Tuesday, 14 February 2017

Algebra... Which is larger? (I)



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

Explain your answer clearly with examples.
Indicate any assumptions made.


Enter your response in Comments.
This question is compulsory.

46 comments:

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

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  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

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  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


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  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.

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  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.

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  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.

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  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.

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

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  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.

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  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.

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

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  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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  11. This comment has been removed by the author.

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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

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  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

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  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.

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

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  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

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    Replies
    1. it also depends on the value of the number

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

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  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

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

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    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.

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  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

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  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

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    Replies
    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

      Delete
  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.

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

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  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.

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    Replies
    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

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  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

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    Replies
    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"

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  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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  23. This comment has been removed by the author.

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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.

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  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.

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  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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  27. This comment has been removed by the author.

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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.

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  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.

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  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

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