Deep Knowledge of fractions!

This lesson will provide you with a solid introduction to fractions. The lesson is deep, so take your time as you read. Do not rush over the information.

Fraction is part of a whole. The following illustrate the concept. The figure has 4 parts and only 1 part of the figure is shaded.

Representation of one-fourth
Now, suppose you go to Domino's pizza, you may order a medium pizza. If your pizza has 8 slices and you did not eat the whole pizza, this means that you only ate parts of the whole pizza.

Let's say you don't have a big appetite and eat only 2 out of those 8 slices. The following figure illustrate the situation

representation of two-eighths
We write  
2 / 8
 and we call 2 the numerator and we call 8 the denominator.


A (/) can also be used to separate the numerator with the denominator.

2 / 8
 = 2/8


Because
2 / 8
 is more appealing, we prefer to use it instead of 2/8


The expression 
2 / 8
  can also mean 2 divided by 8


If you use a calculator, the answer will be 0.25 and 0.25 is a decimal. Don't worry about this now. I will teach you decimals in a different unit.

Common sense also tells us that if we eat 2 slices and there are 8 slices, well, we ate only one-fourth of the pizza.

How can we rearrange the slices so you see the one-fourth? May be you know already!If you don't, try the following:

You make 4 piles with your slices with each pile having 2 slices.

representation of how one-fourth = two-eighths
Eating 2 slices out 8 is the same as eating 1 pile out of those 4 piles.

We can then write  
1 / 4
  which is also equal to 0.25 or 2/8
Although they both have different numerators and denominators, they are both equal.

Equivalent fractions

Equivalent fractions

Something interesting!

1 / 4
 =   
2 / 8


We call
1 / 4
 and   
2 / 8
  equivalent fractions


Something interesting!

1 / 4
 =   
2 / 8


We call
1 / 4
 and   
2 / 8
  equivalent fractions


Other examples are:

1 / 2
 and   
5 / 10


1 / 3
 and   
4 / 12


2 / 5
 and   
4 / 10


Important observations:

Notice that to get from 1/4 to 2/8, all we need to do is to multiply both numerator and denominator by the same number that is 2.

In the same way, to get from 1/2 to 5/10, we can multiply both numerator and denominator by 5.

2/8 and 5/10 are called higher terms. Be careful! It is not because 2/8 is bigger than 1/4 and 5/10 is bigger than 1/2.

Compared to 1/2, 5/10 is a higher term only because it has a bigger numerator and a bigger denominator. However, we saw before that 1/2 = 5/10 = 0.5

Notice too that you can go from a higher term to a lower term. For instance, to bring 5/10 to a lower term, all you need to do is to divide both numerator and denominator by 5. You will get 1/2

Going from higher terms to lower terms means that you are simplifying. To get the simplest form, divide the numerator and the denominator by the largest number that divides into both evenly.

For instance, to bring 10/40 to its simplest from, divide both 10 and 40 by 10. You will get 1/4.



Still struggling with fractions? Get rid of your fears and frustrations once and for all!

Buy my ebook. It offers a thorough coverage of fractions!


Fractions ebook cover




 Homepage                     

 Comparing            

 Adding     

 Subtracting             

 Improper              

 Multiplying                

 Dividing                          

 Complex

 History




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