Shreya bought `5 3/4` litres of milk on Monday and `4 2/3` litres of mile on Tuesday. How many litres of milk and she buy together in two days?

Options

A. `5 3/4` litres
B. `6 1/4` litres
C. `10 5/12` litres
D. `9 3/4` litres

Answer

To solve the problem of how many liters of milk Shreya bought together on Monday and Tuesday, we can follow these steps:

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

**For Monday:**
Shreya bought \(5 \frac{3}{4}\) liters of milk.
- To convert this to an improper fraction:
\[ 5 \frac{3}{4} = \frac{(5 \times 4) + 3}{4} = \frac{20 + 3}{4} = \frac{23}{4} \]

**For Tuesday:**
Shreya bought \(4 \frac{2}{3}\) liters of milk.
- To convert this to an improper fraction:
\[ 4 \frac{2}{3} = \frac{(4 \times 3) + 2}{3} = \frac{12 + 2}{3} = \frac{14}{3} \]

### Step 2: Add the Improper Fractions
Now we need to add the two improper fractions together:
\[ \frac{23}{4} + \frac{14}{3} \]

To add these fractions, we need a common denominator. The least common multiple (LCM) of 4 and 3 is 12.

**Convert each fraction:**
- For \(\frac{23}{4}\):
\[ \frac{23}{4} = \frac{23 \times 3}{4 \times 3} = \frac{69}{12} \]

- For \(\frac{14}{3}\):
\[ \frac{14}{3} = \frac{14 \times 4}{3 \times 4} = \frac{56}{12} \]

Now we can add them:
\[ \frac{69}{12} + \frac{56}{12} = \frac{69 + 56}{12} = \frac{125}{12} \]

### Step 3: Convert the Improper Fraction Back to a Mixed Number
Now we convert \(\frac{125}{12}\) back to a mixed number:
- Divide 125 by 12:
\[ 12 \text{ goes into } 125 \text{ a total of } 10 \text{ times (since } 12 \times 10 = 120\text{)} \]
- The remainder is:
\[ 125 - 120 = 5 \]
Thus, we can express \(\frac{125}{12}\) as:
\[ 10 \frac{5}{12} \]

### Final Answer
Shreya bought a total of \(10 \frac{5}{12}\) liters of milk over the two days.

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