*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.

That is, only one part, piece, share, slice… or more parts/pieces/shares/slices of an entire thing.

In short, a fraction can be from a very tiny part to a huge chunk or many, many parts of the whole thing* – and anything in between.*

**Why bother?**

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 top number, above the fraction line, is called the **numerator**.

It shows how many parts out of a whole.

In our simple example, 1 indicates one part out of 2 parts.

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 Family**

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.

**Proper Fractions**

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.

For instance, ½ = 0.5 , ¼ = 0.25 and ¾ = 0.75. A proper fraction is also called a **common** fraction.

**Top-heavy Fractions**

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.

**Mixed Fractions**

As the name implies, this is a ‘mix’ of whole numbers and fractions.

For example, 1½ = 1.5, 1¼ = 1.25 and 1¾ = 1.75.

Appropriately, a mixed fraction is also called a **mixed number**!

**Top-heavy Fractions to Mixed Fractions**

A top-heavy fraction *(an improper fraction)* can be converted to a mixed fraction.

#### Step-by-step examples

1) Two children share three bars of chocolate *.*

First, they each get one.

Two bars gone. One red left.

Then, they share the red *bar*, to get a half each.

In total, each child will have one-and-half bars.

2) Four children share five bars of chocolate.

First, every child gets one.

Four bars taken. One green remaining.

Next, they share the green bar and get a quarter each.

Therefore, every child will receive a total of one and a quarter bars.

3) Four children share seven bars of chocolate.

First, every child gets one bar.

Four bars gone. Three blue left.

Now, let’s divide *each* blue bar into *quarters* to share for *four* children.

The children share *every* blue bar to get a quarter from each whole bar.

*See the different shading/hatching patterns.*

Hence three quarters, 3 x ¼. Or three-quarters of a whole, ¾.

Finally, the share of each child adds up to one and three-quarters.

That is how top-heavy fractions change to mixed fractions.

**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!

#### Step-by-step examples

a) The first two children have one and a half bars each.

That makes three whole bars shared by two children or 3/2.

b) The next group of four children have one and a quarter bars each.

Every two of them will have two and a half bars.

Therefore, a group of four children will have twice of that of two children!

*That is, double. Then double again.*

The result is five bars shared by four children or 5/4.

c) The last four children have one and three-quarters each.

Now, every pair of children will have three and a half bars each.

Finally, this group of four will share seven bars of chocolate or 7/4.

That’s how mixed fractions (mixed numbers) go back to top-heavy fractions (improper fractions).

**Tip**!

**Tip**!

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)*.

**Further readings**:

1) *Colouring/shading fraction shapes and tracing shapes, images & text*

2) *Illustrated, visual fractions*

or

*
(Also, available as a workbook, colour workbook and colour e-books)*.

3) *How to add visual fractions*

or

*(Also, available as a workbook and colour workbook)*

__Series 1__

Colouring Workbook | Paperback | Colour Paperback |

Workbook | Colour Workbook | Colour eBook |

__Series 2__

Colouring Workbook | Paperback | Colour Paperback |

Workbook | Colour Workbook | Colour eBook |

Series 3:

*Coming soon!*

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