Question

Dear Mitch,

Do you know a way to do those really hard subtract problems like 586 – 178 without any borrowing?

Thank you for reading this even if you don't know how.

From Clive Curry

Brooklyn, New York

(But we used to live in England)

Answer

Dear Clive Curry,

Yes, I do!

I know a way to make the kind of subtraction problems you're thinking of much easier than they'd be if you just did them the "normal" or "regular" way that most people learn in school).

It just involves playing with the problem a little before doing the subtraction.

Here, let's take a look at the one you asked about: 586 – 178.

__STEP 1__:

First, for any subtraction involving 3-digit numbers that is given horizontally it is a good idea to rewrite it vertically.

Why?

Because very often when you line things up so the tens, ones, hundreds, etc., are in columns, it helps you see things you might not see when you just have a bunch of numbers written across a line (and the things you see can really help make the work much easier.)

So, back to the one about which you inquired: 586 – 178:

586

__-178__

When it comes to subtraction problems you can add anything you like to the top number (officially, the "minuend") as long as you add the same amount to the bottom number (officially, the "subtrahend").

What?

Yes, look: If you have $9 in your pocket and you want to buy something that costs $2 you have $9 - $2, but iif someone gives you an extra dollar before you make that purchase you have $10 - $2.

But if the reason the person gave you the extra dollar was that he found out that the item you were about to buy went up in price from $2 to $3, in stead of 9 - 2 you would have:

($9 + $1)

- __($2 + $1)__

(or)

($10)

– ( __$3)__

Well, the original problem, 9-2 = 7,

just as the new version, 10 – 3 = 7.

That's how adding the same thing to both the top and bottom numbers gives you the same answer in a subtraction problem!

So how can this help with 586 – 178 ?

Like this: First make 586 into 600. How?

Add 14, but don't forget to you have to do the same thing to the bottom number to keep things right.

So instead of 586 - 178,

you get:

(586 + 14)

- __(178 + 14)__

which equals:

600

- __192__

__Step 2__: Add however many to the bottom number as you need to get a nice even easy number (one that's all zeros except the first digit).

Adding 8 to 192 makes 192 into 200,

And don't forget that you have to do the same thing to the top number:

So you get

608

- __200__

You still have a big 3-digit subtraction problem, BUT most people would say that they can either do this new one in their head or (at least) do it without worrying about any of the carrying stuff (really called "regrouping").

One more example, though this time we'll try skipping right to the most helpful part.

So if you are given this:

387

__- 218__

Add whatever is necessary to make the bottom an easy number to work with (Here, 82). Then do the same thing to the top number.

(387 + 82)

-__ (218 + 82)__

Which gives you:

(469)

- (__300)__

169

Hope this helps,

Mitch