1. Simplifying algebraic fractions
Why is
In other words, why is 5 compared to 10 equal to 1 compared to 2?
The reason is very important:
Factors
Factors
and we can preserve the value of the comparison by dividing away a factor of 5 from both the numerator and the denominator at the same time.

2. NOTE: When simplifying a fraction, we are writing down the smallest possible values of the numerator and the denominator whilst STILL PRESERVING THE VALUE OF THE FRACTION…
DON’T EVER FORGET THAT A FRACTION IS SIMPLY A RATIO i.e. IT IS A COMPARISON BETWEEN THE VALUE OF TWO QUANTITIES (a numerator and a denominator) OF THE SAME KIND.
In other words, both 1 and 2 are smaller than 5 and 10 but 1 still half the value of 2 and 5 is still half the value of 10.
The only two operations that allow us to simplify a fraction and preserve its value are MULTIPLICATION and DIVISION.
DON’T EVER FORGET THIS!!!!!!!

3. 100 is half of 200, right??
70 is half of 140, right??
In both cases, the smaller quantity is half of the larger quantity … and that common sense is what tells us to write:
The only two operations that allow us to simplify a fraction and preserve its value are MULTIPLICATION and DIVISION.

4. So, it seems that we always have to factorise numerators and denominators if we are to simplify a fraction and preserve its value.
Is it true to say that: ?
OF COURSE IT’S NOT TRUE!!!
SO THIS COMMON SENSE IS WHAT SHOULD STOP US FROM THINKING AND WRITING THIS:
Junk alert!!!

5. Grade 9 - Simplifying algebraic fractions1.
Have we preserved the value of the fraction? Well, let’s see …. Let x = 5 and y = 2:
We have preserved the value of the fraction by factorising numerators and denominators and dividing away factors common to both numerator and denominator.

6. Grade 9 - Simplifying algebraic fractions

7. Grade 9 - Simplifying algebraic fractions
1. Factorise the numerator (if possible)
2. Factorise the denominator (if possible)
3. Divide away factors common to the
numerator and denominator
4. Write down the fraction in its simplified
form