Find the sum:
`5/(8)+8/ ( 28)`

Answer

To find the sum of the fractions \( \frac{5}{8} + \frac{8}{28} \), we will follow these steps:

### Step 1: Find the LCM of the denominators
The denominators are 8 and 28. We need to find the least common multiple (LCM) of these two numbers.

**Prime Factorization:**
- The prime factorization of 8 is \( 2^3 \) (which is \( 2 \times 2 \times 2 \)).
- The prime factorization of 28 is \( 2^2 \times 7 \) (which is \( 2 \times 2 \times 7 \)).

**Finding the LCM:**
To find the LCM, we take each prime factor with the highest power:
- For the prime number 2, the highest power is \( 2^3 \).
- For the prime number 7, the highest power is \( 7^1 \).

Thus, the LCM is:
\[ LCM = 2^3 \times 7^1 = 8 \times 7 = 56 \]

### Step 2: Convert the fractions to have the same denominator
Now that we have the LCM, we will convert both fractions to have a denominator of 56.

**Convert \( \frac{5}{8} \):**
To convert \( \frac{5}{8} \) to a denominator of 56, we multiply both the numerator and the denominator by 7:
\[ \frac{5}{8} = \frac{5 \times 7}{8 \times 7} = \frac{35}{56} \]

**Convert \( \frac{8}{28} \):**
To convert \( \frac{8}{28} \) to a denominator of 56, we multiply both the numerator and the denominator by 2:
\[ \frac{8}{28} = \frac{8 \times 2}{28 \times 2} = \frac{16}{56} \]

### Step 3: Add the converted fractions
Now that both fractions have the same denominator, we can add them:
\[ \frac{35}{56} + \frac{16}{56} = \frac{35 + 16}{56} = \frac{51}{56} \]

### Final Answer
The sum of \( \frac{5}{8} + \frac{8}{28} \) is:
\[ \frac{51}{56} \]

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