Question

Find the product {7/9+4/5} x 3x8

Answer 1

To find the product \(\left(\frac{7}{9} + \frac{4}{5}\right) \times 3 \times 8\), we first need to add the fractions \(\frac{7}{9}\) and \(\frac{4}{5}\).

1. **Finding a common denominator**:
The denominators are \(9\) and \(5\). The least common multiple (LCM) of \(9\) and \(5\) is \(45\).

2. **Converting fractions**:
- For \(\frac{7}{9}\):
\[
\frac{7}{9} = \frac{7 \times 5}{9 \times 5} = \frac{35}{45}
\]
- For \(\frac{4}{5}\):
\[
\frac{4}{5} = \frac{4 \times 9}{5 \times 9} = \frac{36}{45}
\]

3. **Adding the fractions**:
Now, we can add the fractions:
\[
\frac{35}{45} + \frac{36}{45} = \frac{35 + 36}{45} = \frac{71}{45}
\]

4. **Calculating the product**:
Now, we multiply \(\frac{71}{45}\) by \(3 \times 8\):
\[
3 \times 8 = 24
\]
So we have:
\[
\frac{71}{45} \times 24 = \frac{71 \times 24}{45}
\]

5. **Calculating \(71 \times 24\)**:
\[
71 \times 24 = 1704
\]
Now the expression becomes:
\[
\frac{1704}{45}
\]

6. **Simplifying the fraction**:
We can simplify \(\frac{1704}{45}\). First, we divide the numerator and the denominator by their greatest common divisor (GCD).
The GCD of \(1704\) and \(45\) is \(9\):
\[
\frac{1704 \div 9}{45 \div 9} = \frac{189}{5}
\]

Therefore, the final answer is:
\[
\boxed{\frac{189}{5}} \text{ or } 37.8
\]