10 Maths Tricks For Calculating Numbers In Head

10 Maths Tricks: In this post, I will tell you 10 awesome maths tricks which will help you in competitive exams as well as in daily life. Make sure to bookmark this website for more such maths tricks as we will upload such posts in the future.

10 Maths Tricks For Calculating Numbers In Head

Trick 1: Tests of Divisibility

Divisibility by 2: A number is divisible by 2 if the unit digit is 0,2,4,6,8

Divisibility by 3: A number is divisible by 3 if the sum of its digits is divisible by 3

13131 is divisible by 3 because 1+3+1+3+1=9 which is divisible by 3

13132 is not divisible by 3 because 1+3+1+3+2=10 which is not divisible by 3

Divisibility by 4: If the last two digits are divisible by 4.

12348 is divisible by 4

Divisibility by 5: If the unit digits are 0 or 5.

12315 is divisible by 5

Divisibility by 8: If the last three digits are divisible by 8

Divisibility by 9: If the sum of the digits is divisible by 9.

13131 is divisible by 9

Divisibility by 10: If the unit digit is 0.

Trick 2: Divide Big Numbers with Approximation

Example1: Suppose we have to divide 3996/78
  • Now let’s calculate the approximate value, 4000/80 = 50
  • Now 3996/78+2
  • 3996 + 2 x 50 = 4096
  • 4096/(8 x 10) = 51.36
Example2: Suppose we have to divide big numbers like 79267/21089
  • Cancel the last 2 digits from both numerator and denominator.
  • 792/210
  • Now 210 – 10 =200
  • 800/200 = 4
  • 792 – 10×4 = 752
  • 752/(2 x 100) = 3.76
Example3: 
  • 807/413-13 => (approximately) 800/400= 2 so now
  • 807-13*2/400 = 781/400 = 195/100 = 1.95 

Trick 3: Divide non-divisible number by 5 

Condition for this trick the number should not be divisible by 5.
Just multiply the numerator by 2 and add a decimal after the second last digit.
  • 231/5 = 231×2 = 46.2
  • 892/5 = 892×2 = 178.4
  • 999/5 = 999×2 = 199.8

Trick 4: Divide non-divisible number by 25 

Condition for this trick the number should not be divisible by 25.
Just multiply the numerator by 4 and add a decimal from the last two digits.
  • 231/25 = 231×4 = 9.24
  • 892/25 = 892×4 = 35.68
  • 999/25 = 999×4 = 39.96

Trick 5: Divide non-divisible number by 125 

Condition for this trick the number should not be divisible by 125.
Just multiply the numerator by 8 and add a decimal from the last two digits.
  • 231/125 = 231×8 = 1.848
  • 892/125 = 892×8 = 7.136
  • 999/125 = 999×8 = 7.992

Trick 6: Find a square of a number ending with 5

Suppose we need to find (25)²
Step 1: Write the square of 5 i.e. 25
Step 2: Multiply the 1st number with a greater number to itself. 2×3 = 6
Final answer 625
  • (55)² = 5×6(25) = 3025
  • (15)² = 1×2(25) = 225
  • (45)² = 4×5(25) = 2025
  • (3.5)² =3×4(25) = 12.25 

Trick 7: Find the square of any number

Suppose we need to find (43)²
Step 1: Write the square of 4 and 3 together i.e. 1609
Step 2: Multiply the numbers and power digits = 4x3x2 = 24
Step 3: Add 24 before unit digit in 1609
1609
+24
——-
1849
——-
Final answer 625
  • (26)² = 0436 + 24 = 0676
  • (14)² = 0116 + 8 = 0196

Trick 8: Adding Fraction whose numerator is 1

Add the denominators = numerator
Multiply the denominators = denominator
1      1    6
— + — = —
4      2    8

Trick 9: Multiplying Number less than 100

Suppose we need to multiply 91×94
100-91 = 9, 100-94= 6
Then we will get:
91    94
9      6

Cross subtract we will get the same value i.e.  91-6=85, 94-9=85

Multiply 9×6 = 54

Answer: 8554

Trick 10: Multiplying Number Greater than 100

Suppose we need to multiply 105×106
105-5 = 100, 106-6= 100
Then we will get:
105    106
5          6
Cross add we will get the same value i.e.  105+6=111, 106+5=111
Multiply 5×6 = 30
Answer: 11130

Share on:

Leave a Comment