Sujata bought `2 3/4` kg of sugar. Her mother bought `1 1/4` kg of sugar. How much more sugar did Sujata buy than her mother ?

Options

A. `1 1/2` kg
B. 4 kg
C. 1 kg
D. `5/4` kg

Answer

To find out how much more sugar Sujata bought than her mother, we can follow these steps:

### Step 1: Convert Mixed Fractions to Improper Fractions
First, we need to convert the mixed fractions of sugar bought by Sujata and her mother into improper fractions.

- **Sujata's sugar**:
- Mixed fraction: \(2 \frac{3}{4}\)
- To convert it:
\[ \text{Improper fraction} = 4 \times 2 + 3 = 8 + 3 = 11 \quad \text{(so, } \frac{11}{4}\text{)} \]

- **Mother's sugar**:
- Mixed fraction: \(1 \frac{1}{4}\)
- To convert it:
\[ \text{Improper fraction} = 4 \times 1 + 1 = 4 + 1 = 5 \quad \text{(so, } \frac{5}{4}\text{)} \]

### Step 2: Subtract the Two Fractions
Now that we have both quantities in improper fractions, we can find out how much more sugar Sujata bought than her mother by subtracting the two fractions.

\[ \text{Difference} = \frac{11}{4} - \frac{5}{4} \]

Since the denominators are the same, we can subtract the numerators directly:

\[ = \frac{11 - 5}{4} = \frac{6}{4} \]

### Step 3: Simplify the Fraction
Next, we simplify \(\frac{6}{4}\):

\[ \frac{6}{4} = \frac{3}{2} \quad \text{(by dividing both numerator and denominator by 2)} \]

### Step 4: Convert Improper Fraction to Mixed Fraction
Finally, we convert \(\frac{3}{2}\) back to a mixed fraction:

- Divide 3 by 2:
- 3 divided by 2 gives 1 with a remainder of 1.

So, \(\frac{3}{2} = 1 \frac{1}{2}\).

### Final Answer
Sujata bought \(1 \frac{1}{2}\) kg more sugar than her mother.

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