Division by Splitting

The trick is easiest to use when the number being divided is a little over 100. To speed up the calculation, split the number being divided into two parts so that one part is 100. Then divide both parts of the number by the second number and add the results.

112 ÷ 4 = ??

Time for you to try.

Division by 5

It is quite easy to divide a number by 5 if you follow the rule:”Double and then divide by 10″.

75 ÷ 5 = ?

Double of 75 is 150
Dividing by 10 gives 15

Answer = 15

44 ÷ 5 = ??

Double of 44 is 88
Dividing by 10 gives 8.8

Answer = 8.8

Time for you to try

Squaring any 3 digit number.

By this method, you can square any 3 digit number.

This trick involves rembering the same two rules “Single digit is squared” and “Pair of digits multiplied and doubled”

(234) = ??

We move right to left.

Step - 1 As per the rule, single digit is squared

i.e Square of 4 = 4 x 4 = 16 (1 of 16 will be carried over)

Step - 2 Apply the rule “Pair of digits multiplied and doubled” on the pair - 4 and 3

i.e 4 x 3 = 12, Double of 12 is 24

1 carried from the previous step gets added to 24, which makes it 25 (2 of 25 will be carried to the next step)

Step 3 - Apply the rule “Pair of digits multiplied and doubled” on the pair 4 & 2 and rule “Single digit is squared” on 3. Add the result

i.e 4 x 2 = 8, Double of 8 is 16

Square of 3 is 9

Add 16 and 9 = 25

2 carried from the previous step gets added to 25, which makes it 27 (2 of 27 will be carried to the next step)

Step 4 - Apply the rule “Pair of digits multiplied and doubled” on the pair - 3 and 2

i.e 3 x 2 = 6, Double of 6 is 12

2 carried from the previous step gets added to 12, which makes it 14 ( 1 of 14 will be carried to the next step)

Step 5 - Apply the rule “Single digit is squared” on 2

i.e Square of 2 = 2 x 2 = 4 (1 carried from the previous step gets added to 4, which makes it 5 )

Thus the answer is 54756

Time for you to try

Want to practice again?

Squaring any 2 digit number.

By this method, you can square any 2 digit number.

This trick involves remembering two rules “Single digit is squared” and “Pair of digits multiplied and doubled.”

Have fun with the trick

(34) = ??

We move right to left.

Step - 1 As per the rule, unit place digit is squared

i.e Square of 4 = 4 x 4 = 16 (1 of 16 will be carried over)

Step - 2 Apply the rule “Pair of digits multiplied and doubled” on 4 and 3

i.e 4 x 3 = 12

Double of 12 is 24

1 carried from the previous step gets added to 24, which makes it 25 ( 2 of 25 will be carried to the next step)

Step - 3 Apply the rule “single digit is squared ” on tens’s place digit i.e. 3 in this case.

i.e 3 x 3 = 9

2 carried from the previous step gets added to 9, which makes it 11

Thus the answer is 1156

Time for you to try

Squaring of numbers near the base

This is easy especially when the numbers to be squared are near the base 10, 100, and 1000 and so on.

12² = ??

First find the difference between 12 and the base (i.e 10)

12 is 2 more than 10 so the difference is 2

Now add 2 to 12 to get the left part of the answer i.e 14

For the right part of the answer, write the square of the difference i.e 2 x 2 is 4

Answer 144

14² = ??

First find the difference between 14 and the base (i.e 10)

14 is 4 more than 10 so the difference is 4

Now add 4 to 14 to get left part of the answer i.e 18

For the right part of the answer we square the difference i.e. 4 x 4 is 16

Since the base 10 has only one zero, right part of the answer should also be a one digit number.

Thus put 6 on the right side and carry over one to the left side.

The left side thus becomes 18 + 1 = 19

Answer 196

98² = 9604

First find the difference between 98 from the base (i.e 100)

98 is 2 less than 100 so the difference is 2

Now subtract 2 from 98 to get the left part of the answer i.e 96

For the right part of the answer write the square the difference i.e 2 x 2 is 4

Since the base 100 has two zeros, right part of the answer should also be a two digit number.
Put a 0 before 4 to make it a 2 digit number. Thus the right part becomes 04.

Answer = 9604

Squaring of numbers that end in 1 or 9

The trick is to multiply the whole numbers on the either sides of the number that you are squaring and then add 1.

21² = 441

As the number to be squared ends in 1.

• Multiply the two whole numbers on the either
  sides of 21.

  20 x 22 = 440

• Add 1 to 440440 + 1 = 441

19² = 361

As the number to be squared ends in 9.

• Multiply the two whole numbers on the either
  sides of 19.

  18 x 20 = 360

• Add 1 to 360360 + 1 = 361

Time for you to try

Squaring of numbers that begin with 5

You can square any number with this trick which begins with 5 in seconds without much of calculation.

To get the left part of the answer, always add 25 to ones digit.
To get the right part of the answer, always square the ones digit.

54² = 2916

As the number to be squared begins with 5 we can use this trick.

• Add the 25 to ones digit (i.e 4)4 + 25 = 29 (left part of the answer)

• Square the ones digit4 x 4 = 16 (right part of the answer)

Answer 2916

As the number to be squared begins with 5 we can use this trick.

• Add the 25 to ones digit (i.e 2)2 + 25 = 27 (left part of the answer)

• Square the ones digit2 x 2 = 04 (right part of the answer)

Put 0 before 4 to make it a double digit number.

Answer 2704

Time for you to try

Squaring of numbers that end in 5

You can square any number with this trick which ends in 5 in seconds without much of calculations.

75² = 56 25

As the number to be squared ends in 5 we can use this trick.

• Multiply 5 by 5 and write the answer 25 on the right side.

• Then multiply 7 by 8 (7 + 1) and write the answer 56 on the left side.

Answer 5625

305²= 93025

• Multiply 5 by 5 and write the answer 25 on the right side.
• Then multiply 30 x 31 (30 + 1) and write the answer 930 on the left side.

Answer 93025

Time for you to try

Multiplying two numbers whose difference is two.

You can use this trick for calculations such as 11 x 13, 13 x 15, 24 x 26 etc. where the numbers differ by 2.

Square the number between these two numbers and then subtract 1 from the result.

Time for you to try

Cross Multiplication

This is a very powerful trick. You can multiply any 2 digit number by another 2 digit number.

22 x 31 = ?? (Write the multiplicants is the this form)