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No Regrouping Needed!

Why does this alternative to regrouping work?  I have noticed an image similar to this on Pinterest/Facebook.

• Wow!
• Cool, I’ve never seen this before!
• How does this work?!
• Why does this work?!

I thought I would take a moment to explain why this works.  A simple piece of ribbon gives us a chance to explore this concept.  Above I used smaller numbers to demonstrate.  100-88=12, but subtracting one from the minuend and subtrahend gives us the same answer.  99-87=12 also.  When moving the ribbon down the number line we can see how the distance on the number line stays the same because we took the same amount from both the numbers.  Hence, the ribbon remains the same size because the distance doesn’t change.

The distance = the difference.  As long as the distance is constant between the numbers this will work.

Now, you tell me, will this work if, instead of subtracting one, I subtract five from the minuend and subtrahend?