Mental Maths with Tricks and Shortcuts

Mental Math with Tricks and Shortcuts

11 if the number has an even number of digits that are all the same: 33, 4444, 777777, and etc.

11 if, beginning from the right, subtracting the smaller of the sums of the even digits and odd digits

results in a number equal to 0 or divisible by 11:

406857/11 Even = 15 Odd = 15 = 0

1049807/11 Even = 9 Odd = 20 = 11

12 if test for divisibility by 3 & 4 work

15 if test for divisibility by 3 & 5 work

Others by using tests above in different multiplication combinations

SQUARE ROOTS Examples

Separate the number into groups of 2 digits or less beginning from the right

(66049)1/2 6 60 49

What number can be squared and be less than 6 = 2 with a reminder of 2

Bring down the second group of digits next to the remainder to give 260

Double the first part of the answer to get 4, divide into 26 of the 260 to get 6 as a trial number

Use 4 & 6 to get 46 and multiply by 6 to equal 276 which is larger than 260, therefore try 5

Use 4 & 5 to get 45, 45 x 5 = 225, 260 – 225 = 35, bring down the 49 to get 3549

Double the 25 to get 50, divide 50 into 354 to get 7 as a trial second part of divisor

Use 50 & 7 to get 507 and multiply 507 x 7 to get 3549 with no remainder.

See complete calculations below:

6 60 49 (257 = Answer

4

45)260

225

507)3549

3549

-------------

0

CUBE ROOTS

Memorize the following:

Cube of 1 = 1, 2 = 8, 3 = 27, 4 = 64, 5 = 125, 6 = 216, 7 = 343, 8 = 512, 9 = 729

Note: no result ends in the same digit

(300763)1/3 Divide in to groups of 3 from right = 300 763

Note: the number ends in a 3. Last digit of cube will be 7 if this is a cube without a remainder

Since 7 cubed = 343 and 6 cubed = 216, the left most group of 300 is between them and we must use

the smaller, or 6.

The answer is 67 This method works up to 1,000,000 for true cubes