From slicing a pizza into \(\displaystyle \frac{1}{2}\) , measuring \(\displaystyle \frac{3}{4}\) cup of sugar, to sharing \(\displaystyle \frac{1}{3}\) of a chocolate bar with a friend, fractions show up not just in our math books, but everywhere around us. And just like there are different ways to divide things in real life, there are different types of fractions to match.
Whether you're just beginning to learn about types of fractions, looking to refresh for a test, or simply aiming to get ahead in math, this guide is for you.
Read on to find simple definitions of each type of fraction, a clear comparison between them, answers to commonly asked questions, and a quiz to test your knowledge.
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A fraction is a way of showing a part of a whole. When something is split into equal parts, a fraction tells us how many of those parts we have.
For example, if you cut a cupcake into 6 equal pieces and eat 1, you've eaten \(\displaystyle \frac{1}{6}\) of the cupcake.
Every fraction has two parts:
Numerator: the top number, which tells us how many parts we have (like how many slices of pie you ate)
Denominator: the bottom number, which tells us how many equal parts the whole is divided into (like the total number of pie slices)
Fractions are closely related to division. In fact, every fraction is like a division problem in disguise.
For example, \(\displaystyle \frac{1}{6}\) represents the division of 1 by 6, showing that we have 1 part out of 6 equal parts that make up the whole.
See how Mathnasium’s proprietary teaching approach, the Mathnasium Method™, helps students learn and master any math topic, including types of fractions.
Based on the relationship between the numerator (the top number) and the denominator (the bottom number), there are three main types of fractions:
A proper fraction is a fraction with a value less than one whole (such as \(\displaystyle \frac{2}{4}\) or \(\displaystyle \frac{3}{5}\)). This means that, in a proper fraction, the numerator is smaller than the denominator.
Think of it this way: If a book has 8 chapters and you’ve read 3, what fraction of the book have you finished?
That’s right, \(\displaystyle \frac{3}{8}\) .
Now ask yourself: Is 3 less than 8?
If it is, then the fraction is less than a whole book, and that makes it a proper fraction.
An improper fraction is a fraction whose value is greater than one whole (such as \(\displaystyle \frac{3}{2}\) or \(\displaystyle \frac{8}{3}\) ). In an improper fraction, the numerator is greater than the denominator.
Imagine this: Each sandwich is cut into 4 equal parts. If someone eats 5 of those parts, how much did they eat?
More than a whole sandwich! Since \(\displaystyle \frac{5}{4}\) is greater than 1, it’s an improper fraction.
A mixed number is a combination of a whole number and a proper fraction (such as \(\displaystyle 1\frac{1}{4}\) or \(\displaystyle 3\frac{2}{5}\) ). The value of a mixed number is always greater than one whole.
Let’s think about this: What if you poured 1 full cup of juice… and then poured half of another cup? How much juice did you pour in total?
That’s right, \(\displaystyle 1\frac{1}{2}\) cups.
Now ask yourself: Is that more than one whole cup?
It is, so we call that a mixed number because it’s part whole and part fraction, all in one.
Mixed numbers are closely related to improper fractions. In fact, every mixed number can be rewritten as an improper fraction, and vice versa.
To convert a mixed number into an improper fraction:
For example, to convert \(\displaystyle 1\frac{1}{2}\) :
\(\displaystyle 1 \times 2 + 1 = 2 + 1 = 3\) , so the improper fraction is \(\displaystyle \frac{3}{2}\) .
Even though unit fractions are part of proper fractions, we often talk about them on their own, and for a good reason.
A unit fraction is a fraction where the numerator is always 1 (such as \(\displaystyle \frac{1}{2}\), \(\displaystyle \frac{1}{3}\), or \(\displaystyle \frac{1}{5}\)).
Why do we call them “unit” fractions?
Because they represent one equal part of something that’s been divided into many. They’re the simplest kind of fraction and the first step to understanding how fractions work.
We also call unit fractions the building blocks of all fractions because you can combine them to create larger fractions. Let’s see how.
Imagine a chocolate bar split into 8 equal pieces.
If you take 1 piece, what fraction do you have?
The answer is \(\displaystyle \frac{1}{8}\) which is a unit fraction.
Now, if you take 1 more piece, how much do you have in total?
\(\displaystyle \frac{1}{8} + \frac{1}{8} = \frac{2}{8}\)
And if you take another?
\(\displaystyle \frac{2}{8} + \frac{1}{8} = \frac{3}{8}\)
…and so on.
So far, we’ve looked at how a single fraction can be classified based on its parts.
Now, let’s take it a step further.
When we compare two or more fractions, we can group them into different types based on how they relate to each other. This gives us three more types of fractions you’ll often see in math:
Like fractions are fractions that have the same denominator.
This means the whole has been divided into the same number of equal parts, which makes them easy to compare or combine.
For example, \(\displaystyle \frac{2}{5}\) and \(\displaystyle \frac{4}{5}\) are like fractions. Both are based on fifths, so we can easily add, subtract, or compare them.
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Unlike fractions have different denominators.
That means the wholes have been split into a different number of parts, so we can’t directly compare or combine them.
For example, \(\displaystyle \frac{1}{4}\) and \(\displaystyle \frac{2}{3}\) are unlike fractions. One is based on fourths, the other on thirds, so we need to find a common denominator before doing math with them.
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Equivalent fractions are fractions that have different numerators and denominators but represent the same value when we simplify them.
What do we mean by this?
Well, if we look at \(\displaystyle \frac{1}{2}\) and \(\displaystyle \frac{4}{8}\) , we might not tell right away that they are equivalent. But we can check by simplifying \(\displaystyle \frac{4}{8}\) .
To simplify a fraction, we divide the numerator and denominator by the greatest common factor (GCF), the largest number that goes evenly into both.
For 4 and 8, the GCF is 4:
\(\displaystyle \frac{4}{8} \div \frac{4}{4} = \frac{1}{2}\)
So, \(\displaystyle \frac{4}{8}\) simplifies to \(\displaystyle \frac{1}{2}\), which means they are equivalent fractions.
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With so many types of fractions to keep track of, it helps to see them all side by side.
Here’s a quick table to compare all 7 types of fractions we’ve explored: what they are, how they work, and how they’re used.
It’s time to practice what you’ve learned about types of fractions. Here are six questions to test your understanding.
When you’re done with our quiz, check your answers at the bottom of the guide.
1. Which of these is a proper fraction?
a) \(\displaystyle \frac{5}{3}\)
b) \(\displaystyle \frac{1}{2}\)
c) \(\displaystyle \frac{3}{3}\)
d) 2
2. What do we call fractions that have the same denominator?
a) Equivalent fractions
b) Unit fractions
c) Like fractions
d) Mixed numbers
3. Which of these are like fractions?
a) \(\displaystyle \frac{1}{4}\) and \(\displaystyle \frac{2}{3}\)
b) \(\displaystyle \frac{3}{5}\) and \(\displaystyle \frac{3}{4}\)
c) \(\displaystyle \frac{2}{6}\) and \(\displaystyle \frac{5}{6}\)
d) \(\displaystyle \frac{4}{7}\) and \(\displaystyle \frac{5}{8}\)
4. Which of these is a unit fraction?
a) \(\displaystyle \frac{2}{3}\)
b) \(\displaystyle \frac{4}{1}\)
c) \(\displaystyle \frac{1}{10}\)
d) \(\displaystyle \frac{3}{1}\)
5. What do we call fractions that look different but have the same value?
a) Unlike fractions
b) Proper fractions
c) Mixed numbers
d) Equivalent fractions
6. Which of the following is a mixed number?
a) \(\displaystyle \frac{2}{2}\)
b) \(\displaystyle \frac{1}{2}\)
c) \(\displaystyle \frac{5}{1}\)
d) \(\displaystyle \frac{4}{5}\)
Learning about the different types of fractions doesn’t always come without questions, and that’s totally normal!
We’ve put together a list of questions students often ask at Mathnasium of West Chester, along with answers to help you feel more confident with fractions.
Most students are introduced to basic fractions in 2nd or 3rd grade, starting with simple ideas like halves, thirds, and fourths.
As they move into the 3rd to 5th grade, they begin learning about different types like proper, improper, and equivalent fractions.
More advanced types, like mixed numbers or comparing fractions, are explored throughout upper elementary and into middle school.
Whole numbers like 1, 2, or 10 aren’t technically types of fractions, but they can be written as fractions.
For example, 3 is the same as \(\displaystyle \frac{3}{1}\), which means "three wholes."
So while whole numbers aren’t one of the types we listed, they do show up in fraction form, especially when working with improper fractions or mixed numbers.
Yes! That’s what we call an improper fraction, like \(\displaystyle \frac{5}{3}\) or \(\displaystyle \frac{9}{4}\).
These show more parts than one whole, and they’re often written as mixed numbers to make them easier to picture.
Yes, it is! If you see a fraction like \(\displaystyle \frac{4}{1}\), it means 4 wholes.
It’s just another way to write a whole number, and it often shows up in math when you're dividing or working with improper fractions.
Nope! In math, you can never divide by zero, so a fraction like \(\displaystyle \frac{3}{0}\) doesn’t make sense.
It’s considered undefined, which means it has no value. Always make sure your denominator is a positive number that’s not zero.
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Using the proven Mathnasium Method™, our specially trained tutors provide face-to-face instruction in a fun and supportive group environment to help students truly understand and enjoy any math class and topic, including fractions typically covered in elementary school math.
Explore how we support elementary school learners:
Students begin their journey at Mathnasium with a diagnostic assessment that helps us identify their current skill level, learning style, and areas for growth. Based on assessment, we create a personalized learning plan that builds confidence and leads to lasting math success.
Whether your student is just starting to learn about fractions, needs help making sense of mixed numbers, or wants to get ahead with advanced fraction skills, schedule an assessment today and see how Mathnasium of West Chester can help.
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Ready to see how you did? Here are the correct answers to the flash quiz.
1. Which of these is a proper fraction?
b) \(\displaystyle \frac{1}{2}\)
2. What do we call a fraction that has the same numerator and denominator?
c) Like fractions
3. Which of these are like fractions?
c) \(\displaystyle \frac{2}{6}\) and \(\displaystyle \frac{5}{6}\)
4. Which of these is a unit fraction?
c) \(\displaystyle \frac{1}{10}\)
5. What do we call fractions that look different but have the same value?
d) Equivalent fractions
6. Which of the following is a mixed number?
b) \(\displaystyle 1\frac{1}{2}\)
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