Unit fractions
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Basics on the topic Unit fractions
Unit Fractions
In this learning text we will explain what is a unit fraction and how we can recognise a unit fraction from other fractions.
Let’s repeat what a fraction is first:
A fraction always represents a part of a whole. For example, if a pizza is divided into four equal pieces, one piece is called $\frac{1}{4}$ of a whole pizza. A fraction has a bottom number which tells us how many parts we divide a whole into. We call this number the denominator. The top number represents how many parts we have in total. We call this number the numerator.
Now we can explain what a unit fraction is.
A unit fraction is a fraction where the numerator is always equal to one. For example $\frac{1}{4}$, $\frac{1}{3}$ or $\frac{1}{2}$.
Recognising Unit Fractions – Examples
Let’s look at a few examples to make sure we know how to recognise unit fractions.
In order to understand the topic completely we will look at unit fractions with different types of representations: squares, rectangles and triangles.
The first fraction is $\frac{1}{4}$ and is represented by a square divided into four equal smaller identical squares and only one small square is shaded. $\frac{1}{4}$ is a unit fraction as the numerator is equal to one and only one part of the diagram is shaded.
The second example is the unit fraction $\frac{1}{3}$. This fraction is represented by a square divided into three identical rectangles. As we explained earlier the unit fraction must have a numerator equal to one and a denominator of three.
The last fraction is also a unit fraction. Here, the unit fraction $\frac{1}{2}$ is represented by a triangle divided into two equal parts where only one is shaded.
All these fractions are unit fractions with the numerator of one.
But not all fractions are unit fractions. There are also non unit fractions Have a look at an example of a fraction that is not a unit fraction.
What is a non unit fraction?
The fraction $\frac{3}{4}$ is represented by a square divided into four equal smaller identical squares. This fraction has three small squares shaded. It is not a unit fraction because the numerator of this fraction is three not one. Remember that unit fractions always have the numerator one.
Comparing Unit Fractions
Let’s look at how we can compare two unit fractions. Notice that all unit fractions have the numerator one. The fractions we will compare have different denominators but the numerators will always be one. Let’s look at how to compare the two unit fractions $\frac{1}{4}$ and $\frac{1}{3}$.
The first unit fraction is showing a rectangle divided into four equal parts where only one bar is shaded and the second unit fraction divides the same rectangle into three equal parts and also one bar is shaded. The second fraction $\frac{1}{3}$ has a smaller denominator (three) than $\frac{1}{4}$ but the bars in the representation of $\frac{1}{3}$ are bigger than each of the bars in the first fraction. This is because the fraction $\frac{1}{4}$ divides the whole into more equal parts than the fraction $\frac{1}{3}$. So, the more parts we have, the smaller the parts. In other words: The greater the denominator, the smaller the fraction.
Unit Fractions – Summary
Let’s review what we learned in this text. There are two rules to remember about unit fractions:
| Rule # | What to remember |
|---|---|
| 1 | Unit fractions always have the numerator one. |
| 2 | The greater the denominator, the smaller each part of the fraction is. |
Remember to practise unit fractions and non unit fractions using our videos, our interactive exercises and printable worksheets.
Transcript Unit fractions
Axel and Tank are at a fudge shop that only sells fudge in unit fractions. There are only two pieces left! "I'll have the one quarter piece, it will be bigger because it has a four in it!" "Fine, I'll take the one third piece, it's probably smaller because it has a three in it." Let's see who gets the bigger piece by learning about unit fractions". A fraction represents a part of a whole. The bottom number tells you how many parts make up the whole, it is called the denominator. The top number is the numerator , and represents how many parts we have. Unit Fractions are fractions that have a numerator of one, such as one quarter, one third and one half. We can represent unit fractions with fraction bars or shapes. Let's see if you can recognise some unit fractions! Here is the first one. What fraction can we see? It has four parts in total so the denominator is four. Three of the parts are shaded in, so the numerator is three. Is three quarters a unit fraction? It is not a unit fraction because it does not have one as its numerator! Let's look at this one. What fraction do we see? It has two parts in total so the denominator is two. One part is shaded in, so the numerator is one. Is one half a unit fraction? One half is a unit fraction because it has one as its numerator! Whilst Axel and Tank wait for their fudge let's look at what they ordered! Tank ordered one quarter and Axel ordered one third! If you look at the denominator and the size of each piece of fudge you might notice something special about fractions! What do you notice? When comparing fraction bars, objects, or shapes that are the same size, the greater the number of parts a fraction has, the smaller each part is! This is because we are dividing the whole into more equal parts! Even though four is a greater number than three, each part in the one quarter fraction bar is smaller than each part in the one thirds fraction bar because there are more parts when something is shared into four quarters than when something is shared into three thirds. Let's review unit fractions! Remember,a unit fraction must have a numerator of one like these fractions! A greater denominator means each part of the unit fraction is smaller because we are dividing the whole into more equal parts. "Hey Tank, do you realise what we've just learnt?" "What do you mean?" "Well, you ordered the one quarter unit fraction piece of fudge, thinking it was going to be bigger than my one third piece of fudge." "Oh no! The bigger denominator means I actually have the smaller piece!"
Unit fractions exercise
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Are the cakes examples of unit fractions?
HintsRemember that a unit fraction always has a 1 as the numerator (the top part of a fraction).
This pizza image shows $\frac1 4$ as there is one slice out of four in total.
Solution- The chocolate cake shows $\mathbf{\frac{1}{6}}$ . The numerator is one so this is a unit fraction. ✅
- The lemon cake shows $\mathbf{\frac{3}{4}}$ . The numerator is more than one so this is NOT a unit fraction. ❌
- The strawberry cake shows $\mathbf{\frac{1}{4}}$ . The numerator is one so this is a unit fraction. ✅
- The fruit pie shows $\mathbf{\frac{2}{6}}$ . The numerator is more than one so this is NOT a unit fraction. ❌
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How much will they each get?
HintsEach of the friends will get one part of the fudge, so the numerator must be one.
How many pieces is the fudge broken into? This is the total number of parts and so will be the denominator.
Solution- The fudge is broken into four parts, so this is the denominator.
- Each friend gets one part, so this is the numerator.
- There are four quarters in the whole.
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Matching unit fractions.
HintsLook at how many parts in total the cake was cut into. This is the denominator.
How many parts are there left? This is the numerator.
This example shows $\frac1 8$.
SolutionHere are the correctly matched labels to each cake.
We can see that the strawberry cake is $\frac1 4$ because there is 1 piece of cake out of a possible 4 slices.
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Who has the biggest piece of fudge?
HintsEach friend used the same size fudge to start with. The denominator tells us how many parts they cut their fudge into.
If Axel ate $\frac1 3$ of a pizza and Tank ate $\frac1 7$ of a pizza, who had the bigger slice?
Solution- The bigger the denominator, the smaller each part.
- Axel broke his fudge into three parts because he had $\mathbf{\frac{1}{3}}$. So his piece was the biggest.
- The other friends broke their fudge into more parts, so each part would be smaller.
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What is a unit fraction?
HintsUnit fractions have 1 as the numerator.
The numerator is the top part of the fraction.
SolutionThe unit fraction is $\frac1 7$ since there is a 1 as the numerator.
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Pizza night.
HintsIf a pizza is sliced into 10 and another is sliced into 6, which would have the smaller pieces?
How many parts are there in total? This is the denominator.
SolutionAfter visiting the fudge and the cake shop, Axel and Tank decided they would have a pizza night. Axel sliced his pizza into 6. Each slice was $\mathbf{\frac{1}{6}}$ of a pizza. He was quite hungry though, so he ate 5 slices. In total that was $\mathbf{\frac{5}{6}}$ of his pizza.
Tank thought he wanted smaller pieces, so he sliced his pizza into 10. Each slice was $\mathbf{\frac{1}{10}}$ of a pizza. He thought that as the pieces were so small, he could have more of them, so he ate 9 slices! That's $\mathbf{\frac{9}{10}}$ of his entire pizza!
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