## Friday, 13 February 2015

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

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

This question is compulsory.

1. 5n. This is because 5 + n is n with an add on of 5, while 5n is 5 x n

1. let's say n is 10.
5 + 10=15 while 5(10) is 50.
Obviously 5n is greater

2. If the variable represent 1, then 5 + n is greater

3. Marcus, based on the examples you used to illustrate the 2 possible scenarios, what assumption(s) did you make about the type of number you use?

4. Good thinking.
2 points for Group 4

2. 5n. 5n is 5 times of n while 5+n is n added to 5. Unless n is a smaller value than 1.

1. Benedict

Good try.
Illustrate the point with examples to make it clearer.
In addition, what assumption(s) did you make about the type of number you use here?

2. 1 point for Group 2

3. 5n
5n is 5xn.so it is bigger. but if n is 1, 5+n is bigger as 5+1=6 while 5x1 is 5

1. Hsien Kit

Based on what you have described, extend it beyond testing with the number "1" and elaborate on the possible scenario.

1 point for Group 2

4. Both can be the answer as if n is 1, 5x1 is smaller than 5+1

1. I mean either one can be larger as if n is 3 5x3 is larger than 5+3

2. Celine

Good thinking.
Now, do the 2 scenario work with just those 2 numbers you have illustrated with?
Think of how to generalising it.
In addition, what assumption(s) did you make to the choice of number you used here?

2 points for Group 1

5. 5n.because 5n is 5xn and 5 +n is 5+n
imagine n is 5
so 5x5 =25 and
5+5=10

1. it depends.
if n is 1 then
5xn=5
5+1=6

2. Jerremy

Good thinking. You have presented 2 scenarios. Are there more scenario?
What assumption(s) did you make about the numbers you use to illustrate the scenarios?

2 points for Group 3

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1. If n is smaller than 1 then 5 + n is bigger.
If n is equal to 1 then 5 + n and 5n is equal.
If n is more than 1 then 5n is bigger

2. Good thinking, Tjin Yao.

You have stated 3 possible scenarios.
However, you'll need to check line 2 "If n is equal to 1 then 5 + n and 5n is equal."
Substitute n = 1 into 5 + n and 5n respectively.
Do you get the same value?

In addition, what assumption(s) did you make about the numbers you use to illustrate the scenarios?

3 points for Group 2

7. both can be bigger than each other. 5xn will be bigger than 5+n but if n=1 than 5+n is bigger

1. Ming En

In this case, you have presented 2 scenarios - however, you mentioned that if n = 1, 5 + n is bigger.
How about other values of n? Will 5n always be bigger than 5+n?

What assumption(s) did you make about the numbers?
1 point for Group 3

8. It depends. if n is 1 then n+5=6 but 5n is 5x1=5. But if n is 2 then n+5=7 then 5n is 2x5=10

1. so 6 is bigger than 5 but 7 is smaller than 10

2. Kevin

You can identified 2 critical numbers that tell the difference - 2 scenarios.
Now, can you generalise what you have described?

In addition, what assumption(s) did you make about the numbers you chose in these 2 scenarios?

2 points for Group 2

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1. uh...wait...change make it as both answers. if n=1, then 5+1=6 and 5x1 equals to five and taking the example from my previous answer. so both re correct

2. Amanda, you have deleted your previous posting.
You've forgotten to draw a conclusion on what you describe in the comment, " if n=1, then 5+1=6 and 5x1 equals to five".

Try giving a more complete answer.

10. lets say n is 2 then 5 + 2 =7 but 5 x 2 = 10

1. Malcolm, you've shown substitution of n value to each expression.
However, you've not concluded with a complete sentence. so, answer "5n" is.....?
In addition, would also numbers give the some conclusion?
Test them out.

11. It can be 5n and 5+n. If n is 2, 5n=5xn=5x2=10 while 5+n=5+2=7. In this situation, 5n is bigger. But if n is 1, then 5n will be bigger as 5+n gives you 5+1=6 while 5n is 5xn which gives you 5x1=5. In this situation 5+n is bigger. So both answers are correct.

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12. It can be the smaller or bigger. If n is 1 then 5+n=6 which is bigger than 5n which is 5. If n is 2, 5n is 10 which is bigger than 5+n which is 7.

13. 5n

5 x n is different from (5+n)
Let n be 10

As such,

5 + n = 5 + 10 = 15
5 x n = 5n = 5 x 10 = 50

See..............

14. Both can be larger than one another.If n is 1, 5+n=5+1//=6.
5n=5x1//=5.
If n is 2, 5+n=5+2//=7
5xn=5x2//=10.

15. I 5n is bigger because 5+n means that 5 is being added to n. But 5n means n being multiplied by 5, which is bigger then 5+n.

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1. it depends
if n equals 1, 5+n is more than 5n
if n equals 2 or more, 5n is more than 5+n

17. 5n is naturally larger in magnitude, but if n=1, then 5 + n would be larger than 5n

18. 5N DUHHHHHHH 5N!1!1!1 5n is 5 x n while 5 + n is 5 + n

19. It depends on context because 5 + 1 is larger than 5 * 1 but 5 * 2 is larger than 5 + 2.

20. either one could be bigger if n was 0.1 5 time 0.1 would be 0.5 but if n is 9 5 times 9 would be 45 and 9 plus 5 would be 14

21. 5 + n is just adding both together while 5 x n is 5 times n. If n is smaller than or same as 1 then 5 + n is bigger but if n is bigger than 1, then 5n is bigger.

22. 5n is larger in the scenario where n is a positive number, because 5+n is 5 added to n and 5n is n multiplied by 5 example: 5+3=8, 5 multiplied by 8=40. . But in the event that n is a negative number, then 5+n is larger example: 5+-3=2, 5 multiplied by -3=-15