Find the sum:
`28/(40)+6/(28)`

Answer

To find the sum of \( \frac{28}{40} + \frac{6}{28} \), we will follow these steps:

### Step 1: Simplify each fraction

1. **Simplifying \( \frac{28}{40} \)**:
- The numerator \( 28 \) can be factored as \( 4 \times 7 \).
- The denominator \( 40 \) can be factored as \( 4 \times 10 \).
- We can cancel the common factor \( 4 \):
\[ \frac{28}{40} = \frac{4 \times 7}{4 \times 10} = \frac{7}{10} \]

2. **Simplifying \( \frac{6}{28} \)**:
- The numerator \( 6 \) can be factored as \( 2 \times 3 \).
- The denominator \( 28 \) can be factored as \( 2 \times 14 \).
- We can cancel the common factor \( 2 \):
\[ \frac{6}{28} = \frac{2 \times 3}{2 \times 14} = \frac{3}{14} \]

### Step 2: Add the simplified fractions

Now we need to add \( \frac{7}{10} + \frac{3}{14} \).

3. **Finding the LCM of the denominators (10 and 14)**:
- The prime factorization of \( 10 \) is \( 2 \times 5 \).
- The prime factorization of \( 14 \) is \( 2 \times 7 \).
- The LCM is found by taking the highest power of each prime:
\[ \text{LCM} = 2^1 \times 5^1 \times 7^1 = 70 \]

4. **Rewriting each fraction with the common denominator**:
- For \( \frac{7}{10} \):
\[ \frac{7}{10} = \frac{7 \times 7}{10 \times 7} = \frac{49}{70} \]
- For \( \frac{3}{14} \):
\[ \frac{3}{14} = \frac{3 \times 5}{14 \times 5} = \frac{15}{70} \]

5. **Adding the fractions**:
\[ \frac{49}{70} + \frac{15}{70} = \frac{49 + 15}{70} = \frac{64}{70} \]

### Step 3: Simplify the result

6. **Simplifying \( \frac{64}{70} \)**:
- The numerator \( 64 \) can be factored as \( 2^6 \).
- The denominator \( 70 \) can be factored as \( 2 \times 35 \).
- We can cancel the common factor \( 2 \):
\[ \frac{64}{70} = \frac{2^6}{2 \times 35} = \frac{32}{35} \]

### Final Answer
The sum \( \frac{28}{40} + \frac{6}{28} \) simplifies to \( \frac{32}{35} \).

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