Find the sum:
`4(3)/(5)+2(7)/(8)`

Answer

To find the sum of the mixed fractions \(4 \frac{3}{5}\) and \(2 \frac{7}{8}\), we will follow these steps:

### Step 1: Convert Mixed Fractions to Improper Fractions
1. For \(4 \frac{3}{5}\):
- Multiply the whole number (4) by the denominator (5): \(4 \times 5 = 20\)
- Add the numerator (3): \(20 + 3 = 23\)
- So, \(4 \frac{3}{5} = \frac{23}{5}\)

2. For \(2 \frac{7}{8}\):
- Multiply the whole number (2) by the denominator (8): \(2 \times 8 = 16\)
- Add the numerator (7): \(16 + 7 = 23\)
- So, \(2 \frac{7}{8} = \frac{23}{8}\)

### Step 2: Find the Least Common Multiple (LCM) of the Denominators
- The denominators are 5 and 8.
- The LCM of 5 and 8 is 40.

### Step 3: Convert the Improper Fractions to Have a Common Denominator
1. Convert \(\frac{23}{5}\) to a denominator of 40:
- Multiply the numerator and denominator by 8:
\[ \frac{23 \times 8}{5 \times 8} = \frac{184}{40} \]

2. Convert \(\frac{23}{8}\) to a denominator of 40:
- Multiply the numerator and denominator by 5:
\[ \frac{23 \times 5}{8 \times 5} = \frac{115}{40} \]

### Step 4: Add the Two Fractions
- Now we can add the two fractions:
\[ \frac{184}{40} + \frac{115}{40} = \frac{184 + 115}{40} = \frac{299}{40} \]

### Step 5: Convert the Improper Fraction to a Mixed Fraction
1. Divide 299 by 40:
- 40 goes into 299 seven times (since \(40 \times 7 = 280\)).
- The remainder is \(299 - 280 = 19\).

2. Therefore, we can express \(\frac{299}{40}\) as a mixed fraction:
\[ 7 \frac{19}{40} \]

### Final Answer
The sum of \(4 \frac{3}{5} + 2 \frac{7}{8}\) is:
\[ 7 \frac{19}{40} \]

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