Students volunteering at a charity event work \frac{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 have divided 4 by 1/2 (not 1/2 by 4).
That is: 4÷12=4×2=84 \div \frac{1}{2} = 4 \times 2 = 8
So, Zack worked 8 shifts.
Explanation
The problem involves understanding how to divide whole numbers by fractions, which is a common area of confusion in math. Zack volunteered for 4 hours, and each shift is 1/2 hour long. The question is: how many half-hour shifts fit into 4 hours?
Zack made a mistake by dividing 1/2 by 4. This operation calculates how many fourths of an hour are in half an hour, which is not what the problem is asking. In this context, we want to know how many 1/2-hour shifts are contained within 4 total hours.
To find that, the correct operation is: Total Time÷Length of One Shift=Number of Shifts\text{Total Time} \div \text{Length of One Shift} = \text{Number of Shifts}
That becomes: 4÷124 \div \frac{1}{2}
When dividing by a fraction, we multiply by its reciprocal: 4÷12=4×2=84 \div \frac{1}{2} = 4 \times 2 = 8
This means 8 half-hour shifts fit into 4 hours.
Here’s a way to think about it visually:
Imagine breaking each hour into two half-hour blocks. In 4 hours, you get:
- 2 half-hours in the first hour
- 2 in the second
- 2 in the third
- 2 in the fourth
That’s a total of 2 × 4 = 8 shifts.
Understanding this kind of fractional division is important in real-life tasks such as scheduling, time management, and even budgeting. Zack’s mistake shows why it’s important to think about what the numbers represent before doing calculations.
