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| BASIC MULTIPLICATION |
EASY MATHEMAGICS MULTIPLICATION TRICKS
CHAPTER 3
EASY MATHEMATICS MULTIPLICATION TRICKS | always helps you to calculate numbers very easily. I am trying to find out
the easiest way to calculate,
practically I have spent all my childhood devising ever-faster ways to perform mental multiplication; they diagnosed
me as hyperactive and told my parents that I had a short attention span and
that I probably would not succeed in school. It was my limited ability to focus
that inspired me to grow fast approaches to do the math.
Possibly I could not sit still long enough to solve math problems with pencil and paper. Once you have mastered in EASY MATHEMAGICS MULTIPLICATION TRICKS with the aid of Mathemagics workbook formulas/techniques described in this EASY MATHEMAGICS MULTIPLICATION TRICKS chapter, you will not want to trust pencil and paper again!
Possibly I could not sit still long enough to solve math problems with pencil and paper. Once you have mastered in EASY MATHEMAGICS MULTIPLICATION TRICKS with the aid of Mathemagics workbook formulas/techniques described in this EASY MATHEMAGICS MULTIPLICATION TRICKS chapter, you will not want to trust pencil and paper again!
In
this EASY MATHEMAGICS MULTIPLICATION TRICKS Multiplication chapter,
you will learn how to multiply 1-digit numbers by 2-digit numbers and 3-digit
numbers in your head. You will also learn an extraordinarily fast way to square
2 numbers of digits. Even friends with calculators will not be able to follow
you. Believe me, practically everyone will be stunned by the fact that such
problems can not only be solved mentally but can be calculated so quickly with
these formulas of maths tricks.
Sometimes I wonder if we were not cheated at school; these maths tricks formulas/ methods are so simple once you learn them.
There
is a small prerequisite to master the mathematical
tricks in this chapter: you must know the multiplication tables up to 10.
In fact, to really advance, you must know the multiplication tables backward
and forwards. For those of you, who need to shake the loose cobwebs, see the
figure below?
When you have your tables down, you are in for some maths fun, since augmentation gives
sufficient chances to imaginative critical thinking.
2-BY-1-MULTIPLICATION PROBLEMS
If he made his way in the last Mathemagics workbook chapters, he acquired the habit of adding and subtracting from left to right. It will also do virtually all the
calculations in this Mathemagics
workbook chapter from left to right. This is, without a doubt, the opposite
of what you learned in school. But soon you will see how much easier it is to
think from left to right than from right to left. (maths tricks, On the one hand, Mathemagics
workbook formulas, you can start saying your answer out loud before you
have finished the calculation - that way; it seems you are calculating even
faster than you!)
Let's face our first
problem:
First, multiply 40 x 7 = 280. Then, multiply 2 x 7 =
14, add 14 to 280 (from left to right, of course) to get to 294, the correct
answer. Below we illustrate this procedure. We have omitted the diagram of the
mental addition of 280 + 14, since in Mathematics
workbook Chapter 1
we learned how to do this calculation.
At the beginning of the Mathemagics workbook, you should observe the problem while
calculating it to recover the next operation. With Mathemagics workbook practice you can give up this step and
calculate the whole thing in your mind.
Let's try another
example of:
The first step is to
divide the problem into small multiplication
tasks that you can easily perform mentally. Since 48 = 40 + 8, multiply 40 x 4
= 160, and then add 8 x 4 = 32. The answer is 192. (Note: If you're wondering
why this process works, see the section "Why do these things work? Math tricks? "End of the Mathemagics workbook chapter.)
Here are two other
mental multiplication problems that you should be able to solve fairly quickly.
Try calculating them in your head before seeing how we did it.
These two examples are
especially simply because they do not require you to carry any number. Another an especially easy type of maths tricks mental
multiplication problem involves numbers that begin with 5. When 5 are
multiplied by an even digit, the first product will be a multiple of 100, which
makes the problem of the resulting sum simple:
Test your hand on the
following problem:
Notice how much easier
this problem is from left to right. It takes much less time to calculate
"400 plus 35" mentally than to apply the pencil and paper method of
"leave the 5 and load the 3"
The following two
problems are more difficult because they force you to carry numbers when you
reach the sum:
As usual, divide these
problems into easier problems. For the one on the left, multiply 30 x 9 plus 8
x 9, which gives 270 + 72. The problem of the sum is a little more difficult
because it involves carrying a number. Here 270 + 70 + 2 = 340 + 2 = 342.
With practice maths tricks, you'll be more adept at
juggling problems like these in your head, and those that require you to carry
numbers will be almost as easy as the others.
Rounding Up
You saw in the last chapter 2 how useful rounding can be when it comes to subtracting. The same goes for multiplication, especially when the numbers you multiply end in 8
or 9.
Ok take the issue of 69
x 6, illustrated below. On the left we have calculated it in the usual way,
adding. On the right, however, we have rounded 69 to 70, which is an easy
number to multiply, and for many people, it is easier to subtract 420 - 6 than
to add 360 + 54 when mentally calculated.
The following example
also shows how much easier it can be rounded.
The subtraction Mathemagics workbook formula/method works especially well for
numbers that are one or two digits of a multiple of 10. It does not work as
well when you need to round more than two digits because the subtraction part
of the problem gets out of control. As it is, you may prefer to continue with
the addition method. Personally, I only use the sum method because in the time
spent deciding which method to use, I could have done the calculation!
In order for you to
perfect your maths tricks technique,
I strongly recommend practicing more multiplication problems of 2 by 1. Below
are 20 problems for you to tackle. I have provided the answers on the back,
including a breakdown of each component of the multiplication. If, after
solving these problems, you would like to practice more, invest yours.
Calculate mentally, and then check your answer with a calculator. Once you feel confident that you can quickly get these
problems in your head, you will be ready to move on to the next level of mental
calculation.
Exercises:
Multiplication 2 per l.
3-BY- MULTIPLICATION PROBLEMS
Now that you know-how
to solve multiplication problems of
2 by 1 in your head, you will find that multiplying
three digits by a single digit is not much harder. You can start with the
following problem of 3 per l (which is really just a problem of 2 per l disguised):
What could be easier?
Let's try other Mathemagics workbook formulas
of 3 by l problem similar to the one you just did, except that we have replaced
the 0 with a 6 so you have another step to perform:
In this case, Mathemagics workbook shows you a simple
add the 6 x 7 product, which you already know to be 42, to the first sum of
2240. Since you do not need to carry any number, it is easy to add 42 to 2240
to reach a total of 2282.
By solving this and
other multiplication problems of 3 by 1, the difficult part may be keeping them
first sum in memory (in this case, 2240) while doing the following
multiplication problem (in this case, 6 x 7). There is no magic secret to
remember that first number, but with practice, I guarantee you will improve your
concentration so that it is easier to keep the numbers while performing other
functions.
Let's try another Maths Tricks problem:
Even if the numbers are
large, the process is just as simple. For example:
When you solve these
problems for the first time, you may have to look down on the page as you go to
remember what the original problem was. This is fine at the beginning. But try
to break the habit so that eventually it retains the problem completely in the
memory.
In the last section on Mathemagics workbook multiplication
problems of 2 by 1, we saw that problems involving numbers that start with 5
are sometimes especially easy to solve. The same is true for 3-by-1 problems:
Keep in mind that as
long as the first product is a multiple of 1000, the problem of the resulting the sum is no problem because you do not have to carry any number and the digit of
the thousands does not change. If you were solving the above problem in front
of an audience, you could say your first product, "3000 ...” loudly
confident that a loaded number would not change it to 4000. (As an added bonus,
by quickly saying the first digit, gives the illusion that you calculated the
answer immediately, even if you practice alone, say that your first product out
loud frees up some memory space while working on the remaining 2 by 1 problem,
which you can also say in loud voice, in this case, "... three hundred
eighty-eight."
Try the same approach
to solve the following MATHEMAGICS MULTIPLICATION TRICKS problem, where the multiplier is a 5:
Because of the first two
digits of the 3-digit number are even, you can say the answer as you calculate
it without having to add anything! Would not you like all the multiplication
problems to be so easy?
Let's intensify the
challenge by testing a couple of problems that require you to carry a number.
In the following two MATHEMAGICS MULTIPLICATION TRICKS problems, you should bring a number to the end of the problem instead of the
beginning:
The first part of each
of these problems is fairly easy to calculate mentally. The difficult part
comes from having the preliminary answer in your head when calculating the
final answer. In the case of the first MATHEMAGICS MULTIPLICATION TRICKS problem, it is easy to add 5400 + 360 = 5760, but you may have to
repeat 5760 several times while multiplying 8 x 9 = 72. Then add 5760 + 72.
Sometimes in this stage, I will begin to say my Answer out loud before
finishing. As I know I will have to charge when I add 60 + 72, I know that 5700
will become 5800, that's why I say "fifty-eight ..." Then I pause to
calculate 60 + 72 = 132. Because I've already loaded, I just say the last two
digits, "... and thirty-two!" And there's the answer: 5832.
The next two problems
require you to carry two numbers each, so it may take more time than you have
already done. But with practice you will become faster:
When you are facing
these problems for the first time, repeat the answers to each part aloud while
calculating the rest. In the first problem, for example, start by saying:
"Twenty-eight eighty plus five hundred and sixty" a couple of times
out loud to reinforce the two numbers in memory as you add them. Repeat the
answer: "thirty-three hundred and sixty", several times while
multiplying 9 x 7 = 63. Then repeat "thirty-three hundred and
sixty-odd" aloud until you calculate the final answer of 3423. Recognize
that adding 60 + 63 will require that you have a 1, you can begin to give the
final answer in a fraction of a second before you know it: "thirty-four
hundred ... and twenty-three!"
Let's finish this a section on multiplication problems
by 3 with some special problems that you can solve in an instant because of they
require an additional step instead of two:
In general, if you know
the product of the last two digits of the first number and the multiplier
without having to calculate it (for example, you can know that 25 x 8 = 200
automatically since 8 quarters equals $ 2.00), reach the final answer Too much
faster. For example, if you know without calculating that 75 x 4 = 300, it is
very easy to calculate 975 x 4:
To reinforce what you
just learned, solve the following MATHEMAGICS MULTIPLICATION TRICKS problems of 3 by 1 in your head; and then check your calculations and answers
with ours (at the end of the Mathemagics
workbook session). I can assure you from experience that doing mental
calculations is like riding a bicycle or writing. It may seem impossible at
first, but once you master it, you will never forget how to do it.
Exercises:
Multiplication 3 per l.
SQUARING 2-DIGIT NUMBERS
Square
numbers in your head (multiply
a number by itself) is one of the easiest but most impressive mental
calculation feats you can do. I can still remember where I was when I
discovered how to do it. I was 14 years old; I was sitting in a bus on the way
to visit my father at work in downtown Cleveland. It was a trip I made often,
so my mind began to wander. I'm not sure why, but I started thinking about the
numbers that add up to 20. How big can the product of two of those numbers be?
1 started in the middle
with 10 x 10 (or 10), whose product is 100. Then, I multiplied 9 x 11 = 99, 8 x
12 = 96, 7 x 13 = 91, 6 x 14 = 84, 5 x 15 = 75, 4 x 16 = 64, and so on. I
noticed that the products became smaller, and their difference with respect to
100 was 1.4, 9, 16, 25, 36 or 12, 22, 32, 42,
52, 62 (see figure below)
I found this amazing MATHEMAGICS MULTIPLICATION pattern. Then I tried
numbers that add up to 26 and I got similar results. First I calculated 132
= 169, then I calculated 12 x 14 = 168, 11 x 15 = 165, 10 x 16 = 160, 9 x 17 =
153, and so on. As before, the distance of these products. From 169 it was 12,
22, 32, 42 and so on (see the figure below).
Actually, there is a
simple MATHEMAGICS MULTIPLICATION algebraic an explanation for this phenomenon (see the last section of this chapter). At that
time, I did not know my algebra enough to show that this pattern would always
occur, but I experimented with enough examples to convince me of it.
Then I realized that
this pattern could help me square numbers more easily.
Suppose I wanted to
square the number 13, I said to myself. Instead of multiplying 13 x 13, why not
gets an approximate answer using two numbers that are easier to multiply but
also add 26? I chose 10 x 16 = 160. To get an answer, just 32 were added (since 10 and 16 are each to 3 of
13). Since 32 = 9, 132 = 160 + 9 = 169. Perfect!
This method is
diagrammed as follows:
Now let's see how this
works for another square:
In square 41, subtract 1 to get 40 and add 1 to
get 42. Then multiply 40 x 42. Do not be scared! This is simply a
multiplication problem of 2 per l (specifically, 4 x 42) in disguise. Since 4 x
42 = 168, 40 x 42 = 1680. Almost ready! All you have to add is the square of 1
(the number by which you went up and down from 41), which gives you 1680 + 1 =
1681
Can it be so easy to
square a 2-digit number? Yes, with this Mathemagics
workbook method and a little practice, you can. And it works if you
initially, round down or up. For example,
Let’s examine 772,
solving it by rounding up and down:
In this Mathemagics workbook instance, the
advantage of rounding is that it has practically ended as soon as you have
completed the multiplication problem because it is simple to add 9 to a number
that ends in 0!.
In fact, for all
2-digit squares, always round up or down to the nearest multiple of 10. Then,
if the number to be squared ends in 6, 7, 8 or 9, it rounds up, and if the
number to be squared ends in 1, 2, 3, 4, rounding down. (If the number ends in
5, do both!) With this strategy, you will add only the numbers 1, 4, 9, 16 or
25 to your first calculation.
Let's try another MATHEMAGICS MULTIPLICATION problem. Calculate 562
in your head before seeing how we did it, then:
Squares numbers that
end in 5 is even easier. As you will always round up and down at 5, the numbers
that will multiply will be multiples of 10. Therefore,
The multiplication and
the addition are especially simple. We have solved 852 and 352,
below:
When you are squaring a number that ends in 5, round
up and down allows you to drop the first part of the answer immediately and
then finish it with 25. To
For example, if you want to calculate 752,
round up to 80 and lower to 70 will give you "Fifty-six hundred ... and
twenty-five!"
For numbers that end in 5, you should not have
problems to beat someone with a calculator, and with a little practice with the
other squares, it will not be long before you can beat the calculator with any
2-digit square number. Even large numbers should not be feared. You can ask
someone to give you a really big 2-digit number, something in the high 90s, and
it seems that you have chosen an impossible problem to calculate. But, in fact,
these are even easier because they allow you to round up to 100.
Let's say your audience gives you 962.
Test it yourself, and then check how we did it.
It was not easy? You
should have rounded up by 4 to 100 and down by 4 to 92, and then multiply 100 x
92 by 9200. At this point, you can say "Ninety-two hundred" aloud, and
then end with "sixteen" and enjoy! The Clap!
Exercises: 2-Digit Squares
Calculate the
following:
