdot \frac{98}{7 z-28} \]

Solution

Solution Steps

To multiply two fractions, multiply the numerators together and the denominators together. Then, simplify the resulting fraction to its lowest terms by finding the greatest common divisor (GCD) of the numerator and the denominator and dividing both by this GCD.

Step 1: Multiply the Numerators and Denominators

To multiply the fractions \(\frac{8-2z}{49}\) and \(\frac{98}{7z-28}\), we first multiply the numerators and the denominators:

\[ \text{Numerator: } (8 - 2z) \times 98 = 784 - 196z \]

\[ \text{Denominator: } 49 \times (7z - 28) = 343z - 1372 \]

Step 2: Simplify the Fraction

Next, we simplify the fraction \(\frac{784 - 196z}{343z - 1372}\). We look for common factors in the numerator and the denominator.

The expression simplifies to:

\[ \frac{784 - 196z}{343z - 1372} = -\frac{4}{7} \]