How many packets of $\frac{1}{16} kg sugar can be made from 3$\frac{1}{4} kg of sugar?

Q: How many packets of $\frac{1}{16} kg sugar can be made from 3$\frac{1}{4} kg of sugar?

To determine how many packets of $\frac{1}{16}$ kg sugar can be made from $3\frac{1}{4}$ kg of sugar, we need to perform a division operation. 1. **Convert the mixed number to an improper fraction:** - $3\frac{1}{4}$ can be converted to an improper fraction as follows: \[ 3\frac{1}{4} = \frac{3 \times 4 + 1}{4} = \frac{12 + 1}{4} = \frac{13}{4} \] 2. **Divide the total amount of sugar by the weight of each packet:** - We need to divide $\frac{13}{4}$ kg by $\frac{1}{16}$ kg to find out how many packets can be made: \[ \frac{13}{4} \div \frac{1}{16} = \frac{13}{4} \times \frac{16}{1} = \frac{13 \times 16}{4 \times 1} = \frac{208}{4} = 52 \] 3. **Conclusion:** - Therefore, 52 packets of $\frac{1}{16}$ kg sugar can be made from $3\frac{1}{4}$ kg of sugar. This confirms that Option 1 is correct. **Explanation for why other options are incorrect:** - **Option 2 (48):** This option is incorrect because the calculation clearly shows that 52 packets can be made, not 48. The division of $\frac{13}{4}$ by $\frac{1}{16}$ results in 52, not 48. - **Option 3 (12):** This option is incorrect because it significantly underestimates the number of packets. The calculation shows that 52 packets can be made, which is much greater than 12. - **Option 4 (64):** This option is incorrect because it overestimates the number of packets. The correct calculation results in 52 packets, not 64. In summary, the correct answer is Option 1, which is supported by the mathematical calculation provided.

Question

Accepted Answer

To determine how many packets of $\frac{1}{16}$ kg sugar can be made from $3\frac{1}{4}$ kg of sugar, we need to perform a division operation.

1. **Convert the mixed number to an improper fraction:**
   - $3\frac{1}{4}$ can be converted to an improper fraction as follows:
   $$
   3\frac{1}{4} = \frac{3 \times 4 + 1}{4} = \frac{12 + 1}{4} = \frac{13}{4}
   $$

2. **Divide the total amount of sugar by the weight of each packet:**
   - We need to divide $\frac{13}{4}$ kg by $\frac{1}{16}$ kg to find out how many packets can be made:
   $$
   \frac{13}{4} \div \frac{1}{16} = \frac{13}{4} \times \frac{16}{1} = \frac{13 \times 16}{4 \times 1} = \frac{208}{4} = 52
   $$

3. **Conclusion:**
   - Therefore, 52 packets of $\frac{1}{16}$ kg sugar can be made from $3\frac{1}{4}$ kg of sugar. This confirms that Option 1 is correct.

**Explanation for why other options are incorrect:**

- **Option 2 (48):** This option is incorrect because the calculation clearly shows that 52 packets can be made, not 48. The division of $\frac{13}{4}$ by $\frac{1}{16}$ results in 52, not 48.

- **Option 3 (12):** This option is incorrect because it significantly underestimates the number of packets. The calculation shows that 52 packets can be made, which is much greater than 12.

- **Option 4 (64):** This option is incorrect because it overestimates the number of packets. The correct calculation results in 52 packets, not 64.

In summary, the correct answer is Option 1, which is supported by the mathematical calculation provided.