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How to Subtract Negative Numbers

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Summary

My favorite way to subtract negative numbers is to change the subtraction problem into an addition problem. I like doing it this way because adding negative numbers is really easy.

It is also pretty easy to convert a subtraction problem to an addition problem. You just have to remember that subtracting any number is the same thing as adding its opposite.

If you have to add or subtract multiple negative numbers, I recommend using the method used to combine like terms.

How to Subtract Negative Numbers

  1. Change the subtraction problem to an addition problem by adding the opposite of the subtrahend
  2. Follow the rules for adding negative numbers.

If you don't like this method, you can check out my page about adding and subtracting integers to see another way to subtract negative numbers. 

Examples

\(3--4\)

\(3+4\)

\(7\)

\(-5-7\)

\(-5+(-7)\)

\(-12\)

\(-8--2\)

\(-8+2\)

\(6\)

\(-3.1--9.5\)

\(-3.1+9.5\)

\(6.4\)

\(1.7--8.2\)

\(1.7+8.2\)

\(9.9\)

\(-2.4--1.3\)

\(-2.4+1.3\)

\(-1.1\)

Why It Works

I like to use money and debt as an analogy to understand how to subtract negative numbers. In this analogy, negative numbers represent debt and positive numbers represent having money

  • The blue X symbols represent the  "taking away" of subtraction.
  • The red Past Due symbols represent $1 of debt.
  • The green $ symbols represent $1 of money. 
  • The gray symbols ($ and Past Due) represent the money or debt that can't be taken away because there isn't any to start with.

\(-4\)\(-\)\(-1\)

If you had $4 of debt and someone asked to take $1 of your debt, that is the same as that person giving you $1. 

\(-4\) \(+\) \(1\)

This means you would have $3 of debt. 

\(-3\)


\(-3\)\(-\)\(4\)

If you had $3 of debt and someone asked to take $4 from you, you wouldn't have any money to give them, so you could owe them a debt of $4 instead.

\(-3\) \(+\) \(-4\)

This means you would have a total of $7 of debt. 

\(-7\)


\(4\)\(-\)\(-2\)

If you had $4 and someone asked to take away $2 of your debt, you wouldn't have any debt to give them, so they could give you $2 instead.

\(4\) \(+\) \(2\)

That would give you a total of $6. 

\(6\)

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