Improper Fraction to Mixed Number — Conversion & Practice

Converting Improper Fractions to Mixed Numbers

Improper fractions allow us to easily perform operations with numbers that aren't integers, but they don't give us clear information at a glance. It can be hard to visualize where $\frac{19}{7}$ is on the number line compared to a mixed number like $2 \frac57$. Sometimes we will need to convert improper fractions to mixed numbers to get clear information. Also remember that mixed numbers are sometimes called mixed fractions.

When do we want to make this conversion? An improper fraction's numerator is greater than its denominator. Our goal is to get a mixed number. A mixed number will be an integer with a proper fraction stuck next to it.

Example: $\frac{23}{6}$

Our first step to converting is to divide the numerator by the denominator.

Remember that mixed numbers have two parts: a whole number and a fraction. The whole number will be the quotient, which is $3$ in this case. The fraction will be the remainder over the denominator. $$\text{Quotient} \frac{\text{Remainder}}{\text{Denominator}} = 3 \frac56$$

Why Does This Work?

This process works because fractions are shorthand for division. Using our last example, the fraction $\frac{23}{6}$ is used to show the value of $23$ divided by $6$.

Practice Problem 1

Let's try out a practice problem to check our understanding.

The first step is to divide the numerator by the denominator. Now we just need to write out our mixed number. The whole number part will be the quotient, and the fraction part will be the remainder over the denominator. $$\text{Quotient} \frac{\text{Remainder}}{\text{Denominator}} = 3 \frac14$$

Practice Problem 2: Bigger Numbers

Big numbers can look daunting at first but we solve them the exact same way as we solve problems with smaller numbers.

The first step is to divide the numerator by the denominator. The quotient will be the whole number part of the mixed number, and the fraction part will be the remainder over the denominator. $$\text{Quotient} \frac{\text{Remainder}}{\text{Denominator}} = 12 \frac{2}{7}$$

Divide the numerator by the denominator

Turning a fraction into a mixed number can be compared to neatly sorting a bunch of tennis balls into equally-sized containers. Each container only holds a certain number of balls (the denominator), and the integer in the mixed number (the $2$ in $2\frac{3}{5}$) is the number of containers that get totally filled. The numerator of the fraction (the $3$ in $2\frac{3}{5}$) is how many balls are left over, and the denominator of the fraction (the $5$ in $2\frac{3}{5}$) is how many balls each container can hold.

To turn a fraction into a mixed number, all you have to do is divide the numerator by the denominator and then leave the remainder as a fraction. In the above example, we have $\frac{13}{5}$ where $13>5$. $$13 = 2\times5+3$$ Since the remainder, $3$, is less than $5$, we leave it as a [proper] fraction. Let's try it with the fraction $\frac{23}{4}$.

$23$ divided by $4$ is $5.75$ in decimal notation, so the answer to the question above is $5$.

When you divide $23$ by $4$, you have $3$ remaining. That means that we can fit $23$ items into $5$ containers, and will have $3$ left over.

The number is $5\frac{3}{4}$. Remember that how much the container can hold is the denominator, the number of containers that are totally filled is the integer, and the number of things left over is the numerator.

(Video) Mixed Numbers

by mathman1024

Here’s a video by mathman1024 that explains mixed numbers, converting a mixed number to a fraction and converting a fraction to a mixed number.

$\large{\text{Summary}}$

Converting from an improper fraction to a mixed number requires division.

1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder is the numerator.
4. Denominator stays the same. $$\text{Numerator}\div\text{Denominator}+\frac{\text{Remainder}}{\text{Denominator}}$$

Let's try this out with the fraction $\frac{15}{4}$.

$$\frac{15}4={\color{purple}{3}}\frac{{\color{orange}{3}}}{4}$$