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. 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
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 onefourth of the pizza. How can we rearrange the slices so you see the onefourth? 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. Eating 2 slices out 8 is the same as eating 1 pile out of those 4 piles.
We can then write
Although they both have different numerators and denominators, they are both equal.
1
4
which is also equal to 0.25 or 2/8
Something interesting!
Other examples are:
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.
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