## Tuesday, 14 February 2017

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

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

This question is compulsory.

1. 5n is larger. If we take n as 5, 5+6=11 while 5x6=30.

2. Both depending on the number n.

if n is 2,
5+2=7
but,
5x2=10

however, if n is 1,
5+1=6
but
5x1=5

1. Good observation :)

3. 5n. 5n is 5 x n. But 5 + n is 5 added to n
if n is 10, then 5 + n = 5 + 10 = 15
and 5n= 5(10) or 5 x 10 is 50

4. Let's say n is 10. 5+10 is 15. So, 5n is 5x10 which is 50. So 5n is bigger than 5+n.

5. It depends on the value of n. If n is of a large value, eg. 2, then 5n will be larger. If n is of a smaller value, eg. 1 then 5+n is larger.

1. Good observation

6. 5n is larger in magnitude.
Example: if 10 is n,
then (5+n) will be (5+10)=15
However, 5n will be (5xn)=(5x10)=50
Thus, 5n is larger in magnitude.

7. 5n is 5xn (multiplication) while 5+n is adding 5+n (addition). As a variable multiplied by a number will always put the variable at the back of the number without any extra symbols while adding a variable and a number would require a "plus" sign. For example, 5x8=40, but 5+8=13. Therefore, 5n is larger than 5+n.

1. Your explanation does not quite tell how you arrived at your conclusion (that is, 5n is larger). You were describing the operational aspect.

8. 5n is larger. 5n means 5 times of n while 5+n means just adding 5 and n. For example, if n is 6, 5+6 would be 11 while 5x6 would be 30.

9. It depends on the value of n. If n is smaller or equal to 1, 5 + n will be larger than 5n as for example, 5 + n = 6 but 5n = 5. However, if n is larger than 1, then 5+n will be smaller than 5n. For example, if n = 2,5 + n = 7 while 5n = 10.

1. An answer that takes into account the 2 "ends" of the numbers. Good.

10. Lets say, n is 2. So 5+n will be 5+2 which will be 7. So 5n will be 5x2 which will be 10. Hence, 5n is greater in magnitude than 5+n.

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12. It depends what the number n is. For example, if n=1, 1+5=6 which is bigger than 1x5=5, which means that 5+n is larger. But also, for example, if n=5, 5+5=10 is smaller than 5x5=25, which means that 5n is larger

1. Good observation.

13. If n=1, then both the digits would be equal; however, if n=2 or more, 5n would be bigger than 5+n e.g. n=2 , so 2x2x2x2x2=32 . 5+2=7

1. Good observation

14. 5n is larger in quantity as 5n is about 5 times larger than 5+n. 5n is five times of n so 5+n is lesser. Take 4a and 4+a as an example. 4a is 4 times of a so 4+a is lesser.
4+a is one 4 and one a so it is lesser.

1. You are making an attempt to generalize.
Before generalising, d test with several numbers first.

15. if n=2, 5n would be greater because multiplying a positive number would make the value larger
but, if n=-2, 5+n would be larger because multiplying negative number would make the value even smaller

1. it also depends on the value of the number

2. You have make a good point - using negative number will bring out an obvious difference.
Your explanation can be further refined.

16. 5n is bigger 5n=n+n+n+n+n vs 5+n=5+n.
But if n is 1, 5n=1x5
5+n=6 then 5+n would be bigger

1. if n is smaller or equal to 1 then 5+n would be bigger

2. Good observation.
You have made a partial conclusion in the "reply" - for numbers smaller or equal to 1
Whereas in your original posting, you have not quite concluded the case on the kind of n values will meet the criteria for 5n is larger.

17. It depends.
if n is 1 and smaller, 5 +n would be larger
if n is 2 and larger, 5n would be bigger.
Example 1: if n=3
5+n=8
5n=15
Example 2: if n is 8
5+n=13
5n=40

Example 3: n=1
5+n=6
5n=5

So it really depends

1. Good observation and illustration.

18. It depends. For example, if n is equal to 3, 5n equals 3x5=15 while 5+n equals to 5+3=8 and so 5n is larger. However is n=1, 1x5=5 and 5+1=6 so 5+n would be larger. So in conclusion, it depends on what n is equal to

1. An answer that takes into account the 2 "ends" of the numbers. Good.
However, your generalization can be sharpened if you carry out testing with converging n values

19. Both can be larger in magnitude depending on the value of n.
(5n = 5*n)
If n is 1, "5+n" will be larger as 5+1= 6 while 5*1=5.
If n is 3, "5n" will be larger as 5*3=15 while 5+3=8.

1. Good observation,
How could we sharpen the justification so that the conclusion can be more specific.

20. 5n is larger than 5+n as n it could be any number, for example n=5. 5x5=25 which is obviously larger than 5+5=10. However for some instances if n=1, 5+n is larger than 5n . since 5x1=5 while 5+1=6. Hence it is not stated that 5+n is always bigger than 5n, or the other way round hence there is no conclusion on which is larger.

1. If you write out the numbers, n, systematically to carry out the testing, you would be able to draw a conclusion based on your observations

21. Example 5 plus n equals 6 will give u 11
but 5 multiplies by 6 will give you 30
My assumption made was both n had same values so 5n is larger

1. You need to carry out testing with a wider range of numbers before making a conclusion.

Also, to improve the clarity of what you described in the 1st line, you could start with...
"If n = 6, 5 plus n will give 11"

22. It depends in the value of n.
e.g.
n=1
5 + n=6
5n=5
In this example, 5+n is larger. However, if it is a bigger number such as 2:
n=2
5+n=7
5n=10
Thus, in this example, 5n is bigger

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24. I will assume that 5n is larger as it is 5xn. e.g.When a number is multiplied by another number, it will be larger than the same expression that uses addition instead of multiplication. If n is 1, then the vice versa will occur.

25. It depends on the value of n. If n is a negative number, 5+n will be bigger. If you use a positive number, 5xn would be larger. For example, 5+-1 will give me 4 while 5x-1 would give me -5.

26. The answer depends on the value of n.
If n=1,
5+n
=5+1
=6

5n
=5x1
=5
5+n>5n

If n=2 or more,
5+n
=5+2
=7

5n
=5x2
=10
5+n<5n
Therefore the answer depends on the value of n.

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28. 5n is bigger than 5+n.
5n is 5 x n or n+n+n+n+n while 5+n is basically just 5+n.
If n is 2, then, 5n would be 2x5 or 2+2+2+2+2 which would be 10, however, 5+n would just be 5+2 which would be 7.However,If n is 1, 5+n would be bigger than 5n.As 5n would be 1+1+1+1+1=5 while 5+n would be 6.
Thus, I conclude that 5n is bigger than 5+n if n is a number above 1 and 5+n would be larger than 5n if n=1 and below.

29. 5n is bigger than 5+n.
5n is 5 x n or n+n+n+n+n while 5+n is basically just 5+n.
If n is 2, then, 5n would be 2x5 or 2+2+2+2+2 which would be 10, however, 5+n would just be 5+2 which would be 7.However,If n is 1, 5+n would be bigger than 5n.As 5n would be 1+1+1+1+1=5 while 5+n would be 6.
Thus, I conclude that 5n is bigger than 5+n if n is a number above 1 and 5+n would be larger than 5n if n=1 and below.

30. The answer depends on what is the value of n. For example, if n = 1, 5 + n would give you 6 while 5n would give you still 5.
If n = (number bigger than 1), 5n would be bigger as eg n=10
5n = 50
5+n = 15
Thus, 5n is bigger