Fractions For Kids Explained: How To Teach Your Child Fractions At Home
When it comes to teaching math at home, it’s fractions your kids and you will probably struggle with most. With words like numerator, improper, mixed number and others making their way into homework and school reports, sometimes even the number of terms relating to fractions for kids can all seem a little overwhelming for parents.
Knowing how to teach your child fractions at home can just be difficult. But having taught in schools and in homes, we’ve been there and done it and can reassure you now – there is a way through, you just have to take it step by step. This blog can help you with teaching fractions, whether you are helping a child in first grade or 4th grade!
- Fractions in a nutshell – The things you may have forgotten since school!
- What does my child need to know about fractions in elementary school?
- Equivalent fractions
- Representing fractions
- Get creative when helping them work out fractions
- Comparing fractions
- Fractions word problems
- Mixed numbers and improper fractions
- Adding and subtracting of fractions
- Adding and subtracting fractions with the same denominator is simple as you just add the numerators and keep the denominators the same.
- Multiplying proper fractions by fractions
- Multiplying fractions by whole numbers
- How to simplify fractions
- How to divide proper fractions by whole numbers
- Fractions, decimals and percentages
- Converting fractions
- Example fractions questions
Fractions in a nutshell – The things you may have forgotten since school!
We understand that fractions can be frustrating for both you and your child, so here’s everything you need to know about them in brief!
What is a fraction?
Fractions are used to represent smaller pieces (or parts) of a whole.
The parts might make up one thing, or more than one thing. Either way, altogether, they make up what’s called a whole.
It’s important to note that a whole can mean more than one thing. It’s useful to think of a candy store as an analogy. For sharing a singular whole amount, you can think of a chocolate bar. For grouping an amount into fractional parts, you can imagine a bag of candy – there are lots of candy in the bag, but you need all of them to make up the whole bag.
What is a child friendly definition of a fraction?
A simple definition of a fraction for children is:
A fraction is any part of a group, number or whole.
What are the parts of a fraction?
A fraction has two parts. They are:
The numerator which is the number above the bar.
The denominator which is the number below the bar.
What is a unit fraction?
A unit fraction has 1 as its numerator (top number), and a whole number for the denominator (bottom number).
Read more: What is a Unit Fraction
What is a proper fraction?
A non-unit fraction is a fraction with a number greater than one as its numerator (top number) and a whole number for the denominator (bottom number) that is greater than the numerator.
Using objects to visualize fractions
When you’re starting out with teaching children fractions, objects or pictures of objects are a great way to understand how they work.
Start with concrete items, like food or counters – you can use pasta pieces or dried beans in place of counters – then draw them as pictures.
Once you’ve got this down, you can move onto using rational numbers (the fancy name for fractions) to represent them. Learning fractions in this order makes it easier to work out fractions of natural numbers later on.
The most important thing to remember when you’re dealing with fractions is to go slow.
There’s so much information to process! Even if something seems easy, take the extra time to really understand the basic concepts behind fractions. It will make life a lot easier when you come to more complex problems that involve converting between fractions, decimals and percentages later on.
Find out more about why we use concrete resources in math.
Examples of fractions in everyday life
You may not even notice, but fractions are all around us! Some examples of everyday fractions include:
- Splitting a bill at a restaurant into halves, thirds or quarters
- Working out price comparisons in the grocery store when something is half price
- Figuring out amounts in the kitchen, for example a recipe could serve 10 people but there are only 4 eating, and this means you’ll need fractions to figure out the correct amount
- Adding up monetary amounts
- Looking at time! Half an hour and quarter past are both common things to hear where time is concerned!
Why are fractions so tricky in elementary school math?
In the first years of school, you learn how numbers work. You learn how to count, and that the number 1 is equal to one object, 2 is equal to two objects, and so on.
You learn that when you count up, the numbers have more value. And then, just when you think you’ve got the hang of numbers, you learn that there are other types of numbers out there, like fractions.
As a child, you are still making sense of the world. So when you learn a set of rules (like how to count with positive whole numbers), you hold onto them. The problem? When you come across things that don’t fit the rules, it’s much harder to understand.
Positive whole numbers (like 1, 2 or 65) are simple. They gain more value as they go up, and they always mean the same thing (1 always means 1, and 2 always means 2). They are also known as natural numbers. Fractions are known as rational numbers, and they follow different rules.
To cut a long story short, understanding how to do fractions can be tricky for elementary school children.
Fractions don’t always mean the same thing. ½ of a cake is not the same as ½ of three cakes, or ½ of a bag of 12 sweets! That’s the first hurdle – the value of a fraction changes depending on the size of the whole.
Secondly, if the bottom number (the denominator) in a fraction gets bigger, the value decreases. On top of all of that, names for fractions don’t always sound like the number they represent, like an eighth for ⅛ or a quarter/fourth for ¼.
The most important thing you can support your child with is their understanding that a fraction is a part of a whole, or a whole is a number of parts. And a unit fraction is an equal part of a whole. If they can grasp this, they can move forward.
More support for math at home is available:
What does my child need to know about fractions in elementary school?
There is a lot to cover with fractions for kids, but to help you out we’ve broken it down into distinct topics.
They’ll also learn that some fractions are equivalent too – for example, 2/4 is the same as ½, or 2/6 is the same as ⅓.
Here’s how to explain it simply using counters (pasta or dried beans are a suitable replacement from the cupboard).
To help your child fully figure out equivalent fractions, point them out wherever you can, (especially ½ and 2/4 at this stage) as this continued repetition will help them to practice until they perfect their knowledge.
Another easy way to practice is to shade in different fractions of shapes, like this:
As children get older they will also need to know a few equivalent fractions with small denominators, and be able to put them in order.
Equivalent fractions is a real leap for many children, and most teachers find it a real stumbling block for many children in their classes.
However, there are three sure-fire ways of helping your child understand how to do equivalent fractions, and you can see them below!
Equivalent fraction playdough
This is a simple, yet very effective activity that can help your child to visualize equivalent fractions in a way that they will understand.
How to run the activity
- Give your child three evenly sized balls of playdough.
- Get them to break one ball down into halves, another into quarters and the third into eight evenly sized pieces.
- Now, use a scale – preferably a balance scale – to show that the half is equal to two quarters and four eighths. (Also, that a quarter is equal to two eighths, and that three quarters is equivalent to six eighths.)
- You could get them to re-form the three original balls of playdough, breaking them down into three, six and nine equal pieces. Again, you can demonstrate that a third is equal to two sixths and three ninths, and that two thirds are the same as four sixths and six ninths.
Equivalent fraction paper strips
All you need for this activity is a sheet of paper, some scissors, and a bit of patience when it comes to cutting the strips!
How to run the activity
- Firstly, cut some strips of paper. They must be paper strips of equal length.
- Fold the first strip in half.
Fold the second strip into quarters.
Fold the third strip into six equal parts or sixths.
Fold a fourth strip into eight equal parts or eighths.
Finally, fold a strip into twelve.
- Next, work with your child to label the strips, so each part on the first strip has ½ written on each part, the second strip is labeled with ¼s, and so on. Now, you / they can show that a half is equal to two quarters, three sixths, four eighths, and six twelfths.
You can then show that a quarter is equal to two eighths and three-twelfths.
You could repeat the process again, folding equal length paper strips into three, six, nine and twelve, showing that two sixths, three ninths and four twelfths are equal to a third.
Using the strips you’ve made, you can do the same for ¾ and ⅔ too!
Get creative when helping them work out fractions
When demonstrating sharing into halves or quarters, it is vitally important to show something being shared into equal parts. By doing this your child will be able to visualize what is happening when you are creating the fraction, and it will help with their understanding.
Playdough is a great place to start when helping your child to work out fractions at a young age, as it is malleable and easy to adapt into different fractions.
However, a firm favorite in primary classrooms is using food to represent fractions, and this is what you can do with your child at dinner time if pizza is on the menu!
Remember to emphasize the importance of every slice of pizza being of equal size.
This is a simple visual representation of a fraction, and you can adapt it to try it with ¼ too.
You can use any food that’s easy to divide up, but make sure to use the language of fractions while you do this (halves, quarters and divide).
At first, your child will largely be focused on the numbers 0-20, but they may also work on some specific larger numbers that are easy to tackle at this age. For example they may be able to tell you that half of 100 is 50, or that one quarter of 100 is 25.
Of course, the value of a fraction depends on the numerator (the top number) and the denominator (the bottom number).
Comparing fractions with the same denominator
As the denominators are the same at this point, you just add the numerators, like this:
¼ + 2/4 = ¾
Which can be shown using paper strips again:
The principle is the same for subtraction at this stage.
Comparing fractions with different denominators
Your child will start to encounter fractions with different denominators, which means there are a few more steps involved.
The language used can be challenging too.
Make sure to use words like denominator, numerator, divide, compare, order, improper fraction and mixed number often to keep key vocabulary fresh in your child’s mind, as this will set them up for the work they will be doing in later grades.
If your child is struggling to grasp the concept of comparing fractions with different denominators, the calculator is a good place to start. You can divide the numerator by the denominator for each fraction, which will result in a decimal. Your child can then perhaps see which fraction is bigger by seeing which decimal number is bigger!
Calculator free way to work out ordering fractions
The process of ordering fractions without a calculator may take a little longer for your child to get to grips with, but it is something they will need to know.
The image below demonstrates how to work out ordering fractions if you don’t have a calculator.
Fractions word problems
Word problems become more common as your child moves up grades, usually involving measurement units, like meters, yards, feet, miles, stones and pounds, and dollars.
Working out fractions of amounts is much easier if you use bars to represent the different parts.
Take for example the question of:
What is 1/6th of 1200 meters?
If you wanted to work out 2/6 of 1200m, you’d just multiply the answer for 1/6 by 2. For 3/6, you’d multiply it by 3.
Bars work really well for learners who like to see things laid out visually. They can be used for other areas of math too – ranging from division, multiplication, addition and subtraction to ratio and proportion – not just fractions!
Mixed numbers and improper fractions
When you have a whole number and a fraction side by side, like 1½ , it’s called a mixed number. You can convert this into a fraction, but the numerator will be bigger than the denominator. In this case 3/2. This is called an improper fraction.
Adding and subtracting of fractions
Adding and subtracting fractions with the same denominator is simple as you just add the numerators and keep the denominators the same.
⅛ + ⅜ = 48
But, when the fractions have different denominators, they need to be made the same before you go any further.
One of the most important things to ensure your child is confident is making different denominators the same, and if this is the case, they’ll feel a lot more sure of their abilities within the next chapter of fraction work.
Multiplying proper fractions by fractions
Having learned an awful lot about fractions already, knowing how to multiply fractions is relatively simple compared to all the other processes your child has learned by this stage.
You just multiply the numerators then multiply the denominators, like this:
2/4 x 3/5 = 6/20
Multiplying fractions by whole numbers
When you’re asked to multiply a whole number by a fraction, it looks a little bit confusing at first. For example:
3 x 3/4
To overcome this daunting problem, you could begin by returning back to paper strips, like so:
Here it is important to remember that the denominator remains the same. If that is proving a stumbling block, you can roll out every math teacher’s best friend: pizza.
If you remember one simple fact, it’s a lot easier.
Any whole number can be made into a fraction by giving it a denominator of 1.
3 = 3/1
That’s because 3/1is the same as 3 ÷ 1, which is 3.
The resulting equation is much easier to solve. Just multiply the numerators together, and then the denominators together.
3/1 x 3/4= 9/4
How to simplify fractions
As the basics of fractions become cemented, students will often be required to write fractions in their simplest form.
This just means that we use the lowest possible numbers when we work out our fractions.
We do this to keep things simple – it stops us from ending up with fractions made up of huge numbers (which can be confusing).
Simplifying fractions is another area which highlights the importance of children mastering their multiplication facts.
For example, even though we know that 2/4 is a perfectly acceptable fraction, we simplify it to 1/2 to keep things easy (using our knowledge of 2’s multiplication facts, consequently, halving).
You can make simplifying fractions easy by practicing finding the greatest common factors of pairs of numbers.
A great technique for finding factors are factor rainbows, an example of which can be seen below.
How to divide proper fractions by whole numbers
Dividing fractions is a simple process, as long as you remember that when you’re using whole numbers in a fraction problem, you can put that number over 1 to make it a fraction too, like this:
3 = 3/1
So if you’re solving a problem like 3 ¾ , turn the 3 into a fraction first.
3/1 / 3/4
Next, flip over the second fraction (turning it into its reciprocal) and change the operation to multiplication.
3/1 x 4/3
Now it’s a simple multiplication problem, just multiply the numerators and the denominators to find your answer.
3/1 x 4/3= 12/3
Don’t forget to simplify the answer! In this case, the answer will be a mixed number.
12/3= 12 / 3 = 4
Fractions, decimals and percentages
Fractions, decimals, and percentages all represent parts, or pieces, of a whole so it’s not surprising that they’re closely related.
It’s good to know how to get from one to the other, especially when you’re ordering or comparing amounts.
Here are some useful equivalents to memorize!
Side note… the division symbol looks like ➗ as it shows a fraction bar (or – its proper name – a vinculum) with a dot above and below it; the top dot signifies a missing numerator and the bottom dot represents a missing denominator. The division symbol itself is a constant reminder of the link between fractions and division!
Your child should get to know the more common equivalents by heart – and learn the strategies for finding common percentages.
For example, to find 1% they must divide the amount by 100, or divide the amount by 10 and the result of this division calculation by 10 again.
Converting fractions into decimals
Divide the numerator by the denominator.
If they do not know their equivalences or if it is a more obscure fraction (which it is unlikely to be), they should revert to using short division.
Converting decimals into percentages
Multiply the decimal by 100. For example, 0.79 would become 79%.
Converting percentages into decimals
Divide the percentage by 100. So, 87% would become 0.87.
Converting percentages into fractions
Put the percentage amount over 100 (e.g. 75% = 75/100), then simplify it – in this case ¾ .
Although there are written methods for converting decimals back into fractions, at this stage it’s best to focus on what’s required for Common Core in elementary school math and for the most part simple equivalences like 0.25 being ¼ will be all that is required (knowing the eighths is helpful too such as 0.375 being the same as three-eighths). Students will also work quite a bit with converting tenths and hundredths from fractions to decimals and decimals to fractions.
It’s worth also reading this article on comparing fractions decimals and percentages.
Example fractions questions
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The content in this article was originally written by primary school teacher Sophie Bartlett and has since been revised and adapted for US schools by elementary math teacher Jaclyn Wassell.