Questions: Multiply. Write your answer as a fraction in simplest form. 5/2 × 7/5 × 2/9

Solution Steps

To multiply fractions, multiply the numerators together to get the new numerator and the denominators together to get the new denominator. Then, simplify the resulting fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD).

We start with the fractions \( \frac{5}{2} \), \( \frac{7}{5} \), and \( \frac{2}{9} \). To multiply these fractions, we calculate the product of the numerators and the product of the denominators:

\[ \text{Numerator} = 5 \times 7 \times 2 = 70 \] \[ \text{Denominator} = 2 \times 5 \times 9 = 90 \]

Next, we simplify the fraction \( \frac{70}{90} \). We find the greatest common divisor (GCD) of 70 and 90, which is 10. We then divide both the numerator and the denominator by their GCD:

\[ \text{Simplified Numerator} = \frac{70}{10} = 7 \] \[ \text{Simplified Denominator} = \frac{90}{10} = 9 \]

Thus, the simplified fraction is \( \frac{7}{9} \).

Final Answer