At the sixth grade social, the teachers want to provide the students with pizza as a treat. Kids love pizza and the sixth graders aren’t any exception to this rule. The teachers want each student to receive two slices of pizza. There are 48 students in cluster 6A, and 44 students in cluster 6B.

When Mr. Scott, the teacher in 6B, calls the pizza place. He learns that there are two different options for slicing the pizza. They can either slice it in \begin{align*}8^{ths}\end{align*} or in 10ths. Mr. Scott isn’t sure at first which way is the better way to go. But because he is a teacher, he quickly figures out the math in his head and orders the pizzas cut into \begin{align*}10^{ths}\end{align*}.

If Mr. Scott ordered the pizzas cut into \begin{align*}10^{ths}\end{align*}, how many pizzas did he order? Will there be any pizza left over for the teachers to have a slice? If Mr. Scott had ordered the pizzas cut into 8ths, how many pizzas would he have ordered? Would there be any left over here?

**Use what you learn in this Concept on fractions to help you figure out the pizza problem.** **Pay attention, after all, there is pizza at stake!!**

### Guidance

Previously we worked on how to write a mixed number as an improper fraction. We can also work the other way around too, we can write improper fractions as mixed numbers.

**How do you write an improper fraction as a mixed number?**

First, remember that when you write an improper fraction as a mixed number, that you are converting a fraction in all parts to wholes and parts.

\begin{align*}\frac{18}{4}\end{align*} If I have eighteen-fourths, I have eighteen parts and the whole has only been divided into 4 parts. This means that \begin{align*}\frac{4}{4}\end{align*} would be considered a whole.

**When the numerator is larger than the denominator, you know that you have more than one whole.**

**To change an improper fraction to a mixed number, divide the denominator into the numerator. This will tell you the number of wholes.**

**If there are any left over, this tells you the fraction part.**

18 \begin{align*}\div\end{align*} 4 \begin{align*}=\end{align*} 4

**But there are 2 left over because 4 \begin{align*}\times\end{align*} 4 = 16 and our numerator is 18. The left over part becomes the numerator over the original denominator.**

**Our answer is** \begin{align*}4 \frac{2}{4}\end{align*} .

**Our answer is** \begin{align*}4 \frac{1}{2}\end{align*}.

Sometimes, you will have an improper fraction that converts to a whole number and not a mixed number.

\begin{align*}\frac{18}{9}\end{align*} Here eighteen divided by 9 is 2. There isn’t a remainder, so there isn’t a fraction. This improper fraction converts to a whole number.

**Our answer is 2.**

**Now it is time for you to try a few on your own. Be sure your fractions are in simplest form.**

#### Example A

\begin{align*}\frac{24}{5}\end{align*}

**Solution:\begin{align*}4 \frac{4}{5}\end{align*}**

#### Example B

\begin{align*}\frac{21}{3}\end{align*}

**Solution: 7**

#### Example C

\begin{align*}\frac{32}{6}\end{align*}

**Solution:\begin{align*}5 \frac{1}{3}\end{align*}**

Now back to the Pizza Problem. There are some facts here to help us with answering the questions.

If each student in each cluster is going to receive two slices of pizza, the first thing we need to do is to multiply the number of students by 2.

48 + 44 \begin{align*}=\end{align*} 92 \begin{align*}\times\end{align*} 2 \begin{align*}=\end{align*} 184 slices

If Mr. Scott ordered the pizzas cut into 10, then he would need \begin{align*}\frac{184}{10}\end{align*}. Here is a real life application of improper fractions. We need 184 slices. The pizzas are cut into \begin{align*}10^{ths}\end{align*}, so that means that we need \begin{align*}\frac{184}{10}\end{align*} of pizza.

How many pizzas is that? To figure this out, we turn \begin{align*}\frac{184}{10}\end{align*} into a mixed number.

\begin{align*}184 \div 10 = 18 \frac{4}{10}\end{align*}

**He would need 18 pizzas and four slices from another pizza. That is the four-tenths. There would be six slices left over, so there would be enough pizza for the teachers too. Mr. Scott ordered nineteen pizzas.**

What if Mr. Scott ordered the pizzas cut into eighths? He would need \begin{align*}\frac{184}{8}\end{align*}. The number of slices did not change, but the way the pizza was sliced did change. How many pizza’s would he need to order if the pizzas were cut into eighths? We need to rewrite the improper fraction to a mixed number.

184 \begin{align*}\div\end{align*} 8 \begin{align*}=\end{align*} 23 pizzas

**There wouldn't be any slices left over, so there wouldn’t be any extras for the teachers.**

**Since Mr. Scott enjoys a good slice of pizza too, he ordered the 19 pizzas that were divided into tenths.**

### Vocabulary

- Mixed Number
- a number made up of a whole number and a fraction

- Improper Fractions
- a fraction where the numerator is greater than the denominator

- Equivalent
- means equal

### Guided Practice

Here is one for you to try on your own.

Express this improper fraction as a mixed number.

\begin{align*}\frac{82}{5}\end{align*}

**Answer**

To convert this improper fraction, we divide 5 into 82 and use the remainder to form a new fraction.

**\begin{align*}16\frac{2}{5}\end{align*}**

### Interactive Practice

### Video Review

Khan Academy Mixed Numbers and Improper Fractions

James Sousa Mixed Numbers and Improper Fractions

James Sousa Example Converting a Mixed Number to an Improper Fraction

James Sousa Example Converting an Improper Fraction to a Mixed Number

### Practice

Directions: Convert each improper fraction to a mixed number. Be sure to simplify when necessary.

1. \begin{align*}\frac{22}{3}\end{align*}

2. \begin{align*}\frac{44}{5}\end{align*}

3. \begin{align*}\frac{14}{3}\end{align*}

4. \begin{align*}\frac{7}{2}\end{align*}

5. \begin{align*}\frac{10}{3}\end{align*}

6. \begin{align*}\frac{47}{9}\end{align*}

7. \begin{align*}\frac{50}{7}\end{align*}

8. \begin{align*}\frac{60}{8}\end{align*}

9. \begin{align*}\frac{43}{8}\end{align*}

10. \begin{align*}\frac{19}{5}\end{align*}

11. \begin{align*}\frac{39}{7}\end{align*}

12. \begin{align*}\frac{30}{4}\end{align*}

13. \begin{align*}\frac{11}{7}\end{align*}

14. \begin{align*}\frac{26}{5}\end{align*}

15. \begin{align*}\frac{89}{8}\end{align*}

16. \begin{align*}\frac{70}{14}\end{align*}