# How to explain this mental math trick with 23-8?

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How do you explain this way of doing mental math?

For 23-8 (a SUBTRACTION problem), you ADD 2 to BOTH sides to make 25-10. Why does this work? How to explain it without just saying "memorize this trick?"

I get confused with mental math myself. Thanks so much in advance!

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You could get out a balance. Show that adding the same amount to each side doesn't change the difference. So, adding 2 to each side just helps us think of the difference easier.

FWIW - Mine find it easier to think 8= 3+5....so subtract 3 first, then 5.

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Thank you, Paula! :001_smile:

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Mine would think, "8 is almost 10, so take 23 - 10 = 13 + 2 (since we had to add 2 to the 8 to make 10) = 15".

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10 = 8 + 2 and 8 = 10 - 2. So by adding 10 then subtracting 2, you wind up with a net addition of 8. This kind of work with making 10's is what I really like about the Asian-based math programs like Right Start and Singapore.

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How do you explain this way of doing mental math?

For 23-8 (a SUBTRACTION problem), you ADD 2 to BOTH sides to make 25-10. Why does this work? How to explain it without just saying "memorize this trick?"

I get confused with mental math myself. Thanks so much in advance!

What you actually do is add a zero by adding 2 and also subtracting 2.

You add 2 to the 23 to make 25, and you add 2 to the 8 and thus TAKE AWAY 10. So, the second 2 is being subtracted.

If you write it out:

23+2 -(8+2)=

23 +2 -8-2= (we can rearrange)

23 +2 -2 -8= (easy to see that +2-2=0)

23-8

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What you actually do is add a zero by adding 2 and also subtracting 2.

You add 2 to the 23 to make 25, and you add 2 to the 8 and thus TAKE AWAY 10. So, the second 2 is being subtracted.

O wow. Lightbulb momemt! Never thought of it as ADDING zero, but yes, this makes perfect sense now. I always wondered, why is it ok to add 2 when that messes up the balance. But even I :tongue_smilie: can see that it's ok to add zero!! +2 and -2 to equal zero, yes! Thank you so much for writing it out in words the way you did, I can understand it much better now!

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O wow. Lightbulb momemt! Never thought of it as ADDING zero, but yes, this makes perfect sense now. I always wondered, why is it ok to add 2 when that messes up the balance. But even I :tongue_smilie: can see that it's ok to add zero!! +2 and -2 to equal zero, yes! Thank you so much for writing it out in words the way you did, I can understand it much better now!

I'm glad I could help :)

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I think the easiest way to see it the difference is 15 is by using a number line. Get out a tape measure, number line, or make one in chalk outside. Get some string or another measuring tape and find out that the difference between 23 and 8 is 15. If you are using string, cut off 15 inches. Now move it up two inches to 10 and 25. The difference doesn't change.

You can also practice outside with numbered boxes made in chalk. If someone moves one box forward and someone else moves one box forward they are still the same difference apart. Or get out a board game that uses spaces. Put two markers and ask how many spaces to catch up. That is a subtraction problem. If one person rolls two and the next one rolls two they are still the same difference apart.

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You'd like Math Mammoth, it teaches concepts like this.

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