Cancelling Algebraic Fractions
When working with fractions you can sometimes divide the top and bottom of a fraction by the same number. This is in mathematics is known as cancelling down or simplifying the fraction. You often have to write a fraction in its simplest terms i.e keep cancellng the fraction until it cannot be cancelled any more.
When cancelling you look for fractions where the numerator (top number) and the denominator (bottom number) are both multiples of the same number. This is known as finding the common factor, which you would then use to divide the numerator and denominator number with in order to simplify the fraction as much as possible.
Simplifying 15ab divide by 3ab
When working with algebraic fractions you will sometimes have to cancel the top with the bottom.
In this example to observe exactly what is going on we shall expand the fraction and work it out in parts for example a2 = a x a;
You can see that we have as and bs on top which correspond with those in the bottom. We simply have cancel those out. Below the corresponding bs have been cancelled out;
There is more letters which can cancel out. The as can cancel out as well.
This leaves;
15 can divide with 3, so we can cancel this out as well;
The answer becomes;
Simplify 3a+6 divide by 3a
We need to factorise the expression. This expression is quite vague, it appears like we can cancel down the as as it is but we could not and cannot. First we need to factorise the top part, we know that
This is where your factorising skills will be useful. When you factorise the numerator you get;
We continue by cancelling out the 3s from the fraction as shown below;
So the final answer for this division becomes;
Simplify 4ab + 8a divide by 12a
Again with this problem, we have to factorise the numerator first. 4ab + 8a2 becomes;
Now we can cancel out as shown below;
Notice the top and bottom are multiples of 4 so we can reduce these as shown below;
That leaves;
Simplifying 2x + x – 3 divide by x – 1
The division is a much more complex problem. In this variation we have to factorise both the numerator and the denominator. We know that;
Here we use the difference of two squares;
[formulae id=”9″]
x² and 1 can be treated as two square numbers…
The answer to the question becomes;
What needs to be cancelled out becomes very clear once you have factorised the expressions;
Therefore the answer becomes;
