# 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 4****7****3**

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 1****9****8**

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

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

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****)****5****8 => 8****5****8 **

Here are some more examples:

**99**** x 11:** **9 + 9 = ****18****, the answer is (9+****1****)****8****9 => 10****8****9**

**66**** x 11:** **6 + 6 = ****12****, the answer is (6+****1****)****2****6 => 7****2****6**

**55**** x 11:** **5 + 5 = ****10****, the answer is (5+****1****)****0****5 => 7****0****5**

**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:

**2****5 x 25: ****2**** x ****3**** = 6, the answer is ****6****25 **

**7****5 x 75: ****7**** x ****8**** = 56, the answer is ****56****25**

**4****5 x 45: ****4**** x ****5**** = 20, the answer is ****20****25**

**9****5 x 95: ****9**** x ****10**** = 90, the answer is ****90****25**

**1****5 x 15: ****1**** x ****2**** = 2, the answer is ****2****25**

**5****5 x 55: ****5**** x ****6**** = 30, the answer is ****30****25**

**8****5 x 85: ****8**** x ****9**** = 72, the answer is ****72****25 **

**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 :) ** **