To make a mocktail , Ashima mixed `2 "" (1)/(3)` L of soda , `1 "" (2)/(3)` L of lime syrup and `1"" (5)/(6)` L of water together . Find the total amount of mocktail she made.

Options

A. `5 "" (5)/(6)` L
B. `2 "" (1)/(6)` L
C. `4 "" (1)/(6)` L
D. `5 "" (1)/(3)` L

Answer

To find the total amount of mocktail Ashima made, we need to add the quantities of soda, lime syrup, and water she used. Let's break down the steps:

### Step 1: Write down the quantities
- Soda: \(2 \frac{1}{3}\) L
- Lime Syrup: \(1 \frac{2}{3}\) L
- Water: \(1 \frac{5}{6}\) L

### Step 2: Convert mixed numbers to improper fractions
1. For soda:
\[ 2 \frac{1}{3} = \frac{2 \times 3 + 1}{3} = \frac{6 + 1}{3} = \frac{7}{3} \]

2. For lime syrup:
\[ 1 \frac{2}{3} = \frac{1 \times 3 + 2}{3} = \frac{3 + 2}{3} = \frac{5}{3} \]

3. For water:
\[ 1 \frac{5}{6} = \frac{1 \times 6 + 5}{6} = \frac{6 + 5}{6} = \frac{11}{6} \]

### Step 3: Find a common denominator
The denominators we have are 3 and 6. The least common multiple (LCM) of 3 and 6 is 6.

### Step 4: Convert each fraction to have the common denominator of 6
1. For soda:
\[ \frac{7}{3} = \frac{7 \times 2}{3 \times 2} = \frac{14}{6} \]

2. For lime syrup:
\[ \frac{5}{3} = \frac{5 \times 2}{3 \times 2} = \frac{10}{6} \]

3. For water:
\[ \frac{11}{6} \text{ (already has the correct denominator)} \]

### Step 5: Add the fractions
Now we can add the fractions:
\[ \frac{14}{6} + \frac{10}{6} + \frac{11}{6} = \frac{14 + 10 + 11}{6} = \frac{35}{6} \]

### Step 6: Convert the improper fraction back to a mixed number
To convert \(\frac{35}{6}\) to a mixed number:
- Divide 35 by 6, which gives 5 with a remainder of 5.
- Thus, \(\frac{35}{6} = 5 \frac{5}{6}\).

### Final Answer
The total amount of mocktail Ashima made is \(5 \frac{5}{6}\) L.

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