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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.

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    $\begingroup$ 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. $\endgroup$ – André Nicolas Dec 4 '14 at 17:52
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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.

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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.

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