### 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

2. Hi Zheng Jie

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

:D

3. This comment has been removed by the author.

4. Take n as 2

5 + 2 = 7

while

5 x 2 = 10

Thus 5n is bigger.

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)

6. Let "n" be 10.

5+10=15

5x10=50

So, 5n is bigger than 5+n.

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.

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

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

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

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

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!

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

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.

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

16. @Richie

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

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!

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)

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

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.

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

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

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?

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

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

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.

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.

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.