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 apples and oranges, which are given as mixed fractions. Let's solve this step by step.

### Step 1: Convert Mixed Fractions to Improper Fractions
First, we convert the mixed fractions into improper fractions.

- For apples:
\[ 3 \frac{1}{2} = \frac{3 \times 2 + 1}{2} = \frac{6 + 1}{2} = \frac{7}{2} \text{ kg} \]

- For oranges:
\[ 4 \frac{3}{4} = \frac{4 \times 4 + 3}{4} = \frac{16 + 3}{4} = \frac{19}{4} \text{ kg} \]

### Step 2: Find a Common Denominator
Next, we need to find a common denominator to add the two fractions. The denominators are 2 and 4. The least common multiple (LCM) of 2 and 4 is 4.

### Step 3: Convert the Fractions
Now we 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 to a Mixed Fraction
Finally, we convert \(\frac{33}{4}\) back to a mixed fraction:
- Divide 33 by 4:
\[ 33 \div 4 = 8 \quad \text{(remainder 1)} \]
So, \(\frac{33}{4} = 8 \frac{1}{4}\).

### Final Answer
The total weight of fruits purchased by Sameera is \(8 \frac{1}{4}\) kg.

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