It depends. If n is 1, then 5+n(6) is more than 5n(5)But if it is more than 1, 5n is more than 5+n.
Are you able to tell the number that determines which is larger?
5n. 5+n is addition, however 5n is 5 multiplied by n. Therefore, 5n is bigger
Is this always the case?
The answer is 5n.5+n is just n added to 5 whereas 5n is 5 multiplied to n.So 5n is bigger.
Are there exceptional cases?
5n. take n = 5. therefore , 5n = 5 x 5 = 25 5 + n = 5 + 5 = 10thus 5n is larger in magnitude
What happens when n = 0?
5n is bigger.5+n is just adding the number5 and n.5n is multiplying 5 with n.
What happens to 5n if n is a negative number?
5n. As 5n is 5*n, which is multiplication while 5+n is only addition
Test this out with a range of numbers!
it depends as if n is a negative no. then 5n will be smaller but if n is a positive no. then it will be bigger
The claim is, as long as n is positive, 5n is always bigger.Test this out with positive proper fractions.
This comment has been removed by the author.
It depends. If n is 1 or if it is a negative number 5n will be smaller than 5+n. However if n is more than 1(not including), 5n will be bigger than 5+n
Is n = 1 the value that determines when which one is larger?
5n is larger. (If n is a positive integer) as compared to 5+n.
Ok, an assumption made is, n is an integer. What if it's a set of real numbers? Does the claim still stand?
The things written on the board related to this qn. If n=1, 5+n>5nIf n=2, 5+n<5nIf 5+n=5n, move n over to the 5n side to become -n. Thus, the equation becomes 5=5n-n=4n, n=5/4=1.25
If n is negative then 5n would be smaller (5 x -3=-15 is smaller than 5 + -3=2) ,however if n is positive then 5n is bigger.However if n were a decimal then it would be smaller. (0.2 x 5=1, 5+0.2=5.2)
Good observation.So, what is the value that determines the change in 'status'?
5n is larger than 5+n because 5n is 5*n and 5 + n cannot be larger than 5 times of ni.e. Take n = 55n = 5*5 = 255+n = 5+5 = 1525 is therefore larger than 15.
I forgot to mention if n is a positive integer.If n is a negative integer,n=-55n = 5*-5 = -255 + n = 5 + -5 = 0And therefore 0 is larger than 25 which means 5+n is the larger number now.
Good explanation.This makes an assumption that the number is an integer.What happens if n is a real number.Does the same apply?
5+n is smaller than 5n as:5+n= 5 PLUS n5n= 5 TIMES nEg.: If n is 2 (this does not apply to 1 or numbers below it), it will become 5+2=7 and 5*2=10.
Elaborate your point further with illustrations
5n is larger than 5+n in magnitude because:(Take n as 5)5 + n = 5 + 5 = 105n = 5 x 5 = 255n is larger than 5+n in magnitude.
Is this true for all values of n?
5n is larger in magnitudeExample: n = 85+n = 5+8=135n = 5x8 = 40Hence 5n is larger in magnitude
Try a wider range of n values
If n = 35n = 5*n =5 *3 =155 + n = 5 + 3=8so 5n is greater than 5 +n
What if n is a negative number?Does your claim still stand?
so if n = -35n = -155+n=5+(-3)= 2so 2 is greater than -15so my claim still stands
IF we assume that n = 2, then5n = 5*2 = 105 + n = 5 + 3 =15
What if we choose n to be a negative number?
so, 5 n is greater than 5 + n
5n is greater than 5 + n as you are multiplying 5 by n in 5n and you are adding 5 and n in 5+n.
Is this the case for all values of n? Test it out!
5n is larger because 5n is multiplied but 5+n is merely an addition. For example,4+4=8 whereas 4x4=16. 16 is a bigger number than 8. Thus, 5n is a larger number.
If n>2, 5+n is bigger. However if n<1, 5n is bigger.
If n>2, 5+n will be bigger. However if n<1, 5n will be bigger.