# Subtracting Negatives

- Author:
- tianguangz, GreenMaths

## Concept

All integers can be subtracted from other integers.
The subtraction of two integers, is simply the sum of the first one and the opposite of the second one.
a - b = a + (-b).
Using this rule we can compute the difference of any two integers.
The model we use below is merely one way of seeing integer subtraction.

## Instructions

Drag the blue and red sliders on the left to create an integer.
A blue dot = +1, a red dot = -1, so 9 blue + 6 red = +9 + (-6) = +3.
Drag the green slider on the right to take away negatives.
Observe how the number changes when you

**take away**the red dots.## Questions

What is 4 - (-3)?
What is (-1) - (-3)?
What is 5 + (-3) - (-3)?
What does this tell you about another way to compute integer subtraction?

## Answers

*What is 4 - (-3)? What is (-1) - (-3)? What is 5 + (-3) - (-3)? What does this tell you about another way to compute integer subtraction?*4 - (-3) = 4 + 3 = 7. 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. (-1) - (-3) = (-1) + 3 = 3 + (-1) = 2. View -1 as "2 blue" plus "3 red". When we remove the "3 red", what is left is "2 blue", or +2. 5 + (-3) - (-3) = 2 - (-3). Seeing 2 as 5 + (-3), or 5 blue plus 3 red, we get 2 - (-3) = 5. We see that adding and subtracting a number are

**inverse operations**: adding a number and then subtracting that number always gives you the original number. Same goes with subtracting then adding.

## Pre-Skills

6.EE.3

## Related Concepts

Adding Integers
Inverse Function

## Inspirations and Applications

[Source] https://www.geogebra.org/material/simple/id/t472usG3
[by] GreenMaths
Another important use of negative numbers is that it

*"completes"*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. On the other hand, whenever you add**or**subtract integers, you always get an integer. This makes the collection of integers**closed**under addition and subtraction.## Common Core

7.NS.1c
7.NS.1d
7.NS.3