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Cool mental math tricks

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WE: Engineering (Energy and Utilities)
Cool mental math tricks  [#permalink]

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New post Updated on: 30 Nov 2017, 14:16
1
Hi all,

I am learning some mental math tricks. So I thought I can add them here as I learn them in hope that it may be useful to someone else too. Please feel free to add any tricks you know.

Trick #1: When multiplying any 2 numbers whose unit digits add to 10 and the other digits are all same, the answer will be the (same number *same number+1) followed by multiplication of unit digits.
Eg1: 25 x 25= (2 x 3) (5 x 5)=625
Eg2: 37 x 33= (3 x 4) (7 x 3)=1221
Eg3: 114 x 116=(11 x 12) (4 x 6)=13224


Trick #2: When multiplying any number by 11, write down the largest digit of the number, sum all the digits in between(carry over if more than 10) and then write down unit digit
Eg1: 11 x 12= 1 (1+2) 2=132
Eg2: 11 x 158= 1 (1+5) (5+8) 8= 1738 [ here since 8+5=13, the 1 is carried over and added to 5+1 and therefore the sum in hundreds place becomes 7]

Trick #3: X% of Y= Y% of X
Eg1: 32% of 50= 50% of 32 =16
Eg2: 6% of 300 =300% of 6 =18

Happy learning everyone :-)
_________________


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The price of success is hard work, dedication to the job at hand, and the determination that whether we win or lose, we have applied the best of ourselves to the task at hand.
~Vince Lombardi


Originally posted by Teerex on 25 Nov 2017, 12:19.
Last edited by Teerex on 30 Nov 2017, 14:16, edited 1 time in total.
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Re: Cool mental math tricks  [#permalink]

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New post 29 Nov 2017, 12:57
1
Trick #4: Squaring numbers between 90 and 99

Eg: 93^2
Step 1: Subtract number from 100 to find difference(100-93=7)
Step 2: Subtract the difference from step 1 from original number. This will become the first digits of the square (93-7=86)
Step 3: Square the difference you found in step 1. If it's single digit, add 0 in front to make it double digit. This will be the last 2 digits of the square( 7^2=49)
Final answer: 93^2=8649

Eg2: 98^2:
Step 1: 100-98=2
Step 2: 98-2=96 (first 2 digits of answer)
Step 3: 2^2=4=04(adding zero b/c it is single digit)
Final answer:9604

***************************************************
Trick#5: Square numbers 40-49:
Eg1: 48^2=?
Step 1: Subtract number from 50 (50-48=2)
Step 2: Subtract the difference found in step 1 from 25. This is the first digits of answer (25-2=23)
Step 3:Square the difference you found in step 1. If it's single digit, add 0 in front to make it double digit. This will be the last 2 digits of the square (2^2=4=04, dding the extra zero)
Final answer=2304

Eg 2: 42^2:
Step 1: 50-42=8
Step 2: 25-8=17
Step 3:8^2=64
Final answer=1764
*****************************************************
Trick#6: Multiply by 99

Eg1: 7 x 99=?
Step 1: Multiply the number by 100 (Eg: 7 x 100=700)
Step 2: subtract the number from the value in step 1 to get final answer (700-7=693)

Eg2: 736 x 99
Step 1: 736 x 100=73600
step 2: 73600-736=72864
*****************************************
Trick #7: Multiply any 2 numbers that end with 1

eg1: 71 x 61=?
Step 1: Multiply the tens digit numbers. These are the first digits of final answer (7 x 6=42)
Step 2: Add tens digit numbers. If sum is more than one digit, carry over to result from step 1. This is the next digit(7+6=13. Since 2 digits, 1 is carried over and added to 42 from previous step. )
Step 3: combine and add 1 at end to get final answer(43-3-1)
Final answer:71 x 61=4331

Eg2: 731 x 991=
Step 1: (73x99= 7300-73=7227)
Step 2: 73+99=172. Keeping digit 2 but carrying over 17 to previous step result(7227+17=7244)
Step 3: 724421 (combining adding adding 1)
_________________


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The price of success is hard work, dedication to the job at hand, and the determination that whether we win or lose, we have applied the best of ourselves to the task at hand.
~Vince Lombardi

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Re: Cool mental math tricks  [#permalink]

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New post 30 Nov 2017, 13:56
Trick 8: multiplying numbers between 11 and 19

Eg1: 12 x 16

Step 1: Add larger number to unit digit of smaller number to get value(16+2=18)
Step 2: Add zero to the value from step 1 (18-0=180)
Step 3: Multiply unit digits of the 2 numbers (6x2=12)
Step 4: Add result from step 2 and step 3 to get final answer (180+12=192)

Eg2: 15 x 19

Step 1: 19+5=24
Step 2: 240
Step 3: 9 x 5=45
Step 4: 240+45=285

****************************************************************************************
Trick 9: Squaring numbers between 10 and 19

Eg1: 17^2=?

Step 1: Add the number to it's unit digit (17+7=24)
Step 2: Add zero to result in step 1(24-0=240)
Step 3: Square unit digit of number (7^2=49)
Step 4: Add result from step 2 and step 3 (240+49=289)

Eg2: 16^2:
Step 1: 16+6=22
Step 2: 220
Step 3: 6^2=36
Step 4: 220+36=256

*****************************************************
Trick 10: Squaring numbers between 20-29

Eg1: 23^2=?

Step 1: Split the number into 20+ X form ( 23=20+3)
Step 2: Multiply X value to 40 ( 3 x 40=120)
Step 3: Square X value (3^2=9)
Step 4: Add Value from step 2 and 3 to 400 to get final answer. (120+9+400=529)

Eg2=27^2=?

Step 1: 27= 20+7
Step 2: 7 x 40=280
Step 3: 7^2=49
Step 4: 400+280+49=729

***************************************************************************
_________________


If you like it, give kudos. Thanks :)


The price of success is hard work, dedication to the job at hand, and the determination that whether we win or lose, we have applied the best of ourselves to the task at hand.
~Vince Lombardi

Re: Cool mental math tricks &nbs [#permalink] 30 Nov 2017, 13:56
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