What is the Inverse Property of Subtraction?

Answer 1

Generally there are only two inverse properties. The inverse property of addition, also known as the additive inverse property, and the inverse property of multiplication, also known as the multiplicative inverse property.

The additive inverse property for say the the integer -5 (integer is a fancy word for number) is the same number but with the opposite sign.

So if you are asked to find the additive inverse for -5 it is asking you to find it's opposite. So the what is the opposite of -5? +5, also written as just plain old 5 without the + sign! If you are asked to find the additive inverse of 5 what would you write? -5 of course!

If you are asked to state in words and numbers the definition of the additive inverse property you would say that "the additive inverse property states that

-a+a=0=a+-a".

Here is another example. Say you are asked "what number can be used to make the following equation true? -5+?=0". What is the inverse of -5? 5 of course. So -5+5=0!

****If you know how to add/subtract positive and negative integers****

The inverse properties deal with negatives and positive integers. If you don't know how to add or subtract and divide and multiply negative and positive integers you should really learn to help you to better understand inverse properties.

If you have studied integers then you know there cannot really be a inverse property of subtraction because the rule for subtracting integers is "Keep, Change, Change". Technically there can be a inverse subtraction property because ( -5)-5=0=(-5)5=0 BUT 5-(-5)=0=5+5 is false because 5+5=10 not 0! When subtracting integers the Keep, Change, Change rule means that if you were given the problem 5-(-5) you would KEEP the first number and sign exactly the same but CHANGE the sign, the minus sign, to a plus sign and then CHANGE the second number (in this case -5) to it's opposite. This changing the second number, (-5), is inverting it to it's opposite (5). So there can technically be a inverse subtraction property but it would be one that isn't reliable in making an equation true because depending on how the numbers are arranged you could get a completely different answer then you would if the numbers were arranged a different way. ( -5)-5=0=(-5)5=0 BUT 5-(-5)=0=5+5 is false because 5+5=10 not 0! But with addition (-5)+5 is the same as 5+(-5) making the following equation true: (-5)+5=0=5+(-5).

I know this is a lot of reading to do but it really is quite simple. I was never any good at math but if I can do it so can you! It may be helpful to learn about integers before you learn about properties. This is found in the pre-algebra section. I hope this does some good for you. Xoxo