## 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. 5n is larger as 5n is 5xn which is 5 groups of n, 5+n is just adding n to 5

2. 5n is larger. 5n is 5 groups of n while 5+n is 5 being added to n.

3. 5n is larger as it simply 5 ^n which is equals to n+n+n+n+n but 5+n is small because it is just adding n to 5

4. 5n is larger than 5+n. This is because, when 5 is multiplied by n, it means 5 groups of n. Whereas, when 5 is added by n, it is smaller than 5 times n. The solution can also be done by substituting a whole number into `n'. Then we can see which answer is bigger, n+5 or n^5. Whereas, the answer will differ when n is substituted by 1. When it is substituted by 1, 5+n will have a greater value when compared to 5^n

5. 5n. Because 5n is 5xn while 5+n is just 5 ADDED to n.

6. Only if n is less or the same as 1, 5+n is bigger but if n is more than 1, 5n is bigger.

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8. Question 2: 5n is larger as 5n is 5 multiplied by n while 5+n is adding 5 and n

9. 5n is larger as 5n=5xn while 5+n is smaller as it is addition

10. 5n is larger as 5n means 5xn,five groups of n,while 5+n is equals to five and n only .

11. It depends on what the number n is. If n is less than 1.25, than 5+n would be bigger than 5n. However if n is larger than 1.25, than 5n would be larger than 5+n

12. It depends on the value of n because if n is negative or less than 1.25, 5+n would be bigger than 5+n but if n were to be more than 1.25(thks nicholas) 5*n would be greater

13. 5n is greater than 5+n as 5n is 5 groups of n while 5+n is just the addition of 5 and n together. However, if n is the same or less than 1, 5n would be smaller than 5+n

14. 5n is greater than 5+n (in terms of algebra, not what the value of n is) as 5n 5xn while, which is 5 groups of n while 5+n is only adding 1 group of n to 5

15. It depends on the value of n. Basically, 5n is equals to 5 groups of n while 5+n is just adding 5 to n. 5n is greater then 5+n if the number is above 1. For example, take n as 2, so 5*2=10 while 5 + 2=7. However, if the number is below 1 or negative, 5n is smaller than 5 + n. For example, take n as 0, so 5*0=0 while 5 + 1=6.

16. It depends on the value of n.
If the value of n is 0, 5 x n=5x0
=0

5 + n=5+0
=5
If the value of n is 1,5 x n=5 x 1
=5

5 + n=5+1
=6

However,this is the only 2 exceptions.If the value on n is greater than 1,5n would be greater.

5n is 5 groups of n,while 5+n is only n plus 5.

Example: 5n=5x2
10

5+n=5+2
=7

Since there is a higher possiblity that 5n is greater than 5+n...

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Explanation:If n is 1.25, then 5+n is bigger. 5+1.25=6.25 which is bigger than 5*1=6.25.
If n is bigger than 1.25, then 5*n is bigger. 5*n(Bigger than 1.25)=n+n+n+n+n which is bigger than 5+n(Bigger than 1.25)=5+n
Conclusion :Depends

19. It depends on the value of n.
If we take 'n' as 1,

5+n=5+1
=6

5n=5 x n
= 5 x 1
=6

In this case 5+n is greater.

If 'n' is 2,

5+n=5+2
=7

5n=5 x n
= 5 x 2
=10

In this case 5n is greater.
Hence the it depends on the value of n.

20. It depends on the value of n.
if the value of 'n' is 0 or 1,

5n will de smaller than 5+n.

If the value of n is more than 2,

5n will be greater than 5+n

21. 5n is bigger than 5+n because 5n is 5 x n where the other is 5+n which results in a different number.

22. 5n is bigger because
5n = 5*n
while
5+n = 5+n
Hence,
5*n > 5+n

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26. It depends on the value of n

If n is 1 or lower,
n=1 or lower
5n=5 or lower

5+n=6

5+n is more.

If n is 2 or higher,
n= 2 or higher
5n=10 or higher

5+n=7

5n is more.

27. 5n is larger.
5n = 5*n