Find the sum
`2(7)/(10)+3(8)/(15)`

Answer

To find the sum of \( \frac{2 \times 7}{10} + \frac{3 \times 8}{15} \), we will follow these steps:

### Step 1: Simplify the fractions
First, we calculate the values of the fractions:
- \( \frac{2 \times 7}{10} = \frac{14}{10} \)
- \( \frac{3 \times 8}{15} = \frac{24}{15} \)

### Step 2: Convert to improper fractions
Now, we can express these fractions as improper fractions:
- \( \frac{14}{10} \) can be simplified to \( \frac{7}{5} \) (by dividing both numerator and denominator by 2).
- \( \frac{24}{15} \) can be simplified to \( \frac{8}{5} \) (by dividing both numerator and denominator by 3).

### Step 3: Find a common denominator
The denominators of our fractions are 5 and 5. Since they are the same, we can directly add the numerators:
- The common denominator is 5.

### Step 4: Add the fractions
Now, we add the fractions:
\[ \frac{7}{5} + \frac{8}{5} = \frac{7 + 8}{5} = \frac{15}{5} \]

### Step 5: Simplify the result
Now, we simplify \( \frac{15}{5} \):
\[ \frac{15}{5} = 3 \]

### Final Answer
The sum \( \frac{2 \times 7}{10} + \frac{3 \times 8}{15} = 3 \).

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