# How to solve a subtraction equation that results in a negative number?

So we're home-schooling our 6-yr old and she's doing basic addition/subtraction/multiplication/division.. and I wrote a subtraction problem backwards by accident the other day, and I can't figure out how to show her how to solve it.

Any help would be appreciated.

The problem: 30 - 45

I know it equals -15, and I know why - but I don't know how to explain how to do the math.

  30
- 45
----


borrow one from the 3, it becomes 2, the 0 becomes 10.. 10 - 5 = 5. Then 2 - 4.. what do you do here? I keep getting -2. Which makes the result -25.

• It makes the result $-20+5$. Which is $-15$. But I think that for people that age, or perhaps any age, one should use the algorithm only when subtracting smaller from bigger. – André Nicolas Dec 4 '14 at 17:52

I'd take out a thermometer and show her $30$ degrees on the thermometer. Then I'd subtract (get colder by) $45$ degrees, ending at $-15$ degrees.

If she hasn't learned about negative numbers yet, you may need to do some extra explaining.

Long subtraction is based off positive numbers, so it doesn't really work if you try to subtract a larger number from a smaller number.

A workaround would be to flip the two numbers, and find the difference using long subtraction. Then, add a negative sign to the answer.

30-45 would become:

 45
-30
----
15


Now just add a negative sign in front of so it turns to -15. This works because a-b = -(-a+b).

However, for simplicity, I would demonstrating the concept using a number line instead of using the above method.