To distribute the pizza equally, we have to divide each pizza into 5.
For pepperoni pizza, if we divide it into 5, we would have:
`1-:5 = 1/5`
For the cheese pizza, if we divide it into 5, we would have:
`1 1/3 -:5`
Before dividing them, express the mix fraction as improper fraction. And express the 5 as a fraction too.
Now that they are both in fractions, to compute, we have to take note of the steps in dividing fractions. That is, flip the second fraction and change the operation from divide to multiply.
Therefore, Sean and his friends should each have `1/5` of pepperoni pizza and `4/15` of cheese pizza.
Sean and his four friends want to share the left over pizzas, so they will divide each leftover pizza equally.
Since there is one pepperoni pizza and 1 1/3 cheese pizzas left, we will add the leftover pizzas and then divide them equally.
=1 + 1 1/3
=1 + 4/3
Therefore, totally 7/3 pizzas are to be distributed among the 5 friends.
Now we divide these pizzas into 5 people, by dividing by 5.
=(7/3) / 5
or (7/3) / (5/1)
hence, 7/3 X 1/5
(7 X 1) / (3 X 5)
=7/15 will be the share of each friend.
It is key to realize that for this question, because it is only asking how much pizza each person gets, the type of pizza (pepperoni versus cheese) is irrelevant. Even if you calculate the two flavors separately then sum the answers, you get the same final answer as if you first added the total amount of pizza then divided by 5 (Sean and four friends makes for 5 people total).
Step 1: Sum the total amount of pizza: 1 + (1 + 1/3) = 2 + 1/3. 2 can also be written as 6/3, making the new equation 6/3 + 1/3 = 7/3.
Step 2: Divide the total amount of pizza (7/3) by 5. (7/3) / 5 gives 7/15.
Therefore, each person gets 7/15 parts of a whole pizza, regardless of flavor.
So we are going to turn Sean and his friends into a fraction 5/1
Now you are going to take the 1 pepperoni pizza and add it with the 11/3 of cheese pizza that is left. You get 2 1/3 but you do not want it in this form you want it as a fraction. So you will take the 2 and multiply by the denominator which the answer will be 6/3 which you will then add to the 1/3.
You will get 7/3 as the amount of pizza left that you want to divide amongst the five people.
7/3 / (5/1) You are going to take the second fraction and flip it and multiply
7/3 X 1/5 = 7/15 So everyone will get 7/15 of pizza that is remaining
If there is 1 pepperoni and 1 1/3 cheese left, you add the 2 together.` `
Equaling 2 1/3
Divide that by 5 (5 friends)
2 1/3 divided by 5/1 = 7/3 x 1/5 (flip the second and change mixed fraction to improper fraction)
This equals 7/15
So each person gets 7/15 of pizza
If there is 1 full pepperoni pizza each person would get 1/5 of each (1 divided by 5 people).
To split the 1 and 1/3 remaining cheese pizza, you have to divide 1 and 1/3 by 5. It is assumed 5 is written over one and 1 and 1/3 can be rewritten as the improper fraction 4/3. In order to divide fractions you can multiply the reciprocal, or flipped fraction. 4/3 divided by 5/1 can be rewritten as 4/3(1/5) which equals 4/15.
Each person gets 1/5 of the pepperoni pizza and 4/15 of the cheese pizza.