How many packets of $\frac{1}{12}$ kg salt can be made from 7$\frac{1}{2}$ kg of salt ?

Q: How many packets of $\frac{1}{12}$ kg salt can be made from 7$\frac{1}{2}$ kg of salt ?

To determine how many packets of $\frac{1}{12}$ kg salt can be made from $7\frac{1}{2}$ kg of salt, we need to perform a division operation. Here's the step-by-step explanation: 1. **Convert Mixed Number to Improper Fraction:** - The given amount of salt is $7\frac{1}{2}$ kg. First, convert this mixed number into an improper fraction. - $7\frac{1}{2} = \frac{15}{2}$ kg. 2. **Division of Fractions:** - We need to find out how many $\frac{1}{12}$ kg packets can be made from $\frac{15}{2}$ kg of salt. - This requires dividing $\frac{15}{2}$ by $\frac{1}{12}$. 3. **Perform the Division:** - Dividing by a fraction is equivalent to multiplying by its reciprocal. - $\frac{15}{2} \div \frac{1}{12} = \frac{15}{2} \times \frac{12}{1}$. 4. **Simplify the Multiplication:** - $\frac{15}{2} \times \frac{12}{1} = \frac{15 \times 12}{2 \times 1} = \frac{180}{2} = 90$. 5. **Conclusion:** - Therefore, 90 packets of $\frac{1}{12}$ kg salt can be made from $7\frac{1}{2}$ kg of salt. **Explanation of Incorrect Options:** - **Option 1 (45):** This option is incorrect because dividing $\frac{15}{2}$ by $\frac{1}{12}$ results in 90, not 45. The calculation does not support this option. - **Option 2 (60):** This option is incorrect because the correct division yields 90 packets, not 60. The arithmetic operation clearly shows that 60 is not the result. - **Option 3 (72):** This option is incorrect because the division of $\frac{15}{2}$ by $\frac{1}{12}$ results in 90, not 72. The calculation confirms that 72 is not the correct number of packets. In conclusion, the correct answer is Option 4 (90), as the mathematical operation of dividing $\frac{15}{2}$ kg by $\frac{1}{12}$ kg results in 90 packets.

Question

Accepted Answer

To determine how many packets of $\frac{1}{12}$ kg salt can be made from $7\frac{1}{2}$ kg of salt, we need to perform a division operation. Here's the step-by-step explanation:

1. **Convert Mixed Number to Improper Fraction:**
   - The given amount of salt is $7\frac{1}{2}$ kg. First, convert this mixed number into an improper fraction.
   - $7\frac{1}{2} = \frac{15}{2}$ kg.

2. **Division of Fractions:**
   - We need to find out how many $\frac{1}{12}$ kg packets can be made from $\frac{15}{2}$ kg of salt.
   - This requires dividing $\frac{15}{2}$ by $\frac{1}{12}$.

3. **Perform the Division:**
   - Dividing by a fraction is equivalent to multiplying by its reciprocal.
   - $\frac{15}{2} \div \frac{1}{12} = \frac{15}{2} \times \frac{12}{1}$.

4. **Simplify the Multiplication:**
   - $\frac{15}{2} \times \frac{12}{1} = \frac{15 \times 12}{2 \times 1} = \frac{180}{2} = 90$.

5. **Conclusion:**
   - Therefore, 90 packets of $\frac{1}{12}$ kg salt can be made from $7\frac{1}{2}$ kg of salt.

**Explanation of Incorrect Options:**

- **Option 1 (45):** This option is incorrect because dividing $\frac{15}{2}$ by $\frac{1}{12}$ results in 90, not 45. The calculation does not support this option.
  
- **Option 2 (60):** This option is incorrect because the correct division yields 90 packets, not 60. The arithmetic operation clearly shows that 60 is not the result.

- **Option 3 (72):** This option is incorrect because the division of $\frac{15}{2}$ by $\frac{1}{12}$ results in 90, not 72. The calculation confirms that 72 is not the correct number of packets.

In conclusion, the correct answer is Option 4 (90), as the mathematical operation of dividing $\frac{15}{2}$ kg by $\frac{1}{12}$ kg results in 90 packets.