## Thursday, 13 February 2014

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

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

This question is compulsory.

1. If n was a number bigger than 1, then 5n would be bigger than 5 + n. However, if n was 1, then 5 + n would be bigger than 5n as 5 + n would equal to 6 and 5n would equal to 1.

1. What's the assumption?
What if we try a number other than an integer?

2. n represents a number.
If n was the number 1, 5n would be 5x1=5 while 5+n=5+1=6
However, if n was 2 (or larger), the equation of 5n would be 5x2(or the larger no.)=10 , whereas 5=n would be 5=2=7

1. What's the assumption?
What if we try a number other than an integer?

3. If n was 1, 5n = 5 x 1 which is 5 and 5 + n = 5+1= 6. Thus, 5 + n is a larger number than 5n.

1. Have you done enough "testing" of numbers to conclude?

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5. You cannot tell.

If n is 1,
5 + n = 6 (BIGGER)
5n = 5

If n is 5,
5 + n = 10
5n= 25 (BIGGER)

1. You have already tested two cases.
Is that enough to conclude?

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7. It depends on what n value is.

If n is 1, then 5+1=6, while 5x1=5, thus 5+n is bigger than 5n in this scenario.

However, if n is 2, then 5+2=7, while 5x2=10, thus 5n is bigger in this scenario.
Thus, which is bigger depends on the value of n.

1. There's an assumption on the type of "n" value we can use.
What's that assumption?
Can we narrow it down to use one "n" value to explain?

8. you cannot tell because if n were 1 5+n would be larger but if n were two 5n would be larger.

1. You have already worked out one case.
What if you test with other n values?

9. 1) You cannot tell.

2) If "n" is 1
5xn = 5x1= 5
5+n = 5+1 = 6
And in this case,
5+n is larger than 5xn

But if "n" is 2
5xn = 5x2 = 10
5+n = 5+2 = 7
And in this case 5xn is larger than 5+n

1. You've already worked out 2 possibilities.
However, is "n = 1" a good number to test? What's the assumption?

10. 5n is bigger than 5+n only if n is NOT equal to 0 or 1 because if it is, then 5n will be equal to 5x0=0 and 5x1=5 and 5+n will be equal 5+0=5 and 5+1=6 so in both cases 5+n will be bigger.
If n is any number bigger than 1, then 5n will be bigger.

1. There's an assumption in the value of n you are using to test / create the scenario.
It seems like you are testing with WHOLE numbers.

2. Yes. If n=1.25, then 1.25+5=6.25 & 5X1.25=6.25, so both will be the same in that case.
If 1/0=n, then both cases will be the infinity. If (square root of -4)=n, then both cases will be, the Unknown
So, there are 4 possibilities.

11. It depends on what n is. If n=1, then 5+n=5+1=6, and 5n=5xn=5x1=5, so 5+n would be bigger. However, if n=a number bigger than 1, example n=2, then 5+n=5+2=7 and 5n=5xn=5x2=10 so 5n would be bigger.

1. Is "n = 1" a good value to test?
What assumption is did you have about the type of numbers that we can use to test the cases?

12. This depends on what n is.
scenario 1:n=1
5x1=5
5+1=6
In this case,5+n is greater
However,if n=5...
5x5=25
5+5=10
Therefore,in this case,5n is greater

1. Have you tested with enough "n" values?

13. The answer can be either one,here is an explanation and examples.
Explanation:5+n means 5 added together with n while 5n means 5 multiplied by n.
Ex. Take n as 4
5+4(n)=9
5x4=45
In this case,5n is greater than 5+n

However,if n were to be 1 then...
the sum of 5+1(n) would be 6
And 5x1(5n)would be 5
In this case,5+n is greater than 5n.

Conclusion:Unless a specific value is given for n,the answer is indefinite.

1. Actually there are only 3 possible scenarios.
Are you able to determine that special "n" value?

14. The answer is indefinite unless a specific value is given to n.
If n is 1, 5 x n will be 5 while 5 +n is 6. If n is bigger than 1,example 2, 5 x n is 10,while n+5 is 7.Thus the answer can be either one.

1. Is "n = 1" the determining value?

15. There is no answer until we know the value of n.
As, if the value of n is 1,
5+1=6, while 5x1 is 5 so the first one is correct.
BUT,
if n = 2 - 5+2=7, while 5x2=10 so the second one is correct.
So it depends on the value of n

1. So, are you able to determine that specific value of "n"?

16. It could be either as it all depends on the value of n. If n was 1, 5n (5xn) would be 5 while 5+n would be 6, therefore 5+n would be larger in value. However, if n was 2, 5n would be 10 while 5+n would be 7, making 5n the one with the larger value.

1. There's an assumption in the "n" value.
In addition, with different values of "n", the situation/ scenario will change.
What kind of "n" values should we test with?

17. We would not be able to know the answer until the value of n is known.
If the value of n = 1, 5+n = 6, while, 5n = 5.
If the value of n = 2, 5+n = 7, while, 5n = 10.

1. What can you conclude from the last 2 lines?
What's the specific value of "n" that will shade more light in the scenarios arise?

18. It depends what n is. If n is a number larger than one then 5n is bigger. If n is 1 then 5 + n is bigger.
Example: n = number larger than 1 e.g. 2
5n = 2 x 5 = 10
5 + n = 5 + 2 = 7 So 5n is bigger
If n = 1
5n = 5 x 1 = 5
5 + n = 5 + 1 = 6
So 5 + n is bigger

1. Is "n = 1" a good number to test?
What's the assumption you have when choosing this value?

19. if n is 1 , 5+1=6 then 5+n=6
then 5n=5 , which means 5+n is bigger
but
if n is 2, 5+n=7
then 5n=10
which means 5n is bigger

1. Why use "n = 1"?
Why not other values for "n"?

20. Depending on n, if it is larger than 1, 5n is larger.

1. Check again!
What assumption did you have about the "n" value?

21. You can't tell whether 5n or 5+n is larger.
Simply it is because we do not know the value of 'n' .

If 'n' would be '1' , 5 x n = 5 x 1 = 5 and 5 + n = 5 + 1 = 6 . (thus 5+n is larger)

If 'n' would be greater than '1' (let's say 5) , 5 x n = 5 x 5 = 25 and 5 + n = 5 + 5 = 10 . (thus 5n is larger)

1. Are there only 2 scenarios?
Why "n = 1"?
Are there other possible values of "n" to consider?

22. We do not know if either sum is larger because it depends on the value of n, which we do not know.

For example, if n is -1, 5+n would equal to 4, which means that this sum is larger as 5n is equal to -5.

If n is 2, then 5n would equal to 10, which is the larger sum as 5+n would equal to 7.

1. 2 scenarios presented here, and you are using quite diverse values like "-1" and "2".
Are you able to narrow down to a specific special value of n?

23. There can be 3 scenarios
1) 5+n is bigger
2) 5n is bigger
3) They are both the same.

Example for 1)
n=1
5+1=6
5x1= 5
Here 5+n is bigger
Example for 2)
n=5
5+5=10
5x5=25
Here 5n is bigger
Example for 3)
n=1.25
5+1.25=6.25
5x1.25=6.25
Here they are both the same.