Whether or not you are a fan of mathematics, 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. Knowing some math tricks could definitely help.
You can solve many arithmetic problems without a calculator almost instantly and in this blog post we are going to show you how.
Math trick 1: 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 11
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)5 => 75
Math trick 2: 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
Math trick 3: 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.
Math trick 4: 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 math tricks that can be used to solve problems in a more elegant way. Are there any other ones that you know? Comment below 🙂
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