Maths trick

Multiplying two digit number by 11 

1. Take a two digit number – Example: 62  
2. Add both the digits – 6+2=8 
3. Place the answer of step 2 in between the 2 digits of the number-   682 
4. On multiplying 62 by 11, answer is:682 

In case the addition of two number is a 2 digit number then add 1 to first digit and subtract 10 from the addition of the 2 digits :- 

Example: 78*11 : 

• 7+8=15 
• (7+1) (15-10) (8) 
• 858 will be the answer 

Multiplying two digit number by 11 

1. Take a two digit number – Example: 62  
2. Add both the digits – 6+2=8 
3. Place the answer of step 2 in between the 2 digits of the number-   682 
4. On multiplying 62 by 11, answer is:682 

In case the addition of two number is a 2 digit number then add 1 to first digit and subtract 10 from the addition of the 2 digits :- 

Example: 78*11 : 

• 7+8=15 
• (7+1) (15-10) (8) 
• 858 will be the answer 

Three digit number divisible by 7 

1. Take a three digit number – Example : 357 
2. Double the last digit of the number: 7*2= 14 
3. Subtract the answer of step 2 from the first two digits of the number: 35-14= 21 
4. Divide the answer of step 3 by 7: 21/7=3 
5. If it is divisible by 7 then the three digit number is also divisible by 7:  357 is divisible by 7 

Multiplying two numbers between 11 and 19  

1. Take two numbers between 11 and 19 – Example : 14*19 
2. Add first number and last digit of the second number, and multiply the answer by 10:(14+9)*10= 230  
3. Multiply last digits of both the numbers:4*9=36  
4. Add the answers of step 2 and 3: 230+36=266  
5. On multiplying 14 and 19, answer is 266 

Squaring using formulas   

1. (a+b)²=a²+b²+2ab
   • 43²= (40+3)² 
   • (40+3)²=40²+3²+(2*40*3)
     
     • =1600+9+240
     • =1849
      
2. (a-b)²=a²-b²-2ab
• 58²=(60-2)²
• (60-2)²=60²-2²-(2*60*2)
  
  • =3600-4-240
  • =3600-236
  • =3364
   

Multiplying numbers between 50-59    
A) If units place digit of both the numbers is either even or odd 

Example: 54 and 56 

1. Add half the sum of units digits to 25
   (4+6)/2 +25= 5+25= 30
2. Multiply the units digits
   2*6=24 ( If the product is less than 10 then precede 0 to it) 
3. Affix answer of step 2 to answer of step 1
   54*56 =3024

Example: 51 and 53 

1. Add half the sum of units digits to 25
   (1+3)/2 +25= 2+25=27
2. Multiply the units digits
   1*3=03 ( If the product is less than 10 then precede 0 to it) 
3. Affix answer of step 2 to answer of step 1
   51*53=2703

B) If units place digit of both the numbers is either even or odd 

Example: 52 and 57 

1. Add half the sum of units digits to 25 ignoring the .5
   (2+7)/2 +25= 4+25= 29
2. Multiply the units digits and add the product to 50
   (2*7)+50=64 
3. Affix answer of step 2 to answer of step 1
   52*57 =2964

Multiplying by 19 

Example: 7867*19 

1. Double the given number
   7867*2=  15734
2. Affix 0 to the answer of step 1 and subtract the given number from it
   157340-7867=149473
   7867*19=149473

Multiplying by 99 

Example: 567898*99 

1. Affix 00 to the given number
   56789800
2. Subtract given number from the number obtained in step 1
   56789800-567898= 56221902
   567898*99= 56221902

Multiplying even number by 5 

Example: 6758 *5 

1. Divide the given number by 2 
   6758/2= 3379
2. Affix 0 at the end of the answer of step 1
   33790
   6758*5=33790

Multiplying by 9 

Example: 7653*9 

1. Add zero at the end of the  number
   76530
2. Subtract the original number from the new number
   76530-7653= 68877
   7653*9=68877

Multiplying by 25 

Example: 147*25 

1. Add two zeros at the end of the number
   14700
2. Divide the new number by 2
   7350
3. Divide the new number by 2
   3675
   147*25 =3675

Multiplying by 15 

Example: 3456*15

1. Add zero at the end of the given number
   34560
2. Divide the new number by 2
   34560/2=17280
3. Add the results of step 1 and 2
   34560+17280= 51840
   3456*15=51840

Multiplying by two digits number that has 9 in units place 

Example:  57*29

1. Add 1 to the two digits number ending by 9
   29+1= 30
2. Multiply the given number by answer of step 1
   57*30= 1710
3. Subtract the given number from answer of step 2
   1710-57= 1653
   57*29= (57*(29+1))- 57=1653

Multiplying odd number by 5 

Example: 5673*5 

1. Divide the given number by 2 
   5673/2= 2836.5
2. Remove the decimal 
   28365 is the answer
   5673*5= 28365

Thanks for reading 😊