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Math Tricks For Everyone - IntoMath

Whether or not you are a math fan, you will appreciate a faster way of solving math problems, without having to struggle through complex solutions or looking for extra math help or a calculator every time.

The good news is that you can solve many arithmetic problems without a calculator almost instantly and in this blog post we are going to show you how.


Instant multiplication of 11 by any two-digit number


Let’s say you need to multiply 11 by some 2-digit number instantly. It is very easy, if you know the secret.


Consider the following problem:

43 x 11


To solve this problem instantly, just add the digits of 43 and put the result in between these digits:


43 x 11: 4 + 3 = 7, the answer is 473


Check the answer by using the calculator to confirm that it works :)


Here are some more examples:

18 x 11: 1 + 8 = 9, the answer is 198

10 x 11: 1 + 0 = 1, the answer is 110

13 x 11: 1 + 3 = 4, the answer is 143


Well, this was only the first part of the trick.

What would the answer be for 78 x 11?

The trick would follow the same pattern, but we now have to carry 1-tens to the head digit.

The result is 7+8=15, so we need to put the right digit in between the digits 7 and 8 as we did in the above section and add 1-tens to the left:


78 x 11: 7 + 8 = 15, the answer is (7+1)58 => 858


Here are some more examples:

99 x 11: 9 + 9 = 18, the answer is (9+1)89 => 1089

66 x 11: 6 + 6 = 12, the answer is (6+1)26 => 726

55 x 11: 5 + 5 = 10, the answer is (5+1)05 => 705



Instant squaring of two-digit numbers ending in 5


As you may already know, the square of a number is that number multiplied by itself.

The algorithm is: Multiply the first digit by the digit 1 more than the given one and put 25 (the square of 5) following the result of the first computation.

Consider the following problems:


25 x 25: 2 x 3 = 6, the answer is 625

75 x 75: 7 x 8 = 56, the answer is 5625

45 x 45: 4 x 5 = 20, the answer is 2025

95 x 95: 9 x 10 = 90, the answer is 9025

15 x 15: 1 x 2 = 2, the answer is 225

55 x 55: 5 x 6 = 30, the answer is 3025

85 x 85: 8 x 9 = 72, the answer is 7225


Left-to-Right addition of numbers


The assumption here is that you are able to add and subtract natural numbers.

We will start with adding two-digit numbers and then will continue with adding three or more digit numbers.

The easiest two-digit addition problems are those that do not require you to carry any numbers.


For example: 87 + 12

To solve this, first add 10 and 87 and then add 2 to the result:

The calculations are as follows: (87 + 10) + 2 = 97 + 2= 99


Here are more examples:

13 + 15 = (13 + 10) +5 = 23 + 5 = 27

18 + 11 = (18 + 10) + 1 = 28 + 1 = 29

Even though this looks very simple, it shows the fundamental method of mental process.

Now let’s try to add the numbers that require us to carry the number:


15 + 17 = (15 + 10) + 7 = 25 + 7 = 32

26 + 26 = (26 + 20) + 6 = 56 + 6 = 62

38 + 67 = (38 + 60) + 7 = 98 + 7 = 105


Try practicing this method and you will be able to add the numbers very fast.

The addition of three-digit numbers looks the same.

Now it is your turn to try:

537 + 467 = (537 + 400) + 60 + 7 = ?

203 + 145 = (203 + 100) + 40 + 5 = ?


Those were a bit more difficult, but if you first practice the addition of two-digit numbers, you will be able to add three-digit numbers instantly as well.


Left-to-Right subtraction of numbers


When doing subtraction of any two-digit numbers, you need to simplify the problem, such that you are left with subtracting or adding a one-digit number.

Let’s consider the example: 96 – 35

To solve this, first subtract 30 and then subtract 5 from the result:

96 – 35 = (96 – 30) – 5 = 66 – 5 = 61

Here are some more examples:


67 – 23 = (67 - 20) – 3 = 47 – 3 = 44

38 – 13 = (38 - 10) – 3 = 28 – 3 = 25

99 – 98 = (99 – 90) – 8 = 9 – 8 = 1


Subtracting looks easy when there is no borrowing (when a larger digit on the right is being subtracted from a smaller one).

The good thing is that subtraction problems can be turned into addition.


Let’s consider an example:

77 – 18


For this example, the best strategy would be to subtract 20 from 77, then add 2.

77 – 18 = 77 – (20 - 2) = (77 - 20) + 2 = 57 + 2 = 59


So, the rule here is: round the second number up to a multiple of ten, then subtract the rounded number and then add back the difference.


Here are some more examples:


64 – 29 = 64 – (30 - 1) = (64 - 30) + 1 = 34 + 1 = 35

91 – 27 = 91 – (30 - 3) = (91 - 30) + 3 = 61 + 3 = 64


There are lots of other mental arithmetic tricks that can be used to solve problems in a more elegant way. Do you know any? Comment below :)

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