Simplification of fractions is most useful when a fraction is almost literally ugly and could be written in a simpler way, i.e. with smaller numbers. This is most often needed at the end of a task or for fractional equations when a fraction is too difficult to calculate.
What does simplifying fractions mean?
The simplification of fractions is essentially the the expansion of fractions the reverse. The aim is to keep the value of the fraction unchanged, but still write it down in a much simpler form, with smaller numbers.
To understand the simplification of fractions, you need to know the fragments of.
Simplifying fractions means dividing the numerator and denominator of the fraction by the same number so that the value of the fraction does not change.
Let's see it in practice!
Simplifying fractions step by step
To simplify fractions, the following rule is applied:
A fraction is simplified by dividing its numerator and denominator by the same integer.
At this point I would like to draw your attention to three things:
- You cannot simplify by 0: since dividing by 0 is meaningless, you cannot simplify to 0.
- You cannot simplify by 1: if you divide a number by 1, you get the same number (3:1=3), so it is impossible to simplify by 1.
- You can only simplify a fraction with a divisor (that you divide by) that can divide both the numerator and the denominator.
Let's look at a concrete example of simplifying fractions.
4 and 8 can also be divided by 2, so:
As you can see, it is still not the right one, because 2 and 4 can be divided by 2:
To avoid always having to divide by another number (here we divided by 2), there is a quicker solution.
The secret is to find the numerator and denominator the biggest common dealer.
You can tell the greatest common divisor of 4 and 8 by heart: it is 4.
Once you have this, you can simplify a fraction in 1 step, very quickly:
Of course, in mathematics, it makes no difference what method you use to simplify a fraction. You can do it in one or more steps. The point is to get a good result.
And if you are solving a fraction problem, you are done if you have simplified the fraction, i.e. written it in its simplest form.
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