Math Tricks for Fast Calculation

Math Tips & Tricks

Divisibility Test
If we divide number a by another number b and the result is a whole number, then the number a is divisible by the number b. In other words, a number a is divisible by the number b if the reminder of a ÷ b is zero. Divisibility rules help us to determine if a number is divisible by another without division process.
  • Any integer is divisible by 1.
  • If the last digit of a number is even, i.e. 0, 2, 4, 6, or 8, then the number is divisible by 2.
  • If the sum of the digits of a number is divisible by 3, then the number is divisible by 3.
  • If the last two digits of the number are divisible by 4, then the number is divisible by 4.
  • If the last digit of a number is 0 or 5, then the number is divisible by 5.
  • If a number is even and divisible by 3, then the number is divisible by 6.
  • Remove the last digit from a number, double it, subtract the product from the truncated original number and continue this process until only one digit remains. If we get 0 or 7, then the original number is divisible by 7.
  • If the last three digits of the number are divisible by 8, then the number is divisible by 8.
  • If the sum of the digits of a number is divisible by 9, then the number is divisible by 9.
  • If the last digit of a number is 0, then the number is divisible by 10.
  • If the difference of the sum of the even digits and the sum of the odd digits is 0 or divisible by 11, then the number is divisible by 11.
  • Remove the last digit from a number, multiply it by 4, add the product to the truncated original number and continue this process until two digits remain. If the result is divisible by 13, then the original number is divisible by 13.
  • Remove the last digit from a number, multiply it by 5, subtract the product from the truncated original number and continue this process as necessary. If the result is divisible by 17, then the original number is divisible by 17.
  • Remove the last digit from a number, double it, add the product to the truncated original number and continue this process as necessary. If the result is divisible by 19, then the original number is divisible by 19.
Have in mind that if a number is divisible by another number, then it is also divisible by each of the factors of that number.

Question 1.
Which of the following numbers are divisible by 2,3 and 5?

a) 12345 b) 12243 c) 1230 d) 30402
Solution:
Since 1230 and 30402 are even numbers, they are potential candidates for solution. Both numbers are divisible by 3 because the sum of the digits of these numbers are divisible by 3. Because the last digit of a number 1230 is 0, then it is divisible by 5. The number 30402 is not divisible by 5. So, the correct solution is c.


Question 2.
Check whether the number 6205 is divisible by 17.

Solution:
Remove the last digit 5 from the number, multiply it by 5 and subtract the product from the truncated original number to obtain

620 − 5 × 5 = 595 Let us repeat the procedure, remove the last digit 5 from the number 595 multiply it by 5 and subtract the product from 59. We get
59 − 25 = 34 Since 34 is divisible by 17, then 6205 is divisible by 17.

Question 3.
If the integer x is divided by 4, the remainder is 3. Find the remainder when 6x is divided by 4.

Solution: The number x can be expressed as x = 4n+3, n ∈ N. So, 6x = 6(4n+3) = 24n+18 or equivalently
6x = 24n + 16 + 2 = 4(6n + 4) + 2 Therefore, if 6x is divided by 4, the remainder is 2.

Multiplication, Addition, and Subtraction Tricks
Adding two or more numbers:
To add two or more numbers round them up to the nearest tenth or hundredth and add rounded numbers. To find the sum of the original equation, we must determine how much we added to the numbers to round them up. If we subtract from the greater of these sums, we obtain the sum of the original equation.

For example, find the sum of 367 and 1389. Firstly, we round them to 370 and 1390 and add these numbers to get 1760. Now, we are determining how much we added to the numbers to round them up.
370−367=3, 1390−1389=1 Finally, the sum of 367 and 1389 is the difference between 1760 and 4, so
1760 − 4 = 1756 multiplication Subtraction of two numbers:
Difference between any two numbers is equal to the distance between these numbers on the number line. Put the numbers to the number line, and find how many units need to reach greater number. For example, find the difference of 83−56. Find these numbers in the number line, then reach the first number with last digit 3. Therefore, 567 = 63. The distance from the 63 to 83 in number line is 20. The result is 207 = 27.


Multiplying numbers by 2:
To multiply any number by 2 just add the number to itself, i.e. double it. Similarly for the multiplying by 4 or by 8.


Multiplying numbers by 10, 100 and 1000:
To multiply any number by 10 just add a zero to the end of the number. To multiply any number by 100 just add two zeros to the end of the number. To multiply any number by 1000 just add three zeros to the end of the number, etc.


Multiplying numbers by 5:
To multiply any number by 5 just add a zero to the end of the number and divide it by 2.


Multiplying numbers by 6:
If we multiply 6 by an even number, the result have the last digit as the number.


Multiplying numbers by 9:
To multiply any number by 9 just multiply it by 10 and subtract the original number from the result.


Multiplying numbers by 11:
Take the original number and put spaces between the first and last digits. Now add the first two, then the second and thirds, etc, and the last two dig- its and put the results in the spaces. For example 351×11. The result is 3(3+5)(5+1)1 ≡ 3861.


Square a two digit number ending in 5:
To square a two digit number ending in 5 just multiply the first digit of the number by itself add 1, and put 25 on the end of the result.


Percentage:
To find a percentage of a number multiply number by the number of percents and move the decimal point over by two places. For example, 6% of 280 is 16.80.


Multiply numbers by drawing lines:
Let us show a way to multiply numbers visually. For example, find the product of 15 × 23. Draw 1 red line and in a short distance draw another 5 blue lines. This represents the number 15. Then draw 2 red lines and then in short distance draw another 3 blue lines. This represents the number 23. Now count the number of intersection points in each corner of the picture. The number of intersection points of red lines will be the first digit of the product. Sum the number of intersection points of blue and red lines will be the middle digit of the product. The number of intersection points of blue lines will be the last digit of the product.

multiplication So, the last digit of the product is 5, the digit in the middle is 4 (13 + 1 = 14) and the first digit is 3 (2 + 1). Similarly, we can derive the rule for multiplication of any two numbers.
Math tricks is a large collection of interesting techniques which can speed up your problem solving skills. These shortcut methods, tips and tricks include addition, subtraction, multiplication, division, fractions, integers, expressions, equations, radical numbers, rational numbers and more. The main objective here is to provide the best and top 100 math tricks for fast calculation.