Students volunteering at a charity event work 1/2-hour shifts. Zack volunteered for 4 hours. He incorrectly divided one half by four to find the number of shifts he worked. How should Zack have calculated the number of his shifts?
The Correct Answer and Explanation is:
Correct Answer:
Zack should divide 4 hours by 1/2 hour to find the number of shifts he worked.
That is: 412=4÷12=4×2=8\frac{4}{\frac{1}{2}} = 4 \div \frac{1}{2} = 4 \times 2 = 8
So, Zack worked 8 shifts.
300-Word Explanation:
Zack volunteered for 4 hours, and each shift is 1/2 hour long. To find out how many of these half-hour shifts fit into 4 hours, we need to divide the total time (4 hours) by the length of one shift (1/2 hour).
This means solving: 4÷124 \div \frac{1}{2}
When dividing by a fraction, you multiply by its reciprocal. The reciprocal of 1/2 is 2/1, which is simply 2. So: 4÷12=4×2=84 \div \frac{1}{2} = 4 \times 2 = 8
Zack should have multiplied 4 by 2, not divided 1/2 by 4. The mistake Zack made was reversing the order. He calculated: 12÷4=18\frac{1}{2} \div 4 = \frac{1}{8}
This result is incorrect because it answers a different question—how much time is one-fourth of a half-hour—which is irrelevant in this case.
Let’s think about it in a real-world example. Imagine each shift is 30 minutes (which is 1/2 hour), and Zack volunteers for 240 minutes (which is 4 hours). To find how many 30-minute shifts fit into 240 minutes: 240÷30=8240 \div 30 = 8
So again, the correct number of shifts is 8.
In summary, when you’re figuring out how many parts (of a certain size) fit into a whole, you divide the whole by the size of the part. That’s why Zack should divide 4 by 1/2—not the other way around. His incorrect method gave a misleading result that doesn’t match the situation.Correct Answer:
Zack should divide 4 hours by 1/2 hour to find the number of shifts he worked.
That is: 412=4÷12=4×2=8\frac{4}{\frac{1}{2}} = 4 \div \frac{1}{2} = 4 \times 2 = 8
So, Zack worked 8 shifts.
Explanation:
Zack volunteered for 4 hours, and each shift is 1/2 hour long. To find out how many of these half-hour shifts fit into 4 hours, we need to divide the total time (4 hours) by the length of one shift (1/2 hour).
This means solving: 4÷124 \div \frac{1}{2}
When dividing by a fraction, you multiply by its reciprocal. The reciprocal of 1/2 is 2/1, which is simply 2. So: 4÷12=4×2=84 \div \frac{1}{2} = 4 \times 2 = 8
Zack should have multiplied 4 by 2, not divided 1/2 by 4. The mistake Zack made was reversing the order. He calculated: 12÷4=18\frac{1}{2} \div 4 = \frac{1}{8}
This result is incorrect because it answers a different question—how much time is one-fourth of a half-hour—which is irrelevant in this case.
Let’s think about it in a real-world example. Imagine each shift is 30 minutes (which is 1/2 hour), and Zack volunteers for 240 minutes (which is 4 hours). To find how many 30-minute shifts fit into 240 minutes: 240÷30=8240 \div 30 = 8
So again, the correct number of shifts is 8.
In summary, when you’re figuring out how many parts (of a certain size) fit into a whole, you divide the whole by the size of the part. That’s why Zack should divide 4 by 1/2—not the other way around. His incorrect method gave a misleading result that doesn’t match the situation.
