# Fractions and Percentages using Little Caesar’s Quattro Pizza

Pizza is a delicious way to talk about fractions and percentages. In the food service industry, catering managers keep track of pizza consumption, which provides important information for future budgeting and planning.

Let us say that a food service manager is catering a pizza party, where the host specifically asks for Little Caesar’s Quattro pizzas.

The Quattro is a specialty pizza that has four sets of toppings: cheese, pepperoni, Italian sausage with bruschetta, and Italian sausage with pepperoni.

## Pizza Slice Counts

During food service, the banquet servers kept the pizzas warm and presentable to the partygoers on multiple serving tables.

The number of empty boxes were counted at the end of the pizza party.

There were 62 boxes delivered to the banquet. When food service concluded, 47 boxes were empty. The remaining boxes had leftover pizza slice that were counted and displayed in the table below.

Box # Cheese Pepperoni Sausage/Bruschetta Sausage/Pepperoni
1 0 0 2 1
2 0 0 1 2
3 1 0 1 2
4 1 1 2 1
5 0 1 2 2
6 0 2 1 1
7 1 2 1 0
8 1 1 1 0
9 0 2 1 1
10 0 1 2 1
11 1 1 2 2
12 1 2 2 0
13 1 2 1 2
14 0 0 1 0
15 1 0 2 1

Pizza is traditionally divided into slices for convenience.

Each slice of the pizza may be considered a sector of the pizza. A sector is a portion of a pizza (or a circle) that has boundaries marked by the two edges of pizza slices and the crust of the pizza (the perimeter).

In the case of the Little Caesar’s Quattro pizza, eight slices are part of one of the four sectors. More precisely, there are two slices of pizza in each sector. Each section contains a specific topping group.

The catering manager can use the leftover slice count data set for predicting customer need, which help control costs. After food service, the manager can also control costs by storing the leftover pizza in the kitchen freezer.

## Pizza Slice Totals

Now, let us look at the slice counts and the totals for each pizza box and totals for each topping group.

# Cheese Pepperoni Sausage/Bruschetta Sausage/Pepperoni Total
1 0 0 2 1 3
2 0 0 1 2 3
3 1 0 1 2 4
4 1 1 2 1 5
5 0 1 2 2 5
6 0 2 1 1 4
7 1 2 1 0 4
8 1 1 1 0 3
9 0 2 1 1 4
10 0 1 2 1 4
11 1 1 2 2 6
12 1 2 2 0 5
13 1 2 1 2 6
14 0 0 1 0 1
15 1 0 2 1 4
T 8 15 22 16 61

There is a total of 61 slices remaining. Eight (8) slices of cheese, fifteen (15) slices of pepperoni, twenty-two (22) slices of sausage/bruschetta and sixteen (16) slices of sausage/pepperoni.

## Fractions and Percentages

We already mentioned the importance of this information for food storage planning. The owner of the catering company wants to know more details about the leftover slices for business analysis.

To deliver that information, we must summarize the leftover slice counts with fractions and percentages.

Toppings Group Counts Fraction Percent
Cheese 8 8 / 61 13%
Pepperoni 15 15 / 61 25%
Sausage/Bruschetta 22 22 / 61 36%
Sausage/Pepperoni 16 16 / 61 26%

Percentages are “fractions of 100” and are best visualized using pie charts.

Let us look at these percentages in the pie chart and see how they relate to the proper fractions that describe each topping group.

First, as soon as we know the total number of leftover slices, we can calculate the unit fraction.

CCSS.MATH.CONTENT.3.NF.A.1 Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.

For total parts T, we know that the unit fraction is 1/T. There are 61 total (equal) leftover slices. This means the unit fraction is 1/61. Let us calculate his unit fraction in decimal form.

`= 1 / 61 = 0.01639`

## The Percentage Package

Decimals help us calculate percentages. In fact, we can look at percentages as if they were “packages” used to described values.

For example, we can convert any decimal into a percentage by “multiplying the number by 100”:

`= 0.01639 * 100 `

before adding a percent sign (%) to the end:

`= 1.639%`

🤔🤔🤔 Pay attention!!

We are not arbitrarily multiplying a number by 100. Instead, we are multiplying a number by exactly 1. Let us recall the identity property of multiplication.

`A x 1 = A`

It is extremely useful. The property says that we can do anything we want to any number as long as the expression simplifies to that same number. In other words, we can say the same things in a different way.

Another way of saying “one” is by saying “one hundred over one hundred” (100/100).

`= 100 / 100 = (100) * (1/100) = 1`

The “per one hundred” (1/100) portion of the above expression is called percent (“per cent”) for simplicity. In other words, the above expression can be re-written as “100 percent”, which is equal to 1.

The same goes for any number, including fractions and decimals.

`= A x 100 * ( 1 / 100) `

Like many things in mathematics, the percent sign (%) is just another symbol used to save time and resources (and reduce error) for communication of specific values.

`= (A * 100) %`

THINK. THINK. THINK.

How would you describe “percent” in scientific notation?

## Percentages with Unit Fractions

We know the unit fraction that describes the total amount of leftover slices, so we can multiply that equivalent percentage by the total amount from each topping group to find each percentage.

Topping Group Counts Multiply by Unit Fraction Percent
Cheese 8 ( 1 / 61 ) * 8 = 13%
Pepperoni 15 ( 1 / 61 ) * 15 = 25%
Sausage/Bruschetta 22 ( 1 / 61 ) * 22 = 36%
Sausage/Pepperoni 16 ( 1 / 61 ) * 16 = 26%

CCSS.MATH.CONTENT.4.NF.B.4.B: Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number.

## Pizza Storage Memo

The catering manager must figure out how many storage containers are required for placing the leftovers in the kitchen freezers. The leftover pizza slices must be separated by topping group for more effective logistics. The storage containers can only hold 3 slices each.

The more urgent matter is storing the pizza in the kitchen freezers.

We must divide each topping group total `{8, 15, 22, 16}` by 3 to get a quotient. However, we are not concerned about the value of each quotient as we are about the amount of storage containers that must be allocated for this task.

Some of these quantities are not whole numbers.

If there are any quantities with decimals (fractional parts), we want to find the best whole number that makes sense in the real world. To do this, we will use the `=CEILING(number)` function, where the result is the smallest integer greater than an input number.

The `=CEILING` function is used everywhere.

Here are a few example:

Using Wolfram Alpha, simply divide each of the topping group totals by 3 and use the `=CEILING` (or the `=CEIL`) function.

Sample Wolfram Alpha input
`=SUM(CEIL(8/3), CEIL(15/3), CEIL(22/3), CEIL(16/3))`

When you add all the calculations, the result is:

`= 3 + 5 + 8 + 6 = 22`

To store the slices of leftover pizza, we need 22 storage containers.

## Conclusion

The catering manager now has a point of reference for future budgeting and planning of pizza parties. About 88% of the total delivered pizza was consumed. The remaining slices show more detail about the popularity of the topping groups.

The specialty pizza discussed in this math practice activity reorganized 496 slices across four equal topping groups for 62 pizzas.

We were able to regroup these slices for analysis that used fractions and percentages as tools. Analysis of business operations may be helpful for making better decisions. With more data sets, the catering manager may be able to minimize costs and optimize procedures.

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