Sarita bought `5 3/4`kg potatoes and `3 1/2` kg tomatoes from a vendor. What is the total weight of vegetables bought by her?

Options

A. `4 1/4`kg
B. `9 1/4`kg
C. `5 1/4`kg
D. None of these

Answer

To find the total weight of vegetables Sarita bought, we need to add the weight of the potatoes and the tomatoes. Let's break it down step by step.

### Step 1: Convert the mixed numbers to improper fractions
1. **Potatoes**:
- Sarita bought \(5 \frac{3}{4}\) kg of potatoes.
- To convert this to an improper fraction:
\[ 5 \frac{3}{4} = \frac{(5 \times 4) + 3}{4} = \frac{20 + 3}{4} = \frac{23}{4} \text{ kg} \]

2. **Tomatoes**:
- Sarita bought \(3 \frac{1}{2}\) kg of tomatoes.
- To convert this to an improper fraction:
\[ 3 \frac{1}{2} = \frac{(3 \times 2) + 1}{2} = \frac{6 + 1}{2} = \frac{7}{2} \text{ kg} \]

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

### Step 3: Convert the fractions to have the same denominator
- The fraction for tomatoes needs to be converted:
\[ \frac{7}{2} = \frac{7 \times 2}{2 \times 2} = \frac{14}{4} \]

### Step 4: Add the two fractions
Now we can add the two fractions:
\[ \frac{23}{4} + \frac{14}{4} = \frac{23 + 14}{4} = \frac{37}{4} \]

### Step 5: Convert the improper fraction back to a mixed number
To convert \(\frac{37}{4}\) back to a mixed number:
- Divide 37 by 4:
- 37 divided by 4 is 9 with a remainder of 1.
- Thus, \(\frac{37}{4} = 9 \frac{1}{4}\) kg.

### Final Answer
The total weight of vegetables Sarita bought is \(9 \frac{1}{4}\) kg.

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