`5(1)/(5)+2(3)/(5)+1(2)/(5)=?`

Options

A. `7(4)/(5)`
B. `8(3)/(5)`
C. `6(2)/(5)`
D. `9(1)/(5)`

Explanation

To solve the expression \( 5\frac{1}{5} + 2\frac{3}{5} + 1\frac{2}{5} \), we will convert each mixed number into an improper fraction, add them together, and then convert the result back to a mixed number if necessary.

### Step 1: Convert Mixed Numbers to Improper Fractions

1. **Convert \( 5\frac{1}{5} \)**:
- The whole number part is 5, and the fractional part is \( \frac{1}{5} \).
- To convert it: \( 5\frac{1}{5} = 5 \times 5 + 1 = 25 + 1 = 26 \).
- So, \( 5\frac{1}{5} = \frac{26}{5} \).

2. **Convert \( 2\frac{3}{5} \)**:
- The whole number part is 2, and the fractional part is \( \frac{3}{5} \).
- To convert it: \( 2\frac{3}{5} = 2 \times 5 + 3 = 10 + 3 = 13 \).
- So, \( 2\frac{3}{5} = \frac{13}{5} \).

3. **Convert \( 1\frac{2}{5} \)**:
- The whole number part is 1, and the fractional part is \( \frac{2}{5} \).
- To convert it: \( 1\frac{2}{5} = 1 \times 5 + 2 = 5 + 2 = 7 \).
- So, \( 1\frac{2}{5} = \frac{7}{5} \).

### Step 2: Add the Improper Fractions

Now we will add the three improper fractions together:

\[ \frac{26}{5} + \frac{13}{5} + \frac{7}{5} \]

Since they all have the same denominator, we can add the numerators:

\[ = \frac{26 + 13 + 7}{5} = \frac{46}{5} \]

### Step 3: Convert the Result Back to a Mixed Number

Now we will convert \( \frac{46}{5} \) back to a mixed number:

1. Divide 46 by 5:
- \( 46 \div 5 = 9 \) (whole number part)
- Remainder: \( 46 - (5 \times 9) = 46 - 45 = 1 \) (remainder)

So, \( \frac{46}{5} = 9\frac{1}{5} \).

### Final Answer

Thus, the final answer is:

\[ 5\frac{1}{5} + 2\frac{3}{5} + 1\frac{2}{5} = 9\frac{1}{5} \]

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