How many packets of `(1)/(16)` kg sugar can be made from `3(1)/(4)kg` of sugar ?

Options

A. 64
B. 52
C. 48
D. 12

Explanation

To solve the question of how many packets of \( \frac{1}{16} \) kg sugar can be made from \( 3 \frac{1}{4} \) kg of sugar, we can follow these steps:

### Step 1: Convert the mixed number to an improper fraction
The total quantity of sugar is given as \( 3 \frac{1}{4} \) kg. We can convert this mixed number into an improper fraction.

\[ 3 \frac{1}{4} = \frac{3 \times 4 + 1}{4} = \frac{12 + 1}{4} = \frac{13}{4} \text{ kg} \]

**Hint:** To convert a mixed number to an improper fraction, multiply the whole number by the denominator and add the numerator, then place that result over the original denominator.

### Step 2: Determine the amount of sugar in one packet
The amount of sugar in one packet is given as \( \frac{1}{16} \) kg.

### Step 3: Calculate the number of packets
To find out how many packets can be made from the total sugar, we divide the total quantity of sugar by the amount of sugar in one packet.

\[ \text{Number of packets} = \frac{\text{Total quantity of sugar}}{\text{Amount of sugar in one packet}} = \frac{\frac{13}{4}}{\frac{1}{16}} \]

### Step 4: Simplify the division of fractions
When dividing fractions, we multiply by the reciprocal of the divisor:

\[ \frac{13}{4} \div \frac{1}{16} = \frac{13}{4} \times \frac{16}{1} = \frac{13 \times 16}{4 \times 1} \]

### Step 5: Perform the multiplication
Now, we can simplify:

\[ \frac{13 \times 16}{4} = \frac{208}{4} = 52 \]

### Conclusion
Thus, the number of packets of \( \frac{1}{16} \) kg sugar that can be made from \( 3 \frac{1}{4} \) kg of sugar is **52**.

**Final Answer:** 52 packets

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