Sameera purchased `3 frac{1}{2}` kg apples and `4 frac {3}{4}` kg oranges. What is the total weight of fruits purchased by her?

Options

A. `8 frac {1}{4}`
B. `1/4`
C. `7/2`
D. `4 frac {1}{8}`

Explanation

To find the total weight of fruits purchased by Sameera, we need to add the weights of the apples and oranges. Let's break down the solution step by step.

### Step 1: Convert the mixed fractions to improper fractions
1. **Weight of Apples**: Sameera purchased `3 frac{1}{2}` kg of apples.
- Convert `3 frac{1}{2}` to an improper fraction:
\[ 3 \frac{1}{2} = \frac{(3 \times 2) + 1}{2} = \frac{6 + 1}{2} = \frac{7}{2} \text{ kg} \]

2. **Weight of Oranges**: Sameera purchased `4 frac{3}{4}` kg of oranges.
- Convert `4 frac{3}{4}` to an improper fraction:
\[ 4 \frac{3}{4} = \frac{(4 \times 4) + 3}{4} = \frac{16 + 3}{4} = \frac{19}{4} \text{ kg} \]

### Step 2: Add the two improper fractions
Now, we need to add the two weights:
\[ \text{Total Weight} = \frac{7}{2} + \frac{19}{4} \]

### Step 3: Find a common denominator
The denominators are 2 and 4. The least common multiple (LCM) of 2 and 4 is 4. We will convert `\frac{7}{2}` to have a denominator of 4:
\[ \frac{7}{2} = \frac{7 \times 2}{2 \times 2} = \frac{14}{4} \]

### Step 4: Add the fractions
Now we can add the two fractions:
\[ \frac{14}{4} + \frac{19}{4} = \frac{14 + 19}{4} = \frac{33}{4} \]

### Step 5: Convert the improper fraction back to a mixed number
To convert `\frac{33}{4}` back to a mixed number:
- Divide 33 by 4, which gives us 8 with a remainder of 1.
- Thus, we can write:
\[ \frac{33}{4} = 8 \frac{1}{4} \text{ kg} \]

### Final Answer
The total weight of fruits purchased by Sameera is:
\[ \text{Total Weight} = 8 \frac{1}{4} \text{ kg} \]

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