Question

Roger says that 10% of a number will always be less than 25% of any other number. Complete one inequality to support Roger's claim and one to show that he is incorrect.

Answer 1

Roger is only correct if you are talking about the same number.
10%of 100 is 10 while 25% of 100 is 25. Ok, roger, you win this round.
However, if you are talking about different numbers, it will vary.
25% of 4 is 1 while 10% of 1000 is 100. In this case, the 10% of 1000 is bigger than the 25% of 4.

Answer 2

Answer:

Roger says that 10% of a number will always be less than 25% of any other number.

Lets say the number are 20 and 50.

When it is correct:

10% of 20 = $0.10\times20=2$

25% of 50 = $0.25\times50=12.50$

We can see that 10% of 20 is less than 25% of 50.

When it is not correct:

10% of 50 = $0.10\times50=5$

25% of 20 = $25\times20=5$    

We can see that the answer is equal here.

So, this claim is not correct that 10% of a number will always be less than 25% of any other number. It can be greater also.