All integers can be subtracted from other integers.[br]The subtraction of two integers, is simply the sum of the first one and the opposite of the second one.[br][br]a - b = a + (-b).[br][br]Using this rule we can compute the difference of any two integers.[br]The model we use below is merely one way of seeing integer subtraction.
Drag the blue and red sliders on the left to create an integer.[br][br]A blue dot = +1, a red dot = -1, so 9 blue + 6 red = +9 + (-6) = +3.[br][br]Drag the green slider on the right to take away negatives.[br]Observe how the number changes when you [b]take away[/b] the red dots.
What is 4 - (-3)?[br]What is (-1) - (-3)?[br][br]What is 5 + (-3) - (-3)?[br]What does this tell you about another way to compute integer subtraction?
[i]What is 4 - (-3)?[br]What is (-1) - (-3)?[br][br]What is 5 + (-3) - (-3)?[br]What does this tell you about another way to compute integer subtraction?[/i][br][br]4 - (-3) = 4 + 3 = 7.[br]To see this, view 4 as "7 blue" plus "3 red". When we remove the "3 red", what is left is "7 blue", or +7.[br][br](-1) - (-3) = (-1) + 3 = 3 + (-1) = 2.[br]View -1 as "2 blue" plus "3 red". When we remove the "3 red", what is left is "2 blue", or +2.[br][br]5 + (-3) - (-3) = 2 - (-3).[br]Seeing 2 as 5 + (-3), or 5 blue plus 3 red, we get 2 - (-3) = 5.[br][br]We see that adding and subtracting a number are [b]inverse operations[/b]: adding a number and then subtracting that number always gives you the original number. Same goes with subtracting then adding.[br]
Adding Integers[br]Inverse Function
[Source] https://www.geogebra.org/material/simple/id/t472usG3[br][by] GreenMaths[br][br]Another important use of negative numbers is that it [i]"completes"[/i]the whole numbers: When you add two whole numbers you always get a whole number, but when you subtract two whole numbers, you don't always get a whole number.[br]On the other hand, whenever you add [b]or[/b] subtract integers, you always get an integer. This makes the collection of integers [b]closed[/b] under addition and subtraction.
7.NS.1c[br]7.NS.1d[br]7.NS.3