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
and we call 2 the numerator and we call 8 the denominator.
A (/) can also be used to separate the numerator with the denominator.
is more appealing, we prefer to use it instead of 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.
Eating 2 slices out 8 is the same as eating 1 pile out of those 4 piles.
We can then write
which is also equal to 0.25 or 2/8
Although they both have different numerators and denominators, they are both equal.
Other examples are:
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.
Test your knowledge with the quiz below:
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