What if I say, math is nothing like a complicated procedure to get a solution or to solve for X (which by the way most of us think is useless), But instead, Math is a sense we develop from our day to day life. It is just a sense of patterns, the patterns which help us in understanding things. (Even that doesn’t make any sense!) But there is creativity in Math and your mind can use the numbers flexibly. Just like we play with chords to create a song, we can temporarily shift the values of numbers in our head and manipulate numbers (that’s brave!) in different ways to get things done. This ability to do calculations swiftly in your head is called Mental Math. It has its benefits and your mind already has it! Come, let’s learn some tricks of Mental Math and make your friends believe that a genie from a magic lamp solves every Math sum for you!
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Compliment the numbers!
The first step is to find a perfect complement for each number. The mathematical complement of a number is the number which when added to it will give numbers like 10, 100 or 1000, etc.
For example – the complement of 4 is 6, the complement of 7 is 3 & complement of 9 is 1. Similarly, the complement of 97 is 3 and complement of 992 is 8.
These complements are like puzzle pieces which fit into each other perfectly to form a beautiful complete number, which makes calculating in head simple. Let them be on tip of your tongue.
Addition made easy
When adding the list of small numbers all you have to do is make a group of complements.
For example – 6+3+5+7+2+8+4 = [6+4]+[8+2]+[7+3]+5 = 10+10+10+5 = 35
Add two numbers by adding complement to one & subtracting from other
For example – 49+27 can be written as 50+26 = 76
Similarly, 99+86 can be written as 100+85 = 185
And 995+468 can be written as 1000+463 = 1463
Memorize the doubles of numbers to quickly add them
For example – 12+13 is just one more than 12+12 = 24+1= 25
Use same addition fact for bigger numbers like 12+13=25 can be used to perform addition 120+130 = 250
Adding 9 to any number is 1 less than adding 10. This makes it easier to add
For example – 9+25 can be consider as 1 less than 10+25=35, which is 34
Similarly, 99+483 will be 1 less than 100+483=583, which is 582
Subtraction is the new Addition!
Now that you know some fastest ways to add numbers in your head, let’s use them to subtract numbers.
If you have to subtract 7 from 16 stop doing it from right to left. What are complements for? 7+3 = 10 and 10+6 = 16
Adding 3+6 to 7 gives 16 Hence 16-7 = 3+6 = 9
Similarly, 842-67 will be
67+3= 70, 70+30= 100, 100+700= 800, 800+42= 842
That will give 3+30+700+42= 775
This method is useful while calculating change at the shop counter.
Divide them to multiply!
Use division strategy to multiply numbers. To multiply 62 by 3 first divide 62×3 as [60×3] + [2×3] = 180+6 = 186
To multiply any number with 5, first multiply the number with 10 and then divide it by 2
For example – 68×5 will be 68×10 = 680 then 680÷2 = 340
To multiply the number by 4 double it 2 times and for multiplying by 8 double it 4 times
Multiplying any two digit number with 11 is the simplest trick ever!
Add both the digits and place their sum in between those two digits to get an answer.
For example – 54×11 = 5 (4+5) 4 = 594
71×11 = 7 (7+1) 1 = 781
Split bills faster
Logic behind dividing numbers quickly is to reduce them in smaller numbers because it is easy to deal with smaller numbers.
For example – 224÷8 = 112÷4 = 56÷2 = 28
Easy tips & discount
To calculate a 10% tip at a restaurant you can use a simple trick. Calculating 10% is the same as multiplying by 0.1(Or shift the point one place to left) For example – 10% of 26Rs. = 2.6Rs. And 10% of 380Rs. = 38Rs.
If there is a 20% discount at the store use the same trick and make it double. For example – 20% of 820Rs is double 82Rs. = 164Rs
To calculate 15% discount calculate 10% and then add its half to the same. For example – 15% of 640Rs. = 64Rs+32Rs. = 96Rs.
Once you master the addition and multiplication tricks, you are a few steps away from finding a square of two-digit numbers. Let’s find squares of 64
steps 1- find squares of both digits separately 6²=36 & 4²=16 write 3616 on one side.
step 2- find a product of both digits, 6×4=24, multiply it by 2 & add 0 after it, that will give another number like 480
step 3- add both the numbers to get square, 3616+480= 4096
To find a square of a number having 5 at its unit place, write 5²=25 and place the product of the remaining digit with it’s sequential.
For example – 75²= [ 7×8 ] 25 = 5625
Can you imagine finding the square root of any perfect square with the help of Mental Math (Pretty easy after this) Well it’s time for you to find out something by yourself and explore different levels of depth of Mental Math (doing 48²+236+84×92+125 in your head!) As I said, Mental Math is not any secret science, it is a sense. It cannot be taught, only be developed by practice in day to day life. See what your brain can achieve by calculating just like you write (from left to right I mean) Then Math will no longer create problems for you, It will help to solve one!