Chap 4 Algebra... Which is larger in magnitude?

Which is larger in magnitude?

5 + n or 5n

Explain your answer clearly with examples.

Enter your response in comments (this is part of your daily work...)

29 comments:

  1. 5+n is having 5 units plus n units, but 5n is 5 times of n, making it much bigger

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  2. Hi Zheng Jie

    Wow! what an early response :D
    Well, perhaps you could further elaborate with examples (i.e. using numbers?)

    :D

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  3. This comment has been removed by the author.

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  4. Take n as 2

    5 + 2 = 7

    while

    5 x 2 = 10

    Thus 5n is bigger.

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  5. When it is 5 + n, it is only 5 and n added together. Whereas 5n is 5 times of n, therefore, 5n is larger.

    eg.

    2 + 4 = 6
    2 x 4 = 8 (larger)

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  6. Let "n" be 10.

    5+10=15

    5x10=50

    So, 5n is bigger than 5+n.

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  7. 5n is larger in magnitude.

    Let "n" be 5.

    5 + n
    = 5 + n (5)
    = 5 + 5
    = 10

    5n
    = 5 X n (5)
    = 5 X 5
    = 25

    From the example, we can see that 5n is larger than 5 + n.

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  8. I think that 5n is larger in magnitude than 5 + n.

    As we all know multiplying numbers verses adding the same numbers. By multiplying the numbers, the equation will be much more than adding the numbers.

    Let me give you an example...

    n = 20

    5 + n = 5 + 20
    = 25

    5n = 5 x n
    = 5 x 20
    = 100

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  9. 5n is larger by magnitude.

    5 + n is only the addition of of the algebraic expression and 5.However,5n is 5 times of n,which is larger.

    eg.

    let n be 5.

    5 + n

    =5+5

    =10

    but,

    5n

    =5x5

    =25

    hence,5n is larger by magnitude than 5 + n

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  10. 5n is larger in magnitude.

    Let's pretend that n means 2

    5 + n = 5 + 2
    = 7

    while

    5 x n = 5 x 2
    =10

    so the above proves that 5n is bigger than 5 + n

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  11. 5n is larger in magnitude.

    Example of why 5n is larger in magnitude than 5+n:

    Let 'n' be 3,

    So 5+n=5+3=8,

    While 5n=5x3=15,

    So 8<15,

    This concludes that 5n is larger in magnitude than 5+n.

    Please note: 5n is the simplified term in algebra that is equal to 5xn.

    Benz Kew

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  12. Thanks to all the inputs so far...

    While the examples given so far shows that magnitude of 5n is bigger than 5+n, does anyone out there think their choice of "n" is biase?

    Would someone brave enough to 'prove' that 5n is less than 5+n?

    Cheers!

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  13. What if I were to use a negative integer?

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  14. @Miss Loh:

    Yes, "n" may be bias. If "n" is 1 or 0, then the sum of 5+n is 6 and 5 respectively while 5n is 5 and 0 respectively.

    To prove it: (Let's compare)

    If "n" is a 1,
    5+n=5+1=6, while
    5n=5x1=5,
    so 6>5.

    If "n" is a 0,
    5+n=5+0=5, while
    5n=5x0=0
    so 5>0.

    @Mr Koh:

    If you were to use a negative integer,
    then let "n" be -2.
    So 5+(-2)=3, while
    5x(-2)=(-10),

    This shows that an addition of a negative integer is more than a multiplication of a negative integer when they are added up. It also can refer to Miss Loh's question that it may be bias as "n" may be a negative integer.

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  15. This is another explanation of mine to show that 5n might be less than
    5 + n is this...

    As we all should know when a positive integer is multiplied by a negative integer the equation will be negative while the sum of a positive integer and a negative integer will be less.

    Let me give you an example...

    n = -20

    5 + n = 5 + -20
    =-15

    5n = 5 x -20
    =-100

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  16. @Richie

    Ah! U let the "meow meow" out of the bag!!!

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  17. Benz and Jasper:

    Good try! U both are very close.
    Are we able to zoom into some specific number so that when N crosses this figure, it affects outcome such that
    5N becomes greater than 5+N
    or
    5N becomes smaller than 5+N

    Cheers!

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  18. Let 5n = (5 + n)
    then 5n -(5+n)=0
    => 4n - 5 = 0
    => n = 5/4 = 1.2

    when n= 1.2, 5n - (5+n)
    n> 1.2 means 5n> (5+n)
    n< 1.2 means 5n < (5+n)

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  19. Ah! Could someone surface any careless 'error' in response by "mancity" ?

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  20. It depends.(To the original question,not 'mancity's response)
    If n is 1 or less,5+n would be greater than 5n
    If n is greater than 1,5+n would be less than 5n.

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  21. There may be different answer according to what the value 'x' is.
    For example,if the value of 'x' is 1,the answer for 5+n = 5+1 = 6. While,5n = 5 x 1=6.
    OR
    If n = 2, 5+n = 5+2 = 7 and 5n= 2 x 5= 10

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  22. Of course , 5n is bigger in value than 5 + n as 5n is 5 times the value of n. For example , let us take n as the number 3.
    n = 3
    5n = 15
    whereas ,
    n = 3
    5 + n = 8.
    So, 5n is definitely bigger than 5 + n

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  23. Let's look at Abilash's reasoning... hm... Do the rest agree?

    By the way, what happens if n is a non-whole number?

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  24. Surely, 5+n is bigger than 5n
    as 5n = 5 x n
    and 5+n = 5 + n
    So 5n is bigger.

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  25. 5n which is in most situations mostly bigger than 5+n because of the fact that naturally it is bigger. For example 5*2=10, 5+2=7.

    But also there are several cases when this 'belief' is proved wrong. If you take 0 or 1 as the value of n, you can see that 5+n actually is bigger than 5n.
    n=0,
    5*0=0, 5+0=5
    n=1,
    5*1=5, 5+1=6
    Also, if n represents a negative integer, 5n would be smaller than 5+n
    5*(-8)=-40, 5+(-8)= -3

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  26. It might be 5n bigger than 5+n but it could also be 5+n that is bigger than 5n but the outcome depends on what the value of n is. If n is 0 or 1 or a negative number, 5+n is bigger than 5n but if n is a number that is 2 or more, 5n is bigger than 5+n. Thus there are no correct answer to your question because either way are right.

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  27. 5+n is lesser than 5n in magnitude because...
    If n=2 ...
    5+n=5+2
    =7

    5n=5xn
    =5x2
    =10

    Since 10 is more than 7,we can conclude that 5n is bigger than 5+n.

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  28. 5n will always be the biggest Let me show you why...

    If, n=3
    5 + n = 8
    5 x n = 15

    If, n=12
    5 + n = 17
    5 x n = 60

    Try any number and you will realise that 5n is always bigger than 5 + n.

    You might be wondering why...Well I will show you.

    5 + n = to 1n and 1 no.5
    5 x n = to 5ns

    So only if n=1 5n will always be larger in magnitude than 5+n.

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