## 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 bigger
b) 5+n is only 5 and the value of n added together whereas 5n is five times the value of n

2. 5+n can also be be bigger if n is less than 1

3. 5+n is technically smaller than 5n as 5n is 5xn but however if n is 1 5+n is bigger then 5n.

4. This comment has been removed by the author.

5. a) It depends on the situation and what x represents.
b) If x is 1, for example, then 5+n would be equal to 5+1=6 and 5n would be equal to 5. If x is more than one, then 5n would be larger.

6. Coefficient = 5 [in 5n]
Constant = 5 [in 5 + n]
(a) 5n (Scenario 1) and 5 + n (Scenario 2) are both larger in magnitude , depending on the situation
(b) Scenario 1 : 5 + n is (5 + n) , 5n is (5 x n) . The one multiplied is larger. Scenario 2 : However, if the value of n is less than 1 or is 1, 5 + n would be larger, as 5n would be less.

7. 5n would be bigger in most cases because it is a multiple of the n and not just an addition.

8. Coefficient is 5n
Constant is 5+n
a)Its depends on what n is
b)if 4n is bigger than 5,5n is the larger in magnitude.But if 4n is smaller than 5,5+n is larger in magnitude.

9. This comment has been removed by the author.

10. This comment has been removed by the author.

11. 5n should have more scenario of when it is bigger than 5+n as it multiplies instead of add

12. a) 5n
b) it is because that 5n is 5 x n but 5 + n is only 5 + n
multiplication in this case will get a bigger answer

13. (a) It depends upon the situation.
(b) Scenario 1 : Let n be 1, which statement is larger? 5n or 5 + n?
5 +1 = 6. On the other hand, 5 x 1 = 5. Hence, 5 + n would be bigger.
Scenario 2 : Let n be 2, which statement is larger? 5n or 5 + n?
5 + 2 = 7. On the other hand, 5 x 2 = 10. Hence 5n would be bigger.

14. The 5 in (5n) is a coefficient.
The 5 in (5+n) is a constant.
a) 5n is larger in magnitude. But in some cases 5+n can be bigger.

b)5n is larger as if you break it up it is 5 x n which is greater than 5+n. However if n is equal to n or lesser, 5+n will be larger.

15. a) 5n
b) For example n=10
So, n+5 will be 15
and 5n (without plus) would mean 5x10=50
15 and 50 has a GREAT difference.

16. (a) 5n is bigger in magnitude.
(b) 5n is a multiplication expression while 5+n is an addition expression.
For example, if n=5.
5n=25
5+5=10
So 5n is bigger.

17. a) 5n
b) n+5 is not more than 5n as 5+n =5+n whereas 5n=5 x n

18. It depends. If n is larger than 1, 5n is bigger. If n is smaller than 1, 5 + n is bigger.

19. This comment has been removed by the author.

20. a) 5n is bigger
b) For example, if n=5, and 5x5=25 is bigger than 5+5=10.
But this does not apply to some cases.

21. 5n is bigger.
5n = 5 x n
5+n < 5n

Lets take n=2
so 5+2=7
5x2=10

so 5+n < 5n

22. (a)5n is larger
(b)n+5 is not bigger than 5n as 5n is 5 times of n whereas n+5 is just 1 n +5

23. a) 5n is bigger
b) n+5 is not bigger than 5n

24. 5n is bigger. It is when the coefficient, n is larger than 1.25.

5+n can be bigger when n is smaller than 1.25
They are the same when n is 1.25.

25. It depends on the number.
If n = 1, 5n is 5 while 5+n will be 6.