Rinda needs to solve the problem 1(2/9)+5(2/3)

Question

. What is the sum?

Answer 1

To solve the expression \( 1\left(\frac{2}{9}\right) + 5\left(\frac{2}{3}\right) \), we can break it down step by step.

1. Calculate the first term: \[ 1\left(\frac{2}{9}\right) = \frac{2}{9} \]

2. Calculate the second term: \[ 5\left(\frac{2}{3}\right) = \frac{10}{3} \]

3. Now we need to add these two fractions: \[ \frac{2}{9} + \frac{10}{3} \]

To do this, we need a common denominator. The least common multiple (LCM) of 9 and 3 is 9. Now, we express \(\frac{10}{3}\) with a denominator of 9: \[ \frac{10}{3} = \frac{10 \times 3}{3 \times 3} = \frac{30}{9} \]

Now we can add the fractions: \[ \frac{2}{9} + \frac{30}{9} = \frac{2 + 30}{9} = \frac{32}{9} \]

Therefore, the final sum is: \[ \frac{32}{9} \]

Alternatively, \(\frac{32}{9}\) can be expressed as a mixed number: \[ 3 \frac{5}{9} \]

Thus, the answer to the problem is: \[ \frac{32}{9} \text{ or } 3 \frac{5}{9} \]