Question 64123
Your first answer is wrong. In rounded terms you have a number of about 8 and take 14 away from it. If I consider the 14 to be made up of two parts (an 8 part and a 6 part) and take them away from the original 8 in turn. Take away 8 first then I would get an answer of 0 and there is still another 6 to be taken away. The approximate answer should be -6.

This could be though of as I have 8 lollies. I want to give one to each of my 14 friends. I can give away the 8 lollies I have and then I will owe 6 more lollies. (I will have -6 lollies). I certainly wouldn't end up having 13 left.

Another idea is being in the lift of a building with below ground level floors. If you start at floor 8 and go down 14 floors you will end up at the floor 6 levels below ground level.

Using the numbers in your original problem you need 7.7 of the 14.1 to take your number down to 0. You have used up 7.7 of the 14.1 leaving (14.1-7.7)=6.4 to still take away from 0. So your first answer is -6.4.

Taking away a negative number gives the same result as adding a positive number. Thinking about the lollies example shows how this can work. I have -6 lollies. If someone takes away my -6 lollies I will have 0 lollies which is the same as if I had added 6 lollies to what I already had (and then gave them to the people I owed them to).

Your second problem is the same therefore as -9.4 + 10.4.
When I add 9.4 to -9.4 I get 0. I will have used up 9.4 of the 10.4 so there is 1 left to still add to the 0. I will end up with an answer of 1.

Your teacher will probably give you a faster way of working out the answer but I have tried to show what is happening in a way that may make it easier to understand (even if I have tended to waffle a bit).