Åk 6–9
 
English/Русский

4.3 Division
Division can also be written as a fraction and in the example below it becomes even clearer if we rewrite them that way.  We begin to explain with a few basic examples:

You hopefully know that
8
8
= 1 and that,
62
62
= 1.


With this then
a
a
equal to 1 a
a
a
= 1.  

If you check the answer by multiplying you get 1· a = a, which is correct.

We can also say that
b · c
b · c
= 1 because the numerator is equal to the denominator.

To simplify the fraction, we normally use simplification by division.  Here are a few examples where we divide both the numerator and denominator with the same number or variable.



A.
3 · a
a
= 3
3 · 2
2
= 3




B.
15 · x3
x
=
15 · x · x · x
x
= 15x2

15 · 6 3
6
=
15 · 6 · 6 · 6
6
= 15 · 62




C.
15x4
5x2
=
3 x4
x2
=
3 · x · x · x · x
x · x
= 3x2

15 · 44
5 · 4 2
=
3 · 44
42
=
3 · 4 · 4 · 4 · 4
4 · 4
= 3 · 42




D.
a2
a5
=
a · a
a · a · a · a · a
=
1
a3
= a2-5 = a-3

32
35
=
3 · 3
3 · 3 · 3 · 3 · 3
=
1
33
= 32-5 = 3-3