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

Which is larger in magnitude?

5 + n or  5n

This question is compulsory.

1. 5n. It is 5n because 5n equals to 5xn but (5+n) equals to 5+n.

Example: n=8 and 5n= 5x8=40
5+8=13 so 5n Is larger

1. But if the number is below one then the answer will be 5+n as when n=1 5x1=5 and 5+1=6

2. 5n because if 5n compare with 5 + n , n might be 3 so 5n is 5 x 3 = 15 while 5+n =8

3. Explanation : If the 5n is larger, it means that 5 x ? equals to example 5 x 2. It equals to 10 .
But if 5 + n is larger, it means that like 5 + ? equals to example 5 x 10 . It equals to 15. In conclusion, both number can be larger than each other in certain cases.

1. Or both can be equal as if the 5 x 1 it equals 5 . 5 + 0 is also equal

2. Example 5 x ? , take ? = 2. It equals to 10 .
Example 5 + ? , take ? = 10 . It equals to 15.
It actually both can be larger than each other in certain cases depending on the value of n.

4. 5n is bigger than 5+n. This is because 5+n is addition and 5n is multiplication. To make it clearer, we can replace n with 10. So, 5+n will be 5+10=15 and 5n will be equal to 5x10=50. therefore,
50(5n) is larger in magnitude than 15(5+n) so 5n is bigger than 5+n.

1. The only case that applies would be if n is equal to 0. Then, 5+n would be equal to 5 and 5n would be equal to 0. Therefore, 5+n would be bigger than 5n.

5. 5n is larger in magnitude. For example, if n = 5, then, 5n will be equal to 5x5=25. And for 5+n, it will be equal to 5+5=10, hence 5n is larger in magnitude as 25 is larger than 10.

1. Unless n is equals to 1, than 5+n will be equal to 5n as the working shows: 5n = 5x1=5, 5+n = 5+1=6.

6. 5n is larger in magnitude. Let's assume that 'n' is the number '6'. In the first example, 5+n = 5+6,which is equal to 11. But in the second example,5n is equal to 5x6, which is equal to 30,thus proving that 5n is bigger than 5+n in magnitude.

1. On the other hand, if n is equal to '-6', then 5+n is larger

7. 5N is larger

5n=5xN
Take N to be 5
5+N: 5+5=10
5N: 5x5=25

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2. Can be equal if N is 1

8. 5n is larger in magnitude as 5+n is just simply the result of the addition of 5 and n, but 5n is 5 consecutive n's multiply with each other, which can be explained by n x n x n x n x n. However, if n is 0 or any negative number, then 5+n is larger.

1. Which means both "numbers" can change position in certain cases.

9. depends on what is n. If n is 1, and the second example equals to 5x1=5,while 5+n=5+1=6. But if n is bigger than 1, for example n=2, 5n=5x2=10 while 5+n=5+2=7. So it is impossible to tell which one is bigger.

10. It can not be confirmed. If N is more than 1, 5n will be more than 5+n. e.g. if n= 4 5N is 20 while n+5 is 9.
but if N is one or less or negative, 5+n is more than 5 N. Eg. n=1 5n= 5 while n+5 is 6.

1. if n is negative, n= -1 5n=-5 while 5+n is 4

11. depends. n could be negative, which means that if it times 5 it would be smaller. if it is a positive number then it is bigger.

12. 5n is bigger.

Examples:

If n equal to 10, than 5n is 50 and 5+n is 15, so 5n is bigger.

If n equal to 2, than 5n is 10 and 5+n is 7, so 5n is still bigger.

13. 5n is larger as 5n is actually 5 x n which is multiplication while 5+n is addition.

14. 5n, unless if n is 1.25(which would give the same answer) or below(which will be smaller). Because 5n is 5*n and multiplying will most of the time give a bigger number unless if the number is below a certain number. Example:5*1.25=6.25, 5+1.25=6.25, 5*2=10, 5+2=7, 5*1=5, 5+1=6

15. If n is bigger than 1.25
5n will be bigger

If n is 1.25
They will be the same

If n is smaller than 1.25
5n will be smaller

16. both magnitudes can larger or smaller than each other.
Take n = 1.
5+n = 5+1 =6
5n = 5 multiplied by 1 = 5.
5+n is larger than 5n.
Take n = 5
5+n = 5+5 =10
5n = 5 multiplied 5 = 25
5n is larger than 5+n.

17. 5n is larger. Let 'n' be 10 so 5+10 is equal 15 but if 5x10is equal to 50 thus 5 n is larger .

Ng choon wee

18. If n is bigger than 1.25
5n will be bigger

If n is 1.25
They will be the same

If n is smaller than 1.25
5n will be smaller

19. 5n if higher than 1, 5+n if lower than 1.
If n>1, then n would increase by 5 times instead of just adding 5 to its value. E.G n=2, 5+2=7. WHEREAS 5x2=10
If n=1, then n would still remain the same after 5 multiplying by 1. If 1 is added to 5, then it would increase by 1.
If n<1, then 5 would go down the number line, as n is not higher than 1. E.G. n=0.1, 5+0.1=0.6. WHEREAS 5x0.1=0.5

20. Depends on what N represents if N represents 2 then 5 + n will be 5+2 which equals to 7 and 5n will equal to 10 in this case 5n value is more, but if N represents 0 then 5+n equals to 5 and 5 times 0 will equal to 0 and in this case 5+n value will be mmore