Savita is dividing `1(3/4)` kg of sweets equally among her seven friends. How much does each friend receive?

Options

A. `3/4` kg
B. `1/4` kg
C. `1/2` kg
D. `3/28` kg

Answer

To solve the problem of how much each friend receives when Savita divides \(1 \frac{3}{4}\) kg of sweets among her seven friends, we can follow these steps:

### Step 1: Convert the mixed fraction to an improper fraction
The mixed fraction \(1 \frac{3}{4}\) can be converted to an improper fraction.

To do this, we multiply the whole number (1) by the denominator (4) and then add the numerator (3):
\[ 1 \times 4 + 3 = 4 + 3 = 7 \]
So, \(1 \frac{3}{4} = \frac{7}{4}\) kg.

### Step 2: Divide the improper fraction by the number of friends
Now, we need to divide \(\frac{7}{4}\) kg by 7 (the number of friends):
\[ \text{Amount each friend receives} = \frac{7}{4} \div 7 \]

### Step 3: Rewrite the division as multiplication
Dividing by a number is the same as multiplying by its reciprocal. The reciprocal of 7 is \(\frac{1}{7}\):
\[ \frac{7}{4} \div 7 = \frac{7}{4} \times \frac{1}{7} \]

### Step 4: Multiply the fractions
Now, we multiply the fractions:
\[ \frac{7 \times 1}{4 \times 7} = \frac{7}{28} \]

### Step 5: Simplify the fraction
Now we can simplify \(\frac{7}{28}\):
\[ \frac{7}{28} = \frac{1}{4} \]

### Conclusion
So, each friend receives \(\frac{1}{4}\) kg of sweets.

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