Which is larger in magnitude?

**5 + n**or

**5n**

Explain your answer clearly with examples.

Indicate any assumptions made.

Indicate any assumptions made.

Enter your response in Comments.

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Which is larger in magnitude?

Explain your answer clearly with examples.

Indicate any assumptions made.

Indicate any assumptions made.

Enter your response in Comments.

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

ReplyDeleteBoth depending on the number n.

ReplyDeleteif n is 2,

5+2=7

but,

5x2=10

however, if n is 1,

5+1=6

but

5x1=5

Good observation :)

Delete5n. 5n is 5 x n. But 5 + n is 5 added to n

ReplyDeleteif n is 10, then 5 + n = 5 + 10 = 15

and 5n= 5(10) or 5 x 10 is 50

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

ReplyDeleteIt 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.

ReplyDeleteGood observation

Delete5n is larger in magnitude.

ReplyDeleteExample: 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.

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.

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

Delete5n 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.

ReplyDeleteIt 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.

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

DeleteLets 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.

ReplyDeleteThis comment has been removed by the author.

ReplyDeleteIt 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

ReplyDeleteGood observation.

DeleteIf 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

ReplyDeleteGood observation

Delete5n 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.

ReplyDelete4+a is one 4 and one a so it is lesser.

You are making an attempt to generalize.

DeleteBefore generalising, d test with several numbers first.

if n=2, 5n would be greater because multiplying a positive number would make the value larger

ReplyDeletebut, if n=-2, 5+n would be larger because multiplying negative number would make the value even smaller

it also depends on the value of the number

DeleteYou have make a good point - using negative number will bring out an obvious difference.

DeleteYour explanation can be further refined.

5n is bigger 5n=n+n+n+n+n vs 5+n=5+n.

ReplyDeleteBut if n is 1, 5n=1x5

5+n=6 then 5+n would be bigger

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

DeleteGood observation.

DeleteYou 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.

It depends.

ReplyDeleteif 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

Good observation and illustration.

DeleteIt 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

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

DeleteHowever, your generalization can be sharpened if you carry out testing with converging n values

Both can be larger in magnitude depending on the value of n.

ReplyDelete(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.

Good observation,

DeleteHow could we sharpen the justification so that the conclusion can be more specific.

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.

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

DeleteExample 5 plus n equals 6 will give u 11

ReplyDeletebut 5 multiplies by 6 will give you 30

My assumption made was both n had same values so 5n is larger

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

DeleteAlso, 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"

It depends in the value of n.

ReplyDeletee.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

This comment has been removed by the author.

ReplyDeleteI 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.

ReplyDeleteIt 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.

ReplyDeleteThe answer depends on the value of n.

ReplyDeleteIf 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.

This comment has been removed by the author.

ReplyDelete5n is bigger than 5+n.

ReplyDelete5n 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.

5n is bigger than 5+n.

ReplyDelete5n 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.

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.

ReplyDeleteIf n = (number bigger than 1), 5n would be bigger as eg n=10

5n = 50

5+n = 15

Thus, 5n is bigger