Chapter I: Basic Number Strategies

Strategy I: Distributive Properties of Numbers

In this course, there are math strategies for understanding
addition, subtraction, multiplication, and other kinds of basic
arithmetic. These strategies are the fundamental building blocks
to understanding the advanced lessons, like math tricks and games,
which are available to you when you subscribe to this course.

The Distributive Property of Numbers is the first math skill you’ll learn. This strategy makes all other strategies much easier to operate and understand. The distributive property of numbers is all about the proper understanding of numbers.

Take a look at this figure:

112,488

The number above has six digits. We know that the 1 on the leftmost side of the number is really 100,000, the 1 next to it has a value of 10,000, and the 2 to the right of it is 2,000.

The number 4 has a value of 400, 8 in the tenths column is really 80, and 8 at the rightmost side of the number is simply 8.

Yes, this may seem redundant to you, as you certainly took these up during your grade school math subjects. However, we tend to treat them like what they look like on paper, strictly numbers ready to be cross multiplied or added by another number below it, just as what we were taught in school. In learning math, it is extremely important to interpret each digit in their rightful places, as we will use this understanding on upcoming strategies.

Now, look at the next problem:

24 x 99 =?

I’ll bet my dad’s money your reaction was to reach out for a calculator of sorts. Well, that wouldn’t serve our purpose here, doesn’t it?

Okay, what has this got to do with the distributive properties of numbers?, you ask.

Instead of lining them up like:

x 99

-----

…and then go through the usual motions of solving them (multiply ones to ones, ones to tenths, and so on), we can look at it another way: isn’t 99 very close to 100?

x 100

------

And so we begin working with that estimation. Now we can multiply 24 by 100 and giving us 2,400, which is very, very close to our answer. Since we added 1 to 99, we can subtract a 24 from 2,400.

  - 24

  -----

That’s still a bit complex for our purposes. Let’s try another approach.

Assume that 2,400 is $24.00, and 24 is 24 cents on the dollar. So what we’re really doing is:

  $24.00

- $00.24

---------

Wait a minute. Isn’t 24 cents really close to 25?

  $24.00

- $00.25

---------

Now, mentally picturing the arithmetic would be much easier. The equation would yield $23.75. Since we added 1 to the subtrahend, we simply subtract one to the answer: $23.76.

Hence, our final answer to the original problem is 2,376.

We decided to go along the currency approach because we are so used to calculating fractions in our local currencies. Oftentimes, we do this sort of mental math in some other transactions. This is the appeal and benefit of a proper understanding of distributive properties. The strategy will allow you to take advantage of numbers and create a “pathway of least resistance” when it comes to solving them. In this case, we resorted to monetary estimates.

It seems like we took the long road of getting to the problem quickly. Obviously, this approach of learning math won’t solve every math problem you meet along the way, but it encourages you to think “out of the box” and go for unconventional and easier ways to calculate mentally.

With much practice on this math strategy, you might be able to solve problems like these lightning-quick:

   687             147            559

   954             892            431

 + 126           + 252          + 817

 ------          ------         ------

Always look for ways to make it easier for you. For instance, manipulate numbers by trying to round them off to the nearest 10’s, 100’s, 1,000’s, and so on. Use half or quarter estimates. By getting around the conventional way of computing, you can solve many problems in your head quickly. This will increase your math skill a hundredfold!

Let’s have another example.

If you had this problem:

24 x 52 =?

Let’s make 24 our “base number”, meaning let’s use 24 as a foundation to build our answer upon. Of course, our manipulation number is 52.

We know that 52 is close to 50, which in turn, is half of 100. Using 100 as our manipulation number, we know that

24 x 100 = 2,400

Yet, we only want half of it since our manipulation number is half of 100, hence, our nearest answer would be 1,200!

Okay, but what about our manipulation number 52?

Simple. Now we have to add 24 x 2 since 52 is really “50 + 2”. You will know immediately that 24 x 2 is 48 since we do that with calculating day-hours most of the time. Now add 48 to 1,200.

24 x 52 = 1,248

Still, at first you may cringe at how long it took us to get at the answer, but when practiced consistently in your head, you’ll realize that this is the more natural way of doing arithmetic. With good practice and trained memory, this math strategy is extremely useful and will make you feel like a genius!

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Fun, isn’t it? And it gets more fun along the way. Subscribe now to our course, and you’ll have access to the more amazing strategies and material:

Chapter I: Basic Number Strategies

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