## 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. 5n is larger as 5n is the same as 5 x n which is bigger than 5+n

2. 5n is larger because 5n is 5 x n while the other one is 5 + n so if n = 3, 5n = 5 x 3 = 15 and 5 + n = 5 + 3 = 8. so 5n is larger

3. (a) 5n is larger.
(b) 5n is 5 x n while the latter is 5 + n . So if we give n a value, let's say 7, 5n would be 5x7=35 which 5+n would be 5+7=12. Based on this example, 5n is larger.

4. 5n is larger because 5+n is adding n with 5 however 5n is 5n which is bigger.. For example n=5 and work out the equation..
5+5= 10
5x5 = 25 so comparing 10 and 25 , 25 is bigger

5. a)5N
b)Assuming N is 7, 5+N is 12, and 5N is 35. Therefore, 5N is bigger.

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7. (a) 5n is larger.
(b) Lets say that n is 5. So 5n is now 5x5 and 5+n is now 5+5. The results of the former (25) is larger than the latter (10).

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10. 5n is larger as long as n's value is not 1.

If n is 1,
5 + n = 5 + 1 = 6
5n = 5 x 1 = 5
So, if n is 1, 5 + n is larger.

If n is above 1, lets say 2,
5 + n = 5 + 2 = 7
5n = 5 x 2 = 10
So, if n is above 1, 5n is larger.

11. It depends,if n=1 5+n would be bigger than 5n.
But if n>1, 5n would be bigger than 5+n.

12. a) It depends on the value of n.
b) If n is 0<n 5+n will be lesser than 5n. Let's say n=3. 5+3=8 while 5x3=15.
However, if n is less than zero or zero, 5n will be lesser than 5+n. Lets say n=0. 5+0=5 while 5x0=0.

13. 5 is the coefficient and n is the constant.
a) 5n is larger
b) If n is 3,
5 + n= 5+3=8
5n= 5 x 3 = 15

14. (a)5N
b)N is 7, 5+N is 12, and 5N is 35. 5N will be bigger.

15. a) 5n is larger.
b) 5n is 5 x n, which is bigger than 5+n. Substituting n with a number for example 5. 5 x 5= 25, and 5+5 is 10. So 5n is larger.

16. a) 5n is larger.
b) 5 and n are place together, so this means 5xn, (5 multiplied by n) whereas 5+n means... well, 5+n. So from here, you can actually see that 5+n means 5 is added to n, but 5xn means that there are 5 ns. For example, n is 6. 5x6 (5n) gives 30, but 5+6 (5+n) gives 11. So, 5n is larger.

17. 5n is bigger
as 5 is placed next to n, it means that it is 5 x n
For example: n=2
5+2=7
5x2=10

18. (a) 5n (if the value of 'n' is the equal for both equations)
(b) Let's assume that 'n' has an equivalent value for both equations. Also, let's assume that n = 5. Knowing this we can calculate that 5 X n = 25 (since 'n' is 5) and 5 + n = 10 (since 'n' is 5). Hence, '5n' is larger than '5+n'.

19. (a) 5n is bigger.
(b) (Assuming that 'n' = 10)So 5+n=5+10=15
But since we all know 5n is 5 x n, 5n is equivalent to 5 x 10 = 50.
So 5n is bigger then 5+n.

20. If n=1 or below 5+n is bigger
if n=above 1, 5n is bigger

21. (a) 5N
(b) 5N = 5xN = N+N+N+N+N
5+N = 5 N
If N = 2,
5N = 5x2 = 10
5+N = 5+2 = 7
Therefore, 5N > 5+N