Multiplication

MULTIPLICATION

CRISS-CROSS MULTIPLICATION

How to multiply two numbers by criss cross method.

Suppose you have to multiply 9X7. This is easy but for concept lets take this example

9 9 -1

7 7 -3

9X7 6 3

(7-1) (-3X-1)

Can you guess what happened? We take base as 10 and write our numbers difference from it.

So we wrote 9 and then -1 as 9 is one less than 10 and 7 is one less than 10.

Now write sum/difference of first number by opposite number difference i.e. (9-3 or 7-1) and multiplication of differences (-1X-3).

Thats it!

Now lets take two two digit numbers.

15 15 +5

17 17 +7

15X17 2[2 + 3]5=235

It works as far as you know 32 rule i.e. if number is greater than equal to 32 and is multiplied by number greater than equal to 32 results in number greater than 1000. So make sure that number multiplication is greater than 32X32 or not! (if number is greater than 100 and is multiplied by 100 or more then it results in five digit number).

Now lets look at another way of multiplication. That is criss cross multiplication.

Lets take same numbers as above for sake of simplicity

15

X17

1. First multiply 5X7=35 write 5 in unit place and keep carry as 3.

2. Multiply 7X1 and 5X1 (opposite pairs) and add them with the carry 3=15 write 5 and keep 1 as carry

3. Multiply 1X1 and add carry 1 to it (1+1=2).

4. So the answer becomes 235.

Lets take another example

47X34

i)First multiply 7X4=28 and write unit digit 8 and carry 2 [47X34 Multiply the colored ones]

ii)Multiply (4X4)+(7X3)+2(carry)=39, write down 9 carry 3 [47X34 Multiply the colored ones and add them and add carry]

iii) Multiply (4X3)+3=15 and write it down. [47X34 Multiply the colored ones and add carry]

iv) So the answer becomes 1598.

Similarly, we can use the same technique with 3 digit numbers.

123X745

1. 3X5=15 write 5 and carry 1. [123X745]

2. 5X2+4X3+1(carry)=23, write 3 carry 2. [123X745]

3. (5X1)+(7X3)+(4X2)+2=36 write 6 carry 3. [123X745]

4. (4X1)+(2X7)+3=21 write 1 carry 2. [123X745]

5. (7X1)+2=9. [123X745]

6. So the answer becomes 91635.

One more thing before wrapping criss cross multiplication, if you have to multiply two numbers close to 100.

For eg. 87X98 can be done by

87 87 13

98 98 2

(87-2 or

98-13)

13X2

85 26

84X88

84 84 16

88 88 12

(84-12 or

88-16)

16X12

7[2 + 1]92 ------ Applying 100 rule.

7392

If numbers are close to 200 then do it as follows

192X188

192 192 8

188 188 12

2X(192-8 or 188-8) ----------But our base is now 200 instead of 100 so double the first number

12X8

360 96 ---------- Apply 100 rule to know that number should be 5 digit

Similarly if numbers are close to 300 then multiply the first number by 3 and so on.

It really saves a lot of time when you have to multiply two big numbers, and believe me if you can multiply so quickly then you will surely get the desired percentile/marks in data interpretation section of CAT/ XAT/ GMAT/ GRE etc.

Now try these (Select Between <<>> to see the answer) :

789X678=<<534942>>

324X234=<<75816>>

987X221=<<218127>>

558X234=<<130572>>

MENTAL MULTIPLICATION

Now lets do it mentally

Suppose you have to multiply 48X3

First multiply 4X3 to get 12 write 1 and multiply 2 by 10 to get 20, and keep it in mind

Now multiply 8X3 to get 24 and add 20=44.

So the answer is 144.

Lets take another example with 3 digit

356X5

First multiply 3X5 to get 15,write 1 and multiply 5X10 to get 50 and keep it in mind.

Now multiply 5X5=25 and add 50 to it=75,write 7 and multiply 5X10 to get 50 and keep it in mind.

Now multiply 5X6=30 and add 50 to it to get 80. And put it down the result as 1780.

The above can be understood by

356X5=15₂5=175₃0=1780.

If both numbers are more than 10, then try this

1.If number is composite then try to break it into small parts like for example 92X72 can be done as 92X9 and then 828X8.

2.If number is prime (or composite) then do it in parts like 92X37 can be done as 92X30 which is equal to 92X3 and append 0 to it=2760, and then 92X7=644 and add them to get 3404.

Can you tell me why above trick works and why above clauses are true?

Now try to the solve above problems mentally.

There might not be a direct question asked in CAT/XAT/GMAT/GRE/SAT etc but this trick comes handy in application of data interpretation questions and quantitative ability.

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Thats it folks, catch you next time, until then if you have any query regarding anything contact me at friggere.Sumit@gmail.com

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