Improper Fractions (KS2): Top-Heavy Fractions Made Easy

Image © Santi Vedri.

An improper fraction is a fraction where the numerator (top part of the fraction) is bigger than the denominator (bottom part of the fraction).

It's an improper fraction because the proper fractions that we're used to have a smaller numerator and larger denominator. You might know it as a top-heavy fraction, which makes perfect sense because the top is bigger (heavier) than the bottom.

A mixed number is a whole number (a number without a decimal point, like 4) and a fraction (like 2/3) put together. Mixing numbers and fractions may seem odd, but it's actually preferred to the improper fraction.

For Example:

-'Three and a half' would look like this: 3  1/2  (this is not 31/2!).

-'One and one fifth' would look like this: 1  1/5.

-'Two and three-quarters' would look like this: 2  3/4.

To Convert Improper Fractions To Mixed Numbers, Ask These Two Questions:

1) How many times does the bottom of the fraction (the denominator) go into the top (the numerator)?

2) What is the remainder?

The answer to the first question will give you your whole number, and the answer to the second question will give you the numerator for the fraction that will go with it.

For Example:

-14/5 = 2  4/5

5 goes into 14 two times, as you can fit two 5s into 14. This means your whole number will be 2 and your remainder will be 4.

Or, 14/5 = 2 r 4.

So, 14/5 as a mixed number would be 2  4/5 (not 24/5, there's a space!).

-23/4 as a mixed number is 5  3/4.

-3/2 as a mixed number is 1  1/2.

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KS2 children will need to be able to turn improper fractions into mixed numbers, and mixed numbers back into improper fractions. Here's how to do it the other way around:

1) Multiply your whole by your denominator.

2) Add your answer to step one to the numerator.

Voila! You take your whole, times by the bottom and add it to the top.

For Example:

-1  2/3 as an improper fraction is 5/3.

-5  3/4 as an improper fraction is  23/4.

-2 11/12 as an improper fraction is 35/12.

-Improper fractions are fractions with a bigger number on top and a smaller number on the bottom.

-A proper fraction is the opposite: smaller on top and bigger at the bottom.

-An improper fraction is also known as a top-heavy fraction.

-A mixed number is a whole number mixed with a fraction.

-In maths, mixed numbers are preferred to improper fractions.

-To convert improper fractions to mixed numbers: find how many times your denominator goes into your numerator completely (your whole) and find the remainder. The whole will go next to the fraction, on the left, and the remainder will be the numerator of your new fraction.

-To convert the other way around: multiply your whole by the denominator, then add the numerator to get an improper fraction again.

Conversions between mixed numbers and improper fractions begin in Year 5, though the concept of mixed numbers is introduced in Year 2.

Year 2: Children learn to count in fractions up to 10, recognising that fractions can be greater than one.

Year 3: Children become more familiar with mixed numbers and the fact that fractions can be greater than one.

Year 4: Children become more experienced with mixed numbers and the fact that fractions can be greater than one.

Year 5: Children begin to recognise the equivalence between mixed numbers and improper fractions; learning how to convert between them either way.

Year 6: Children develop more confidence as they recognise the equivalence between mixed numbers and improper fractions; they can also convert between them more fluently.

There are loads of real-life applications of improper fractions to help you help the kids get to grips with it. Here are some examples:

-"If I have two packets of biscuits and I eat half a packet, how much do I have left? How many halves is that?"

-"Here are three whole sandwiches, each cut into quarters. If I eat just one quarter, how many quarters will be left?"

-"Here is a cake, cut into eight pieces. How many eighths are in a whole? If I bought another cake and cut it into eighths, how many eighths would there be in two whole cakes? If I ate a slice, how many eights would there be left?"

And in each of these examples, there's plenty of opportunity for some hands-on engagement!

Get Cooking: Why not make homemade pizzas from scratch? The process of slicing and inevitable conversation about fractions will come naturally. Other foods you can work with are chocolate bars and cut fruit!

Get Building: Grab some Lego and discuss improper fractions, as you work out how many of the flatter pieces need to be connected to be the same height as a regular block. Then, split up and try to build the same thing (like a wall to protect a toy car): one of you only uses regular blocks and the other only uses the flatter ones. Or learn about fractions while building a sweet dispenser.

Get Baking: Bake some cakes and slice away! Why not be creative with the flavour too?