Simran put `(7)/(6)` kg of sweets, `2` kg of milk, and `1 (2)/(3)` kg of fruits in her bag. How much did her bag weigh now?

Options

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

Answer

To find the total weight of the items Simran put in her bag, we need to add the weights of the sweets, milk, and fruits together. Let's break it down step by step.

### Step 1: Convert all weights to improper fractions
- The weight of sweets is already in fraction form: \( \frac{7}{6} \) kg.
- The weight of milk is \( 2 \) kg, which can be expressed as an improper fraction: \( \frac{2}{1} \).
- The weight of fruits is \( 1 \frac{2}{3} \) kg. We need to convert this mixed number into an improper fraction:
\[ 1 \frac{2}{3} = \frac{3 \times 1 + 2}{3} = \frac{3 + 2}{3} = \frac{5}{3} \]

### Step 2: Add the weights together
Now we have:
- Sweets: \( \frac{7}{6} \)
- Milk: \( \frac{2}{1} \) (which is the same as \( \frac{12}{6} \) when converted to a common denominator)
- Fruits: \( \frac{5}{3} \) (which we need to convert to a common denominator of 6)

To convert \( \frac{5}{3} \) to have a denominator of 6:
\[ \frac{5}{3} = \frac{5 \times 2}{3 \times 2} = \frac{10}{6} \]

Now we can add all the fractions:
\[ \text{Total weight} = \frac{7}{6} + \frac{12}{6} + \frac{10}{6} \]

### Step 3: Combine the fractions
Since all fractions have the same denominator, we can add the numerators:
\[ \text{Total weight} = \frac{7 + 12 + 10}{6} = \frac{29}{6} \]

### Step 4: Final result
Thus, the total weight of Simran's bag is:
\[ \frac{29}{6} \text{ kg} \]