If we care about the way we're facing, we need a more complex math object (a vector) to keep track of our orientation as well as position ("14, facing forward" vs. But mathematically, our endpoint is the same: 8 - (-6) = 8 + 6 = 14. Facing backwards and walking backwards might have us looking at 0 while we advance forward. When doing simple arithmetic, we only track the final location, not orientation. (If you're adventurous, you might start thinking about taking side steps, or jumping, and how that would be represented.) I actually walked around while thinking through the intuition. These explanations are a bit abstract, the walking one is more fun to try directly. In general, if you remove a disadvantage, you have improved your situation - a positive. If I have a debt of \$30, and someone "subtracts it", I've effectively gained \$30. You get the idea.įor older students, "subtracting a negative" can be seen as "cancelling a debt". Or maybe it's an adverb, modifying how we walk (walk forwardly, walk backwardly). In a sense, the addition/subtraction acts as a verb ("face forward" or "face backward"), and the positive/negative acts as an adjective ("regular steps" or "backwards steps"). What if we had faced backwards but walked backwards 6 steps?Īh! The addition/subtraction tells us which way to face, and the positive/negative tells us if our steps will be forward or backward (regardless of the way we're facing). Which means we're pretty close to our starting point, just 2 steps away. What if we had faced backwards and took 6 steps? Which gives us 14 steps from our starting point.
Now, let's say we want to keep facing forward and take 6 more steps. The "+" means "facing forward" and "8" means "8 steps in the direction you're facing". You're facing forward, and take 8 steps forward. Addition and subtraction are related, but slightly different, than positive and negative numbers. Great question! I had to think about it for a bit. After thinking of a better intuition, here was my reply: I've long internalized negatives as "opposite" and subtraction as "opposite of addition" so in my head, I had a notion of "opposite of opposite of addition" which simplifies down to "addition".īut that inner verbalization was still pretty abstract. Compare, order, add, and subtract the positive and negative numbers. Why is 8 - (-6) = 14 the same as 8 + 6 = 14? This index page will link you to all types of addition worksheets, including basic.
#A NEGATIVE PLUS A POSITIVE EQUALS ADDITION HOW TO#
A math teacher recently asked how to explain the concept of subtracting negative numbers to her class.
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