Wednesday, 27 February 2013

Algebra... Which is larger? (I)



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

Explain your answer clearly with examples.


Enter your response in Comments.
This question is compulsory.

42 comments:

  1. It depends. If n is 1, then 5+n(6) is more than 5n(5)
    But if it is more than 1, 5n is more than 5+n.

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    1. Are you able to tell the number that determines which is larger?

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  2. 5n. 5+n is addition, however 5n is 5 multiplied by n. Therefore, 5n is bigger

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  3. The answer is 5n.5+n is just n added to 5 whereas 5n is 5 multiplied to n.So 5n is bigger.

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  4. 5n. take n = 5.

    therefore , 5n = 5 x 5 = 25
    5 + n = 5 + 5 = 10

    thus 5n is larger in magnitude

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  5. 5n is bigger.
    5+n is just adding the number5 and n.
    5n is multiplying 5 with n.

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    1. What happens to 5n if n is a negative number?

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  6. 5n. As 5n is 5*n, which is multiplication while 5+n is only addition

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    Replies
    1. Test this out with a range of numbers!

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  7. it depends as if n is a negative no. then 5n will be smaller but if n is a positive no. then it will be bigger

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    1. The claim is, as long as n is positive, 5n is always bigger.
      Test this out with positive proper fractions.

      Delete
  8. This comment has been removed by the author.

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  9. It depends. If n is 1 or if it is a negative number 5n will be smaller than 5+n. However if n is more than 1(not including), 5n will be bigger than 5+n

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    1. Is n = 1 the value that determines when which one is larger?

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  10. 5n is larger. (If n is a positive integer) as compared to 5+n.

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    1. Ok, an assumption made is, n is an integer.
      What if it's a set of real numbers? Does the claim still stand?

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    2. The things written on the board related to this qn.
      If n=1, 5+n>5n
      If n=2, 5+n<5n
      If 5+n=5n, move n over to the 5n side to become -n. Thus, the equation becomes 5=5n-n=4n, n=5/4=1.25

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  11. If n is negative then 5n would be smaller (5 x -3=-15 is smaller than 5 + -3=2) ,
    however if n is positive then 5n is bigger.
    However if n were a decimal then it would be smaller. (0.2 x 5=1, 5+0.2=5.2)

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    1. Good observation.
      So, what is the value that determines the change in 'status'?

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  12. 5n is larger than 5+n because 5n is 5*n and 5 + n cannot be larger than 5 times of n

    i.e. Take n = 5
    5n = 5*5 = 25
    5+n = 5+5 = 15
    25 is therefore larger than 15.

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    1. I forgot to mention if n is a positive integer.

      If n is a negative integer,

      n=-5
      5n = 5*-5 = -25
      5 + n = 5 + -5 = 0
      And therefore 0 is larger than 25 which means 5+n is the larger number now.

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    2. Good explanation.
      This makes an assumption that the number is an integer.
      What happens if n is a real number.
      Does the same apply?

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  13. 5+n is smaller than 5n as:
    5+n= 5 PLUS n
    5n= 5 TIMES n
    Eg.: If n is 2 (this does not apply to 1 or numbers below it), it will become 5+2=7 and 5*2=10.

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    Replies
    1. Elaborate your point further with illustrations

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  14. 5n is larger than 5+n in magnitude because:
    (Take n as 5)
    5 + n = 5 + 5
    = 10
    5n = 5 x 5
    = 25

    5n is larger than 5+n in magnitude.

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  15. 5n is larger in magnitude

    Example: n = 8
    5+n = 5+8=13

    5n = 5x8 = 40

    Hence 5n is larger in magnitude

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  16. If n = 3
    5n = 5*n
    =5 *3
    =15
    5 + n = 5 + 3
    =8
    so 5n is greater than 5 +n

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    1. What if n is a negative number?
      Does your claim still stand?

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    2. so if n = -3
      5n = -15
      5+n=5+(-3)
      = 2
      so 2 is greater than -15
      so my claim still stands

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  17. IF we assume that n = 2, then
    5n = 5*2
    = 10
    5 + n = 5 + 3
    =15

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    1. What if we choose n to be a negative number?

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  18. 5n is greater than 5 + n as you are multiplying 5 by n in 5n and you are adding 5 and n in 5+n.

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    1. Is this the case for all values of n? Test it out!

      Delete
  19. 5n is larger because 5n is multiplied but 5+n is merely an addition. For example,
    4+4=8 whereas 4x4=16. 16 is a bigger number than 8. Thus, 5n is a larger number.

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  20. If n>2, 5+n is bigger. However if n<1, 5n is bigger.

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  21. If n>2, 5+n will be bigger. However if n<1, 5n will be bigger.

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