## Dario purchased a party size sub, and he decides to share it with 3 of his friends. So, he cuts the sub into 4 equal pieces. Howev

Question

Dario purchased a party size sub, and he decides to share it with 3 of his friends. So, he cuts the sub into 4 equal pieces. However, another one of his friends also showed up, and there are now 5 people in total

Part A

Now that the sub will be shared equally among 5 people, will each person get more or less sub? Briefly state why you think so.​

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6 days 2023-01-24T00:41:58+00:00 2 Answers 0 views 0

1. They get less sub because a larger piece is being split between multiple people causing the the pieces to be smaller in order to be equally split

2. The amount that each person would get after the sub is divided in 5 people equally is lesser than the amount of sub that they were getting when there were 4 people.

### How to interpret the division?

When ‘a’ is divided by ‘b’, then the result we get from the division is the part of ‘a’ that each one of ‘b’ items will get.
Thus, if 10 mangoes are there, and 2 people, then 10 ÷ 2 is the number of mangoes each person would get, which is 5.
Division, thus, can be interpreted as equally dividing the number that is being divided in total x parts, where x is the number of parts the given number is divided.
Thus, $$a \div b = a$$ divided in b equal parts.
Also, we can write: $$a \div b = a \times \dfrac{1}{b}$$
(it is since a = a times 1 so $$a/b = 1 \times (a/b) = (1/b) \times a$$ )
Firstly the sub was divided in 4 parts,
and when 5 people came, so it was  decided to share the sub in 5 equal parts.
The more we increase the number in which the considered thing (here sub) is to be divided, the lesser each part would be.
Let the sub is measured as ‘a’ units.
• Case 1: Previously when 4 people were there:
Each person would get: $$\dfrac{a}{4}$$
• Case 2: When there got 5 people:
Each person would get: $$\dfrac{a}{5}$$
We know that:
$$4 < 5$$
Multiply both the sides by ‘a’, assuming ‘a’ is positive, we get:
$$4a < 5a$$
Divide both the sides by 20:
$$\dfrac{4a}{20} < \dfrac{5a}{20}\\\\\dfrac{a}{5} < \dfrac{a}{4}$$
Thus, the amount that each person would get after the sub is divided in 5 people equally is lesser than the amount of sub that they were getting when there were 4 people.