Find the sum
`2(3)/(4)+5(5)/(6)`

Answer

To solve the problem of finding the sum \( \frac{2 \times 3}{4} + \frac{5 \times 5}{6} \), we will follow these steps:

### Step 1: Simplify each fraction
First, we simplify each fraction:

1. For \( \frac{2 \times 3}{4} \):
\[ \frac{6}{4} = \frac{3}{2} \quad \text{(dividing numerator and denominator by 2)} \]

2. For \( \frac{5 \times 5}{6} \):
\[ \frac{25}{6} \quad \text{(this fraction is already in simplest form)} \]

### Step 2: Find a common denominator
Next, we need to find a common denominator for the fractions \( \frac{3}{2} \) and \( \frac{25}{6} \). The least common multiple (LCM) of 2 and 6 is 6.

### Step 3: Convert fractions to have the same denominator
Now we convert \( \frac{3}{2} \) to have a denominator of 6:
\[ \frac{3}{2} = \frac{3 \times 3}{2 \times 3} = \frac{9}{6} \]

Now we have:
\[ \frac{9}{6} + \frac{25}{6} \]

### Step 4: Add the fractions
Since both fractions now have the same denominator, we can add them:
\[ \frac{9 + 25}{6} = \frac{34}{6} \]

### Step 5: Simplify the result
Now we simplify \( \frac{34}{6} \):
\[ \frac{34 \div 2}{6 \div 2} = \frac{17}{3} \]

### Final Answer
Thus, the final answer is:
\[ \frac{17}{3} \]

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