Monday, April 18, 2011

Chapter 4: Algebra... Which is larger in magnitude?

Similar but Different
The two 5s below affect the expressions differently. One known as coefficient while the other is known as a constant. Which is which?

(a) Which is larger in magnitude (size)?

5 + n or  5n

1. (a) 5n is larger.

(b) Let us take n as 3. So, the first equation is 5+3=8. The other equation is 5(3)=15. Thus you can see that 5n is larger. The only thing that may change this is that n is 1, as 5+1=6 and 5(1)=5. So 5+n is larger in this case, which may not usually happen.

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3. a) We cannot say that either of the numbers are bigger

b)This is so as we don't know the value of n. For example if n is 20, 5+n is equal to 25 while 5n will be equal to 125. However if n is 1, 5 + n is 6 while 5n will be 5.

4. It depends for example, if n=0, then if 5+0=5, and 5x0=0, then 5+n would be larger in magnitude.
If n=5, then 5+5=10, and 5x5=25, then 5n would be larger.

5. a) 5n is larger.

b) 5n is larger, as times will always give a bigger answer compared to a addition, with the same variable, coefficient, and constant.
i.e. n=2
5+n=5+2
=7
5n=5x2
=10
Thus, the 5n is bigger than 5+n.
However, 5+n would be larger if n=1.
i.e. n=1
5+n=5+1
=6
5n=5x1
=5
Thus, the 5+n here is bigger.

6. a) It depends on the variable n.

b(i) If n is equal to 1,
then 5 + n
= 5 + 1
= 6
however,
5n = 5 x 1
= 5.

b(ii) If n is equal to 5,
then 5 + n
= 5 + 5
= 10
however,
5n = 5 x 5
=25.

7. It depends on what the 'n' is. For example if 'n' is 0, the '5+n' will be larger than '5n'. In another case if the 'n' is 3, '5n' will be larger than '5+n'.

8. (a) It depends on what number does "n" stands for.

(b)For example "n" is equal to 5. Then 5x5=25 and 5+5=10.
This example clearly shows us that 5n is larger in magnitude than 5+n. But this can be simply proven wrong, as "n" can also be zero. Then 5x0=0 and 5+0=5.
This also clearly shows that 5+n is larger in magnitude than 5n. So we cannot say which one is larger with this much of information.We need more information like what does "n" stands for. So that it will be easier to say which one is larger in magnitude.

9. a) The answer for this depends on the variable, n.

b) Look at the two expressions. If n is 0 or 1, if you add/multiply them, 5+n is bigger (5+1=6, 5(1)=5/5+0=5, 5*0=0). But, if n is more than 1, the bigger expression will be 5n. Therefore, to find out which expression is bigger, you need more details, like 'n is more than/less than ___'.

10. (a)Well we can't say either of them is bigger. It all depends on the the value of N.

(b) In the case where n is 0, 5+0=5
5x0=0
So in this example 5+n is bigger.
In this case, n is 3, 5+3=8
5x3=15
So it really depends on variable n. :D

11. A) The answer depends on the variable 'n' .

' If ' statements ahead! caution

B) The answer depends on the variable because

If 'n' = 1

5(n)=5(1)=5
5+n=5+1=6

now statement ' 5+n ' Wins!!!

Then,
If 'n' =2
5(n)=5(2)=10
5+n=5+2=7

now statement ' 5n ' Wins!!!

Therefore ,The answer depends on the variable 'n' .

12. (a) Which is larger in magnitude (size)?

5 + n or 5n

Ans for A:It depends as n is a variable it can be any no so it can be both now let me explain.......
ANS for B:It depends as n is a variable and it can be any number.So here a case on where 5+''n'' is bigger then ''5n''
Let ''n'' be 0 so
5+0 is 5 then'5*0 is 0 so it is bigger

but here the next case
let n be 10 so:

5+10=15 then 5*10=50
s0 5n is now bigger!

13. 5n is larger.Lets say n is 5.
5n=5x5=25,while 5+n=10,so 5n is larger

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15. a) The answer can be either larger or smaller in magnitude.

(b) For example, let me take n as 0.
5+0=5, but, 5x0=0
This shows that 5+n is bigger than 5n.(n can be also number 1)

For the next example, let me take n as 5.(Works for any integer bigger than 1)
5+5=19, but, 5x5=25
This shows that 5n is bigger than 5+n

This shows that the answer depends on the variable that is n!

16. 5n.

We take the value of n as 10 for example.
5+n in this example would be 15.
5n=5xn=5x10 (in this example) =50
So obviously 5n is bigger as 5n is 5 times of n while 5+n just n+5

17. (a)Depends but more often, 5n is bigger.

(b) Let's take the value of n to b 5. 5+n=10 while 5n=5x5=25. So 5n is bigger.

18. depends for (a).

If n is infinite, there will be no answer.
If n is zero, 5+n is bigger
If n is 1, 5+n will STILL be bigger.
but these are only exceptions.
In a normal case like from 2 to lets say 100 it will all be 5n.

19. It depends for both!
REASON:
(Comparing A(More) to B)-If n is 0
5+0>5x0
5 > 0
(Comparing A(Less) to B)-If n is 5
5+5<5x5
10 < 25

So it depends on what is n

20. Usually, I would say that 5 + N is smaller, as 5N literally means 5 X N. Full-stop. The end. But there's a loophole. You might say "Argh it must be 5N as the biggest one!", but think about it this way. We were not specified what number N represents or how much significance it has. So, if N was the number 0, it will be 5 + N as the biggest as nothing can be multiplied with 0. But if N was any number thats above 0, like N > 0, then it will definitely be 5N. So it really depends so. But to this question, I think that the answer is really unknowable.

21. a) It depends.

b)
if n stands for 0,
5 + n = 5 + 0 = 5
5n = 5 x 0 = 0
5 + n would be larger.

if n stands for 7,
5 + n = 5 + 7 = 12
5n = 5 x 7 = 35
5n would be larger.

Thus, it depends on what n stands for in the question.