Three teacher share 2 packs of paper equally. how much paper does each teacher get? mark all that apply. A. 3 halves of a. pack B. 2 thirds of a pack. C. 3 sixth of a pack. D. 1 half of a pack. E. 1 third of a pack.
The correct answer and explanation is:
To solve the problem:
Three teachers share 2 packs of paper equally.
We are asked to figure out how much paper each teacher gets when 2 packs are shared equally among 3 people.
Step-by-Step:
We divide the total number of packs by the number of teachers: 23 packs per teacher\frac{2}{3} \text{ packs per teacher}
So each teacher gets two-thirds of a pack.
Now we evaluate the answer choices:
- A. 3 halves of a pack → 32=1.5\frac{3}{2} = 1.5 packs (Too much – incorrect)
- B. 2 thirds of a pack → 23\frac{2}{3} pack (Correct)
- C. 3 sixths of a pack → 36=12\frac{3}{6} = \frac{1}{2} pack (Too little – incorrect)
- D. 1 half of a pack → 12\frac{1}{2} pack (Too little – incorrect)
- E. 1 third of a pack → 13\frac{1}{3} pack (Too little – incorrect)
✅ Correct Answer: B. 2 thirds of a pack
Explanation (300 words):
To find how much paper each teacher gets, we divide the total amount of paper (2 packs) by the number of teachers (3). This is a classic example of dividing a whole quantity equally among a group.
Mathematically, we calculate: 2 packs3 teachers=23 pack per teacher\frac{2 \text{ packs}}{3 \text{ teachers}} = \frac{2}{3} \text{ pack per teacher}
This means each teacher receives two-thirds of one pack.
Let’s understand this visually. If each pack were cut into three equal parts, we’d have a total of 6 equal parts from 2 packs:
- Pack 1: 3 parts
- Pack 2: 3 parts
That gives 6 parts in total. Sharing these 6 equal parts among 3 teachers means each teacher gets 2 parts.
Each part is one-third of a pack, so 2 parts equals: 23 of a pack\frac{2}{3} \text{ of a pack}
Now let’s break down the other choices:
- A. 3 halves = 1.5 packs – Too much. Each teacher can’t get more than 1 pack.
- C. 3 sixths = 0.5 pack – Not enough. It underestimates the fair share.
- D. 1 half = 0.5 pack – Also too little.
- E. 1 third = 0.333… pack – Only works if 1 pack is shared among 3, not 2.
So, the only accurate answer is B. 2 thirds of a pack.
This reinforces the concept that dividing whole numbers by other whole numbers often results in fractions, and those fractions can be visualized and verified with real-life models.