Section 4

Multiplying two digit numbers with 99

Let us try 23 x 99

Take the number 23

Subtract 1 from 23 and write down the answer : 22

Take the number 22

Subtract each of these digits from 9

9 - 2 = 7
9 - 2 = 7


Answer: 23 x 99 = 2277

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Let us try 38 x 99

Take the number 38

Subtract 1 from 37 and write down the answer : 37

Take the number 37

Subtract each of these digits from 9

9 - 3 = 6

9 - 7 = 2

Answer: 38 x 99 = 3762

Section 3

Multiplying digits with 111

Let us try 213 x 111

Take the number 213

Write the right most digit as is : 3

Move to the left to add 3 + 1 = 4

Add all three digits 2 + 1 + 3 =6 (Note: this step works only while multiplying 111 with 3 digit numbers)

Add the first two digits 1 + 2 = 3

Write the first digit as is : 2

Answer: 213 x 111 = 23643

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Let us try 355 x 111

Take the number 355

Write the right most digit as is : 5

Move to the left to add 5 + 5 = 10

Carry over the 1 from 10 to the next step

Add all three digits 3 + 5 + 5 (+1 carried over)=14 (Note: this step works only while multiplying 111 with 3 digit numbers)

Carry over the 1 from 14 to the next step

Add the first two digits 3 + 5 (+1 carried over)= 9

Write the first digit as is : 3

Answer: 355 x 111 = 39405

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Section 2

Multiplying digits with 11

Let us try 23 x 11

Take the number 23

Write the right most digit as is : 3

Write the left most digit as is : 2

Add 2 + 3 = 5

Answer: 23 x 11 = 253

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Let us try 57 x 11

Take the number 57

Write the right most digit as is : 7

Write the left most digit as is : 5

Add 5 + 7 = 12

In this case we will carry over the 1 from 11 and add it to the left most digit.

Answer: 57 x 11 = 627

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Let us try 663 x 11

Take the number 563

Write down the right most digit as is 3

Add the last two digits 3 + 6 = 9

Add the first two digits 6 + 6 = 12 In this case just write down 2 and carry over 1

Write down the left most digit 5 and add it to the carried over 1 which gives us 6

Answer: 663 x 11 = 6293

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Section 1

Squaring numbers that end with 5

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Squaring means multiplying a number by itself.

Let us try 25²

which means 25 x 25

The number other than 5 in 25 is 2

The number after 2 is 3

2 x 3 = 6


We know that 5 x 5 = 25

The answer:

25² = 625   (Here I will show arrows to the earlier calculations)

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Let us try 45²

which means 45 x 45

The number other than 5 in 45 is 4

The number after 4 is 5

4 x 5 = 20



We know that 5 x 5 = 25

The answer:

45² = 2025   (Here I will show arrows to the earlier calculations)

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Let us try 115²

which means 115 x 115

The number other than 5 in 115 is 11

The number after 11 is 12

11 x 12 = 132



We know that 5 x 5 = 25

The answer:

45² = 13225   (Here I will show arrows to the earlier calculations)

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Phases

Option 1

Phase 1 - 4 sutras

Phase 2 - next 4 sutras

Phase 3 - next 4 sutras

Phase 4 - last set of 4 sutras

Option 2

Phase 1 - Multiplication

Phase 2 - Division

Phase 3 - Complex Algebra

Option 3 (selected)

Phase 1 - Beginner

Phase 2 - Intermediate

Phase 3 - Expert

List of tutorials

Beginner

• Squaring two and three digit numbers that end in 5.
• 25 x 25
• 45 x 45
• 115 x 115
• Multiplication of two or three digit numbers with 11.
• 23 x 11
• 57 x 11
• 663 x 11
• Multiplication of three digit numbers with 111.
• 213 x 111
• 355 x 111
• Multipliation of any two digit number with 99.
• 23 x 99
• 37 x 99

Intermediate (Phase II)

Expert (Phase III)