This is my first post about visual maths fractions and I wish it to be brief and to the point.
What is a fraction?
Fraction is a part or parts of a whole.
What is the point of understanding or learning fractions?
It is boring anyway, according to children!
Well, it turns out that people use fractions, in one form or another, in everyday life just like arithmetic.
How to represent a fraction
A fraction is shown using a fraction line that looks like a long, horizontal dash with a pair of numbers, one on either side.
The bottom number, below the fraction line, is the denominator.
It means the total parts, how many parts are there altogether, to make a whole.
In this case, the whole shape consists of just two parts – one shaded (red) and one unshaded (clear).
The fraction line, between the numerator and denominator, is a division operator just like a ÷ sign.
Fractions, decimal fractions, percentages and ratios are all the same thing, simply expressed differently.
That’s, the very same numbers or values but said, written or presented in different ways. For instance;
- A half or one-half equals ½, 0.5, 50% and 1:1 (equal parts or even chance).
- A quarter or one-quarter equals ¼ , 0.25, 25% and 1:3.
Basic types of fractions
A fraction can be classified as a proper fraction, top-heavy fraction or mixed fraction.
I will try to use simple and similar examples for maximum clarification and consistency.
This is when the top number (numerator) is less than the bottom number (denominator), resulting a decimal fraction or value that is less than one whole or 1.
As the name suggests, the top number (numerator) is heavier or bigger than the bottom number (denominator). The resultant decimal fraction or value is bigger than one whole (1).
Examples, 3/2 = 1.5, 5/4 = 1.25 and 7/4 = 1.75. A top-heavy fraction is also called an improper fraction; i.e the opposite of a proper fraction for not having a numerator that’s less than the denominator.
As the name implies, this is a ‘mix’ of whole numbers and fractions.
Top-heavy Fractions to Mixed Fractions
A top-heavy fraction (an improper fraction) can be converted to a mixed fraction.
Mixed Fractions to Top-heavy Fractions
A mixed fraction can be converted back to a top-heavy fraction.
It is the opposite (reverse or inverse operation) of previous examples.
So, let’s gather our children to add up how much chocolate each group got!
That’s how mixed fractions (mixed numbers) go back to top-heavy fractions (improper fractions).
Doubling a number, then doubling it again is the quickest and safest way if someone is struggling with their 4 times table.
This technique also works in reverse for divide by 4; by halving a number, then halving it again.
Someone still has problems with doubling and halving?
Well, then they are in trouble! (Seriously, especially at small numbers.)
That’s it for this post of Understanding Fractions Visually.
Corrections and comments?
Please, keep them coming!
Thanks for reading.
About the author
Eng S Jama is an experienced electronics engineer turned an educational tutor and a self-published author.
Fractions Visually is for children who think fractions are no fun and grown-ups who have never found the best visual resources to master basic maths fractions.
Ages 5-11, Year groups 1-6 and Key Stages 1-2.
Or internationally equivalents in primary curriculum (infants and junior schools).
1) Colouring/shading fraction shapes and tracing shapes, images & text
2) Illustrated, visual fractions
(Also, available as a workbook, colour workbook and colour e-books).
3) How to add visual fractions
|Colouring Workbook||Paperback||Colour Paperback
|Workbook||Colour Workbook||Colour eBook|
|Colouring Workbook||Paperback||Colour Paperback|
|Colour Workbook||Colour eBook|
Series 3: Coming soon!