## Friday, 21 February 2014

### Investigation: Algebra

There are two questions for you to attempt over the weekend.

Question 1 - To be done on a piece of writing paper.

QUESTION 1
Investigate the following question and prove that they are similar / different.

QUESTION 2
Which is larger, 5 + n or 5n?

1. Question 2
It depends,as if n is 1,5+n would be bigger than 5n because 5+1 is 6 while 5n would give us 5(1)=5.However,for numbers bigger than 1,5n would be bigger than 5+1.For example,if n is 5,5n would give us 5(5)=25 while 5+n would give us 5+5=10.

2. 5n is larger than 5 + n because if n is 5, 5 x 5 will be 25 while 5 + 5 will be 10. But if the value of n is 1, none of them is larger than the other.

3. It depends on the value of n if n is 10, 5+10=15 and 5 x 10=50, so 5xn is bigger. But if n = 1, n+5=6 while n x 5= 5 and n+5 will be bigger

4. There are two answers to this question.

If the value of n is 1 or smaller, then (5 + n) > 5n.
For example, if n = (-1), then 5 + (-1) = 4 and 5n = (-5) and therefore 4 > (-5) and
(5 + n) > 5n.

If the value of n is 2 or larger, then 5n > (5 + n).
For example, if n = 4, then 5(4) = 20 and 5 + 4 = 9, therefore 20 > 9 and 5n > (5 + n).

5. 5n is usually bigger than 5+n in most situations except this condition-> (when n is 1)
5n=5x1=5 which is smaller than 5+n=5+1=6. In other situations, (e.g.when n is 2 or 6)
5n=5x2=10 which is bigger than 5+n=5=2=7 / 5n=5x6=30 which is also bigger than 5+n=5+6=11 and in some situations, both are the same.

6. It depend on what number is n.If n is 1, 5+n is bigger .If n is 2,5n i bigger.

7. It depends on what number is n. it can be any number like 8, 10. Sometimes, 5n can be bigger than 5+n, but some other time, 5+n is bigger. and most rarely, they are the same

8. 5n would usually be larger than 5+n when n is 2 or more but when n is 1, 5+n would be larger than 5n.

9. It really depends on the value of n but usually 5n is bigger except if n is 1 or 0 then 5+n will be bigger.

10. In this case, both of them can be larger than the other. Because, if n= 1, 5+n will be 5+1=6 and 5n= 5x1=5, so 5+n will be larger. However, if n= is a number that is greater than 1, example: 2, 5+n= 5+2=7 and 5n= 5x2=10, so 5n will be larger.

11. This comment has been removed by the author.

12. Second Question
Which is Larger, 5 + n or 5 N
Let N be 4
So 5 + N = 5 + 4 = 9
So 5 N = 5 of N = 5 x 4 = 20
so obviously, 5 N > 5 + N
However, It can be 5 + N > 5 N because:
Let N be 1
So 5 + N = 5 + 1 = 6
So 5 N = 5 of 1 = 5 x 1 = 5
So as you can see, it really depend on what is the number.

13. The answer to this question varies, it is based one the value of the algebra. For example, If n=1, 5+n= 5+1=6, 5n= 5x1=5. For this case 5+n is greater than 5n.
For another case, if n=5, 5+n= 5+5=10, 5n= 5x5=25. In this case, 5n is larger than 5+n, thus the answer of this question varies. It can be either larger or smaller than the another number.

14. 5+n or 5n can be larger as the value of n can determine which one is larger.If n is 2 ,then 5+n will be 5+2 which adds up to 7.For 5n , it would be 2x5 which is 10. Thus 5n would be larger in this scenario.In another scenario,if n is 1,5n+1 would be 6 and 5n would be five. Therefore 5+n can also be larger

15. There are various answers to this question.
1)If the value of n is smaller than/equals to 1,then (5 + n) < 5n.
E.g (5+1 = 6 ) ＞(5x1)
2)If the value of n is greater then 1,then 5n > (5 + n).
E.g
n = 4, then 5(4) = 20 and 5 + 4 = 9, therefore 20 > 9 and 5n > (5 + n).

16. It really depends, because if "n" is 10, 5 X 10 is 50, while 5 + 10 is 15, so in this case, 5n is larger than 5+n.

But, if "n" is 0.5, 0.5 X 5 is 2.5, while 0.5 + 5 is 5.5. So it really depends what "n" is.

17. Question 2)
If the value of n is 1,then 5n < 5+n as 5xn=5x1=5 and 5+n =5+1=6
But if the value of n is bigger than one e.g. (2 to infinity), 5n> 5+n
because if n is 2, 5xn=5x2=10 while 5+n=5+2=7

18. It depends on what n = to.
Example if n=5
It would be
5+5=10
5x5=25
Example if n=1
5+1=6
5x1=5
By looking at this we understand that it depends on what n = to.

19. It basically depends what n's value is.For example,if n=2 ,then 5+2=7 which is smaller than 5x2=10.However,if n=1,5+n will be larger than 5n as 5+1 is larger then 5x1.

In a nutshell, the result of both will depend on the value of n

20. It depends on the value of n. For instance if n is equal to 1 then 5n is smaller than 5 + n. If n is equal to 4 then 5n is larger than 5+n

21. It totally depends on what n equals to e.g. if n equals to a negative integer or less than 1 ,then 5n would be smaller,but if n equals to a positive integer larger than 1 ,then 5n would be larger.

22. If n is 1,then5n is smaller because the ans is 5 and 5+n is 6.If n is 2, then5n is greater than 5+n because the ans is 10 and 5+n is 7.

23. 5+n is just 5 added by another n,but 5n means 5 X n.Take an example.Say n is 5.so 5+5=to 10,while 5X5=25.Hence,5n is bigger than 5+n.

24. 5n.Let n be 3. So when adding 5+n=>5+3=8. However 5n represents 5 x n=>so 5 x 3 =15 thus 5n is bigger