Questions: Find the product and write it in lowest terms. 6/7 * 9/4

Solution Steps

To find the product of two fractions and write it in lowest terms, we need to multiply the numerators together and the denominators together. Then, we simplify the resulting fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD).

To find the product of the fractions \( \frac{6}{7} \) and \( \frac{9}{4} \), we multiply the numerators and the denominators: \[ \text{Numerator: } 6 \cdot 9 = 54 \] \[ \text{Denominator: } 7 \cdot 4 = 28 \] Thus, the product of the fractions is \( \frac{54}{28} \).

Next, we simplify \( \frac{54}{28} \) by finding the greatest common divisor (GCD) of 54 and 28, which is 2. We then divide both the numerator and the denominator by the GCD: \[ \text{Simplified Numerator: } \frac{54}{2} = 27 \] \[ \text{Simplified Denominator: } \frac{28}{2} = 14 \] Therefore, the simplified fraction is \( \frac{27}{14} \).

Final Answer