A **mixed number** is a whole number and a proper fraction. Mixed numbers or mixed fractions are used to express an amount greater than a whole but less than the next whole number. Mixed numbers can be formed from improper fractions. They're useful in describing units that cannot be equally divided.

Fractions by themselves are often easy to understand. Whole numbers are easy. When fractions and whole numbers get together, though, the mixed numbers can be much more challenging to understand.

You are probably familiar with **fractions**, which are usually parts of a whole and always existing (in proper form) between the whole numbers $0$ and $1$:

- $\frac{1}{2}$
- $\frac{3}{4}$
- $\frac{7}{8}$
- $\frac{1}{16}$
- $\frac{25}{32}$

**Improper fractions** can be whole numbers in disguise:

- $\frac{4}{2}=2$
- $\frac{9}{3}=3$
- $\frac{100}{10}=10$

Or improper fractions can be mixed numbers awaiting simplification:

- $\frac{4}{3}=1\frac{1}{3}$
- $\frac{7}{3}=2\frac{1}{3}$
- $\frac{105}{10}=10\frac{1}{2}$

After simplifying these improper fractions, you are left with a whole number plus a remainder, which is the additional fraction.

The combination of a whole number and a proper fraction is called a mixed number.

Suppose you have a set of baseball trading cards for your favorite team. It is $17$ cards. One card is $\frac{1}{17}$, a fraction of the whole set. The entire collection is $\frac{17}{17}$, or $1$ whole.

What if a friend gives you a handful of additional trading cards?

You count the new cards – your friend gave you $5$ cards. You now have more than one whole set, but you do not have a complete second set of $17$ cards, so you have a mixed number.

So, how many sets of baseball cards do you have?

- Original set: $\frac{17}{17}$ or $1$ whole set
- New cards: $5$
- Tot Sets: $1$ & $\frac{5}{17}$ or $1\frac{5}{17}$

You have $1$ and $five-seventeenths$ $\left(\frac{5}{17}\right)$ sets of baseball trading cards.

Mixed numbers can be used to describe everything from batches of baked cookies to timings of movies to any unit or set that can be divided into parts.

Pizza, cookies, cupcakes, and many other foods lend themselves to breaking up into whole units and fractions, which means they can also form mixed numbers.

Your math club orders pizzas cut into $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$16th$}\right.$ slices for your Math Night. You ordered $15$ pizzas, but not every pizza was consumed.

That means the adoring crowd of math lovers ate $14$ whole pizzas, and $9$ slices, each $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$16th$}\right.$.

That makes the mixed number, $14\frac{9}{16}$.

Let's solve another one.

A high school soccer team fields $11$ players, so the complete team is $\frac{11}{11}$ or $1$ team. On the sidelines, however, are another $8$ players. Not quite a second team.

What is the mixed number showing how many teams the high school has?

$One$ whole team, plus $\frac{8}{11}$ more, so $1\frac{8}{11}$.

Earlier, we mentioned that improper fractions were disguising whole numbers or mixed numbers in them. They are improper because their numerators are not smaller than their denominators:

- $\frac{11}{8}$
- $\frac{5}{2}$
- $\frac{14}{7}$
- $\frac{64}{24}$

To convert an improper fraction to its mixed number form, we divide the numerator (top number) by the denominator (bottom number).

The whole number you get is the whole number part of a mixed number, and the remainder is the numerator of the fraction part of the mixed number.

The denominator of your mixed number is the same denominator from your improper fraction.

Let's look at an example:

$\frac{11}{8}=?$

$\frac{11}{8}=1$, with $3$ remaining

$\frac{11}{8}=1\frac{3}{8}$

Here is another one:

$\frac{5}{2}=?$

$\frac{5}{2}=2$, with $1$ remaining

$\frac{5}{2}=2\frac{1}{2}$

Our third example:

$\frac{14}{7}=?$

$\frac{14}{7}=2$, with nothing remaining

$\frac{14}{7}=2$

And one last example:

$\frac{64}{24}=?$

$\frac{64}{24}=2$ with $16$ remaining

$\frac{64}{24}=2\frac{16}{24}$, which simplifies...

$\frac{64}{24}=2\frac{2}{3}$

In the last example, notice that we reduced the fractional part down to it's simplest form.

Mixed numbers become improper fractions easily by multiplying the whole number times the fraction's denominator and adding the numerator. It is a counterclockwise process.

Here is $5\frac{6}{7}$ being converted to an improper fraction:

$5\times 7=35$ $35+6=41$ $5\frac{6}{7}=\frac{41}{7}$

Here are five word problems for you to solve:

- In the mixed number $3\frac{7}{10}$, what is the whole number, and what is the fraction?
- Is $\frac{27}{9}$ a proper fraction, improper fraction, mixed number, or whole number? Can it simplify to another form?
- Change $\frac{13}{8}$ to a mixed number.
- What is $\frac{56}{50}$ as a mixed number?
- Change the mixed number $3\frac{7}{8}$ to an improper fraction.

Take a fraction of a second to think about each before you peek!

- In the mixed number $3\frac{7}{10}$, the $3$ is the whole number, and $\frac{7}{10}$ is the fraction.
- The number $\frac{27}{9}$ is an improper fraction. It can be simplified to the whole number $3$.
- To change $\frac{13}{8}$ to a mixed number, divide $13$ by $8$ and use the remainder as the new numerator: $1\frac{5}{8}$.
- The number $\frac{56}{50}$ is $1\frac{3}{25}$ as a mixed number.
- The mixed number $3\frac{7}{8}$ becomes the improper fraction $\frac{31}{8}$.

After working your way through this lesson and video, you have learned:

- What mixed numbers are
- How to convert improper fractions into mixed numbers
- How to solve mixed fractions

Instructor: **Malcolm M.**

Malcolm has a Master's Degree in education and holds four teaching certificates. He has been a public school teacher for 27 years, including 15 years as a mathematics teacher.

Malcolm has a Master's Degree in education and holds four teaching certificates. He has been a public school teacher for 27 years, including 15 years as a mathematics teacher.

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