Work out the following :
`1/2+3/5`

Answer

To solve the problem \( \frac{1}{2} + \frac{3}{5} \), we will follow these steps:

### Step 1: Identify the denominators
The denominators of the fractions are 2 and 5.

### Step 2: Find the Least Common Multiple (LCM)
We need to find the LCM of the denominators 2 and 5. The LCM of 2 and 5 is 10.

### Step 3: Convert the fractions to have a common denominator
Now we will convert both fractions to have the common denominator of 10.

- For \( \frac{1}{2} \):
- We divide the LCM (10) by the denominator (2):
\[ \frac{10}{2} = 5 \]
- We then multiply the numerator (1) by this result:
\[ 1 \times 5 = 5 \]
- So, \( \frac{1}{2} \) becomes \( \frac{5}{10} \).

- For \( \frac{3}{5} \):
- We divide the LCM (10) by the denominator (5):
\[ \frac{10}{5} = 2 \]
- We then multiply the numerator (3) by this result:
\[ 3 \times 2 = 6 \]
- So, \( \frac{3}{5} \) becomes \( \frac{6}{10} \).

### Step 4: Add the converted fractions
Now we can add the two fractions:
\[ \frac{5}{10} + \frac{6}{10} = \frac{5 + 6}{10} = \frac{11}{10} \]

### Step 5: Convert to a mixed number (if necessary)
Since \( \frac{11}{10} \) is an improper fraction, we can convert it to a mixed number:
- Divide the numerator (11) by the denominator (10):
- 11 divided by 10 gives a quotient of 1 and a remainder of 1.
- Therefore, we can express \( \frac{11}{10} \) as:
\[ 1 \frac{1}{10} \]

### Final Answer:
So, \( \frac{1}{2} + \frac{3}{5} = 1 \frac{1}{10} \).

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