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

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

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)

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.

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

ReplyDeleteBut if it is more than 1, 5n is more than 5+n.

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

Delete5n. 5+n is addition, however 5n is 5 multiplied by n. Therefore, 5n is bigger

ReplyDeleteIs this always the case?

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

ReplyDeleteAre there exceptional cases?

Delete5n. take n = 5.

ReplyDeletetherefore , 5n = 5 x 5 = 25

5 + n = 5 + 5 = 10

thus 5n is larger in magnitude

What happens when n = 0?

Delete5n is bigger.

ReplyDelete5+n is just adding the number5 and n.

5n is multiplying 5 with n.

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

Delete5n. As 5n is 5*n, which is multiplication while 5+n is only addition

ReplyDeleteTest this out with a range of numbers!

Deleteit 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

ReplyDeleteThe claim is, as long as n is positive, 5n is always bigger.

DeleteTest this out with positive proper fractions.

This comment has been removed by the author.

ReplyDeleteIt 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

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

Delete5n is larger. (If n is a positive integer) as compared to 5+n.

ReplyDeleteOk, an assumption made is, n is an integer.

DeleteWhat if it's a set of real numbers? Does the claim still stand?

The things written on the board related to this qn.

DeleteIf 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

If n is negative then 5n would be smaller (5 x -3=-15 is smaller than 5 + -3=2) ,

ReplyDeletehowever 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)

Good observation.

DeleteSo, what is the value that determines the change in 'status'?

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

ReplyDeletei.e. Take n = 5

5n = 5*5 = 25

5+n = 5+5 = 15

25 is therefore larger than 15.

I forgot to mention if n is a positive integer.

DeleteIf 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.

Good explanation.

DeleteThis makes an assumption that the number is an integer.

What happens if n is a real number.

Does the same apply?

5+n is smaller than 5n as:

ReplyDelete5+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.

Elaborate your point further with illustrations

Delete5n is larger than 5+n in magnitude because:

ReplyDelete(Take n as 5)

5 + n = 5 + 5

= 10

5n = 5 x 5

= 25

5n is larger than 5+n in magnitude.

Is this true for all values of n?

Delete5n is larger in magnitude

ReplyDeleteExample: n = 8

5+n = 5+8=13

5n = 5x8 = 40

Hence 5n is larger in magnitude

Try a wider range of n values

DeleteIf n = 3

ReplyDelete5n = 5*n

=5 *3

=15

5 + n = 5 + 3

=8

so 5n is greater than 5 +n

What if n is a negative number?

DeleteDoes your claim still stand?

so if n = -3

Delete5n = -15

5+n=5+(-3)

= 2

so 2 is greater than -15

so my claim still stands

IF we assume that n = 2, then

ReplyDelete5n = 5*2

= 10

5 + n = 5 + 3

=15

What if we choose n to be a negative number?

Deleteso, 5 n is greater than 5 + n

ReplyDelete5n is greater than 5 + n as you are multiplying 5 by n in 5n and you are adding 5 and n in 5+n.

ReplyDeleteIs this the case for all values of n? Test it out!

Delete5n is larger because 5n is multiplied but 5+n is merely an addition. For example,

ReplyDelete4+4=8 whereas 4x4=16. 16 is a bigger number than 8. Thus, 5n is a larger number.

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

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

ReplyDelete