A 4-foot-long sandwich is cut into servings that are each ; foot long. How many servings will there be after the sandwich is cut?
The correct answer and explanation is:
To solve the problem:
Question:
A 4-foot-long sandwich is cut into servings that are each ½ foot long.
How many servings will there be after the sandwich is cut?
✅ Correct Answer:
8 servings
🧠 Explanation (300 words):
This is a division problem involving fractions. We are asked to find how many ½-foot servings can be made from a 4-foot sandwich. Essentially, we are dividing the total length of the sandwich by the length of one serving: Number of servings=412\text{Number of servings} = \frac{4}{\frac{1}{2}}
Dividing by a fraction means multiplying by its reciprocal. The reciprocal of 12\frac{1}{2} is 22. So: 412=4×2=8\frac{4}{\frac{1}{2}} = 4 \times 2 = 8
So, you can get 8 equal servings of ½ foot each from a 4-foot-long sandwich.
🔍 Why This Works:
Imagine a sandwich that’s exactly 4 feet long. If you want each serving to be ½ foot in size, you can line up half-foot segments end-to-end along the sandwich:
- First serving: 0 to 0.5 feet
- Second: 0.5 to 1 foot
- Third: 1 to 1.5 feet
- Fourth: 1.5 to 2 feet
- Fifth: 2 to 2.5 feet
- Sixth: 2.5 to 3 feet
- Seventh: 3 to 3.5 feet
- Eighth: 3.5 to 4 feet
Each time you slice a ½-foot piece, you’re using up part of the sandwich. After 8 pieces, you’ve used the full 4 feet.
🧮 General Rule:
If you’re cutting an item of length L into pieces of length s, the number of pieces is: Ls\frac{L}{s}
Here: 412=8\frac{4}{\frac{1}{2}} = 8
Final Answer: ✅ 8 servings.