### Extended multiplication techniques:

#### Multiplying 2-digit number with same number in unit digit and ten‟s digit add up to 10:

*Example: (43×47)*

In this example unit digit is same i.e. 4. And (3+7=10). So,

Answer: (3×7) =21 is in RHS. And {(4+1) ×4} =20 in LHS. So final answer is 2021

#### Multiplying 2-digit number with same number in ten‟s place and unit digits add up to 10:

*Example: (47×67)*

In this type we need to follow a formula for LHS,

{(1 st number‟s ten‟s digit × 2 nd number‟s ten‟s digit) +common digit}= {(4×6)+7} =31.So our LHS is 31.

Now for RHS simply put the square of common digit which 49(7 2 ).

So final answer is 3149

#### Multiply numbers just over 100:

*Example: (103×106)*

Answer: RHS is (3×6) =18 and LHS is (103+6) = 109. So final answer is 10918

#### Find square of number containing repeated digits:

Now what is repeated digit containing number? Some of the examples are 1111, 9999, 2222 etc. And these types of question mostly ask in competitive exam. So understand the below example properly,

1. 1111 2 = In this „1‟ is repeated four times, so „4‟ is in the middle of the final answer, now write 1 to 3 before 4 and 3 to 1 after 4. That is 123 4 324. So final answer is 1234321.

2. 9999 2 = In this „9‟ is repeated four times. Now we put (4 – 1) = 3 times 9 and the 8 in the LHS, i.e. 9 9 9 8. Now for RHS we put 3 times zero then 1, i.e. 0 0 0 1. So answer is 99980001.

3. 3333 2 = In this „3‟ is repeated four times. So we put (4 – 1) = 3 times 8 then 9 in RHS. So, RHS is 8889. For LHS we put 3 times 1 then 0, i.e. 1110. So final answer is 88891110.

#### Special multiplication tips for 5, 25, 125 and 625

Multiplication by 5 |
Multiplication by 25 |
Multiplication by 125 |
Multiplication by 625 |

Put one 0 at the end of the number and divide by 2. Example: (124×5)=1240/2=620 |
Put two 0 at the end of the number and divide by 4. (124×25)=12400/4=3100 |
Put three 0 at the end of the number, divide by 8. (124×125)=124000/8=15500 |
Put four 0 at the end of the number, divide by 16. 1240000/16= 77500 |

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