## Thursday, 20 February 2014

### Algebra... Which is larger? (I)

Which is larger in magnitude?
5 + n or  5n

This question is compulsory.

1. Take n to be 4 for example.
5+4=9
and
5n=5xn
so
5x4=20
20 is bigger than 9.

This shows that 5n is bigger than 5+n.

1. Are there other "Possibilities"?

2. 5n is larger in magnitude than 5+n.
For example, let n be 5.

Lets do 5+n first:
5+n=5+5
=10

Now 5n:
5n=5*5
=25

25 is bigger than 10, therefore 5n is larger in magnitude.

1. You are using one number to do the testing. What if... you choose n = 1?

3. However, if n=1, then:
5n=5*1
=5
and
5+n=5+1
=6
6 is bigger than 5, so in that particular case only, 5+n is greater in magnitude than 5n.

1. OK, here, you've used n = 1 to test.
Is there any other possibility?

2. If n = 0 then 5+n would be bigger than 5*n. This would also happen if n is equal to any negative number. For instance, if n=-5 then 5*n would be -25, and n+5 would be 0

4. (5n) is greater than (5+n).

For example, n= 3

5n= 5x3
= 15
5+n= 5+3
= 8
But there might be certain cases which are different and thus in those cases, (5+n) is bigger than (5n).

1. Give numbers to illustrate what you try to describe in the last line...

5. Everything is possible. if n=1 then n+5 is bigger but if n=2 then 5n is bigger.

6. If n is 13
5+n = 5+13
= 18
whereas, 5n= 65
So, 5n is bigger.

7. 5n = 5xn
5+n = 5+n

It is impossible to know which is larger as we do not know the value on n.
If n is 1,

5x1=5
5+1=6

In this case, 5+n is bigger than 5n.

If n is 2,

5x2=10
5+2=7

In this case, 5n is bigger than 5+n

8. take n=7 for example.
So 5+7=12
5x7 =35

Even if u take other numbers 5n will still be bigger than 5+n

9. All are possible. It depends on what "n" is. if "n" is below 1, Then the second one will be less. If "n" is more than one, then the first one is less

10. All are possible. It depends on what "n" is. if "n" is below 1, Then the second one will be less. If "n" is more than one, then the first one is less

11. Both can be greater, smaller or equal to each other, depending on n.
If n<5/4, 5+n is greater. If n=5/4, they are the same. If n>5/4, 5n is greater,