In this easy-to-follow guide to converting mixed numbers to improper fractions (and back), you’ll find simple definitions and instructions, as well as solved examples with a fun quiz at the end.
Whether you’re just learning about converting mixed numbers in elementary school, preparing for a standardized exam, or need a quick refresher, you’re in the right place!
Visit Mathnasium of La Jolla, a Top-Rated Math Learning Center
Mixed numbers are values that combine a whole number with a fraction.
For instance, in 3 \( \Large \frac{1}{2}\) the 3 is the whole number and \( \Large \frac{1}{2}\) is the fraction.
Let’s use a real-life example.
Imagine you order pizzas for your birthday party. After everyone takes a slice or few, you might have:
In this example, 1 whole pizza represents 1 whole number, and the slices that do not form a whole pizza represent fractions. Together, a whole pizza and the additional slices are a mix of whole numbers and fractions, representing mixed numbers. A mixed number has three parts:
The numerator and denominator together form the fractional part of the mixed number.
Sometimes recipes ask for things like 1 \( \Large \frac{1}{2}\) cups of flour. That's a mixed number!
It means you have one whole cup AND half of another cup. It's like having a whole pizza and half of another pizza.
When you cook, you use mixed numbers to measure the right amount of ingredients, just like you'd use a whole pizza and a half to make a big pizza party!
At Mathnasium, students use real life examples to learn about mixed numbers.
Improper fractions are fractions where the numerator (top number) is greater than or equal to the denominator (bottom number).
On the other hand, proper fractions are fractions where the numerator (top number) is smaller than the denominator (bottom number).
Makes sense?
Let’s work through a few more examples together!
Imagine you have a candy bar that's divided into 4 pieces. If you eat 6 pieces, you've eaten more than one whole candy bar.
This is where the improper fraction comes in.
The fraction \( \Large \frac{6}{4}\) shows that you ate 6 pieces, but there are only 4 pieces in one whole candy bar.
So, that’s why we call \( \Large \frac{6}{4}\) an improper fraction—it tells us you’ve consumed more than a whole candy bar.
Let’s take a look at another example!
Imagine you have a box of crayons with 10 crayons inside. If you use 12 crayons, you’d use more than one whole box.
The improper fraction for this is \( \Large \frac{12}{10}\). It shows you used 12 crayons, even though there are only 10 crayons in one whole box.
Learning to convert mixed numbers to improper fractions may be easier than you think! And it only takes three steps.
Let’s use the mixed number 3 \( \Large \frac{1}{4}\) as an example:
Let's use another example to understand how to convert a mixed number to an improper fraction.
Imagine you're having a pizza party, and you have 3 whole pizzas, each cut into 8 slices, and only 1 slice left of the fourth pizza (that’s 1/8 the fourth pizza).
So, in total you have 3 \( \Large \frac{1}{8}\) pizzas. How many slices is that?
Let’s break it down into a few easy steps:
Each whole pizza has 8 slices.
So, 3 \( \Large \frac{1}{4}\) pizzas are the same as \( \Large \frac{25}{8}\) slices.
That's how you convert a mixed number like 3 \( \Large \frac{1}{4}\) to an improper fraction like \( \Large \frac{25}{8}\).
Converting improper fractions to mixed numbers is almost as simple as the other way around.
Let’s try to convert the improper fraction \( \Large \frac{16}{3}\) into a mixed number as an example:
Some students can get a little confused by the remainder when converting fractions to mixed numbers.
Let’s explore it a bit.
When you change an improper fraction into a mixed number, divide the top number (numerator) by the bottom number (denominator), you'll get a whole number and some “leftovers,” or remainders. For example, when we divided 16 by 3, we got 5 and a remainder of 1.
To write it as a fraction, keep the same denominator (in this case, 3) and use the remainder as the numerator (in this case, 1), and you will get \( \Large \frac{1}{3}\).
Now that we know more about converting improper fractions to mixed numbers, let's take a look at one more example.
Imagine you have 13 cookies and you want to share them equally with 4 friends.
As you are dividing cookies among 4 friends, the cookies become your numerator and friends the denominator: \( \Large \frac{13}{4}\).
So, the improper fraction \( \Large \frac{13}{4}\) can also be expressed as a mixed number 3 \( \Large \frac{1}{4}\).
Practice makes perfect! Here are some more worked-out examples of how to convert improper fractions to mixed numbers, and vice versa.
Example A: Mixed number is 2 \( \Large \frac{3}{4}\)
Answer: Improper fraction is \( \Large \frac{11}{4}\)
Example B: Mixed number is 5 \( \Large \frac{1}{3}\)
Answer: Improper fraction is \( \Large \frac{16}{3}\)
Example C: Mixed number is 7 \( \Large \frac{2}{5}\)
Answer: Improper fraction is \( \Large \frac{37}{5}\)
Example D: Improper fraction is \( \Large \frac{13}{4}\)
Answer: Mixed Number is 3 \( \Large \frac{1}{4}\)
Example E: Improper fraction is \( \Large \frac{22}{5}\)
Answer: Mixed Number is 4 \( \Large \frac{2}{5}\)
Example F: Improper fraction is \( \Large \frac{37}{6}\)
Answer: Mixed Number is 6 \( \Large \frac{1}{6}\)
Practice Converting Improper Fractions & Mixed Numbers with Mathnasium of La Jolla
Ready to put your knowledge to the test? Try these exercises to practice your skills and improve your understanding of converting improper fractions and mixed numbers. Solve these problems then check your answers with the answer key at the bottom of the page.
Convert these improper fractions to mixed numbers:
Converting these mixed number to improper fractions:
However simple converting mixed numbers to improper fractions may seem, sometimes the smallest misstep can change the outcome. Here are some common errors to watch out for:
The denominator, or bottom number, remains unchanged throughout the conversion process.
For example, to convert 3 \( \Large \frac{1}{4}\) to an improper fraction, the denominator stays 4.
Double-check your calculations when multiplying the whole number by the denominator (the bottom number). A common mistake is to multiply the wrong numbers.
For example, to convert 3 \( \Large \frac{1}{4}\) you must multiply 4 𝑥 3.
Always simplify your final answer if possible.
For example, \( \Large \frac{4}{8}\) can be simplified to \( \Large \frac{1}{2}\).
Pay attention to the placement of these parts. The whole number goes before the fraction, and the numerator is the top number of the fraction.
For example, in this mixed number 4 \( \Large \frac{1}{5}\), the 4 is the whole number and 1 is the numerator.
Ensure you're converting to the format requested. If the question asks for an improper fraction, make sure your answer is in that format.
For example, if the questions ask you to convert a mixed number 2 \( \Large \frac{1}{3}\) to an improper fraction make sure you get \( \Large \frac{7}{3}\)
And here are some of the common mistakes students make when converting improper fractions into mixed numbers.
The denominator, or bottom number, remains unchanged throughout the conversion process.
For example, to convert \( \Large \frac{7}{4}\) to a mixed number, the denominator stays 4.
Double-check your calculations when dividing the numerator (top number) by the denominator. A common mistake is to divide the wrong numbers.
For example, if the fraction is \( \Large \frac{18}{5}\) do the division equation like this 18 ÷ 5
The remainder from the division should be written as a fraction with the same denominator as the original improper fraction.
For example, if the remainder is 3 and the denominator is 4, the fractional part of the mixed number would be \( \Large \frac{3}{4}\).
When converting an improper fraction to a mixed number, make sure to include the whole number part, which is the quotient from the division.
For example, if your answer is 1 \( \Large \frac{3}{4}\) don’t forget to place the 1 in front of the fraction!
Pay attention to the placement of these parts. The numerator is the top number, and the denominator is the bottom number.
For example, in this fraction \( \Large \frac{5}{6}\) the 5 is the numerator and the 6 is the denominator.
Our La Jolla math tutors help students practice new concepts taught at their school and help with homework.
Mathnasium of La Jolla is a math-only learning center for K-12 students of all skill levels, including elementary schoolers. Find us on 915 Pearl Street in San Diego.
Using a proprietary teaching approach, The Mathnasium Method™, our specially trained math tutors provide face-to-face instruction in a supportive group environment to help students truly understand and enjoy math.
Explore our approach to elementary school tutoring:
Students begin their Mathnasium journey with a diagnostic assessment that allows us to understand their unique strengths and knowledge gaps. Guided by assessment-based insights, we create personalized learning plans that will put them on the best path towards math excellence.
Whether your student is looking to catch up, keep up, or get ahead in their math class, schedule an assessment, and enroll at Mathnasium of La Jolla today!
Schedule a Free Assessment at Mathnasium of La Jolla
Here are the answers to the 10 exercise problems, let’s see how you did!
Answers to Converting Improper Fractions to Mixed Numbers
Answer 1: 3 \( \Large \frac{2}{5}\)
Answer 2: 3 \( \Large \frac{5}{6}\)
Answer 3: 2 \( \Large \frac{1}{4}\)
Answer 4: 1 \( \Large \frac{5}{8}\)
Answer 5: 1 \( \Large \frac{1}{9}\)
Answers to Converting Mixed Numbers to Improper Fractions
Answer 6: \( \Large \frac{17}{5}\)
Answer 7: \( \Large \frac{13}{3}\)
Answer 8: \( \Large \frac{23}{4}\)
Answer 9: \( \Large \frac{44}{7}\)
Answer 10: \( \Large \frac{43}{6}\)
(858) 291-8186
(858) 291-8186
