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# Mixed Numbers as Improper Fractions

## 2 and 3/4 = [(4 x 2)+3]/4=11/4

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Mixed Numbers as Improper Fractions

Have you ever ordered multiple pizzas and then had to keep track of how many slices were eaten and how many weren't? Well, the sixth graders are having the same sort of dilemma.

Casey ordered eight pizzas for the drama club to enjoy. Each pizza was cut into ten slices. At the end of the pizza party, there were two whole pizzas and two slices left.

How many slices weren't eaten?

Can you express this as an improper fraction of pizza slices? Do you know what an improper fraction is?

This Concept is all about mixed numbers and improper fractions. At the end of it, you will know how to figure all of this out.

### Guidance

In the last Concept on measuring to a fraction of an inch, sometimes we ended up with measurements that included whole inches and parts of a whole inch or a fraction of an inch. When we have wholes and parts together, we have a new type of number. It is called a mixed number.

A mixed number is a number that has both wholes and parts in it.

514

Here we have a mixed number. We have five whole items and one-fourth of a whole.

Now you know how to identify a mixed number. The opposite of a mixed number is an improper fraction.

What is an improper fraction?

An improper fraction is a fraction that has a larger numerator and a smaller denominator.

Huh? What does this mean?

125

Let’s think about what this means. If the denominator tells us how many parts the whole has been divided into, then this whole has been divided into 5 parts. The numerator tells us how many parts of the whole we have in this case, we have twelve parts. What? If we have twelve out of five parts, then we have MORE than one whole. One whole would be five out of five parts, but we have 12 out of 5 parts. This is where mixed numbers come in.

How do we write a mixed number as an improper fraction?

To write a mixed number as an improper fraction, we want to write a fraction in terms of parts instead of in terms of wholes and parts.

Change 213\begin{align*}2 \frac{1}{3}\end{align*} to an improper fraction.

To do this, we multiply the whole number times the denominator and add the numerator. Then we put this over the original denominator.

2 ×\begin{align*}\times\end{align*} 3 + 1 =\begin{align*}=\end{align*} 7

Our original denominator is 3.

Our answer is 213=73\begin{align*}2 \frac{1}{3} = \frac{7}{3}\end{align*}.

Notice that the mixed number and the improper fraction are also equivalent.

Change the following mixed numbers to improper fractions.

#### Example A

313\begin{align*}3 \frac{1}{3}\end{align*}

Solution: 103\begin{align*}\frac{10}{3}\end{align*}

#### Example B

523\begin{align*}5 \frac{2}{3}\end{align*}

Solution:173\begin{align*}\frac{17}{3}\end{align*}

#### Example C

618\begin{align*}6 \frac{1}{8}\end{align*}

Solution: 498\begin{align*}\frac{49}{8}\end{align*}

Now back to the pizza dilemma. Have you figured out the answer? Here is the original problem once again.

Casey ordered eight pizzas for the drama club to enjoy. Each pizza was cut into ten slices. At the end of the pizza party, there were two whole pizzas and two slices left.

How many slices weren't eaten?

Can you express this as an improper fraction of pizza slices? Do you know what an improper fraction is?

First, let's think about how many slices weren't eaten.

Two whole pizzas and two slices = 2210\begin{align*}2 \frac{2}{10}\end{align*}

We can convert that to an improper fraction.

Our answer is 2210\begin{align*}\frac{22}{10}\end{align*} slices of pizza weren't eaten.

### 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 478\begin{align*}4 \frac{7}{8}\end{align*} as an improper fraction.

To do this, we multiply the denominator of the fraction with the whole number and add the numerator. This will give us our new numerator which is put over the original denominator.

398\begin{align*}\frac{39}{8}\end{align*}

### Practice

Directions: Write each mixed number as an improper fraction.

1. 212\begin{align*}2 \frac{1}{2}\end{align*}

2. 314\begin{align*}3 \frac{1}{4}\end{align*}

3. 513\begin{align*}5 \frac{1}{3}\end{align*}

4. 423\begin{align*}4 \frac{2}{3}\end{align*}

5. 614\begin{align*}6 \frac{1}{4}\end{align*}

6. 625\begin{align*}6 \frac{2}{5}\end{align*}

7. 713\begin{align*}7 \frac{1}{3}\end{align*}

8. 825\begin{align*}8 \frac{2}{5}\end{align*}

9. 745\begin{align*}7 \frac{4}{5}\end{align*}

10. 827\begin{align*}8 \frac{2}{7}\end{align*}

11. 834\begin{align*}8 \frac{3}{4}\end{align*}

12. 956\begin{align*}9 \frac{5}{6}\end{align*}

13. 658\begin{align*}6 \frac{5}{8}\end{align*}

14. 923\begin{align*}9 \frac{2}{3}\end{align*}

15. 512\begin{align*}5 \frac{1}{2}\end{align*}

16. 1614\begin{align*}16 \frac{1}{4}\end{align*}

### Vocabulary Language: English

Equivalent

Equivalent

Equivalent means equal in value or meaning.
improper fraction

improper fraction

An improper fraction is a fraction in which the absolute value of the numerator is greater than the absolute value of the denominator.
Mixed Number

Mixed Number

A mixed number is a number made up of a whole number and a fraction, such as $4\frac{3}{5}$.