MATHEMATICAL TRICKS OF MULTIPLICATION AND SQUARE

       Multiplication is very very essential for every person and competitive students. In competitive exam we take a lot of time to calculate the square of a number or a multiplication of two numbers but with these tricks we can easily calculate the multiplication or squares of any number within 5 to 10 seconds.

       You have to keep these tricks in your mind for easy multiplication.

       Let's know the tricks :-

(1) Tricks–1 :-

        When any number has 5 at its unit place, we can easily find the square of its number by applying this trick.

        Suppose "★5" is any number whose unit place is always 5 and "★" refers to the number of any digit ("★" is any number and can be a one, two or more than two digit number). Now to calculate (★5)², first we have to calculate the multiplication of "★" & "(★+1)"   [  i.e :-  ★×(★+1)=y  ] and then 5×5  [ i.e :-  5×5=5²=25 ]. So that the square of the number "★5" is always "y25"  [ i.e :-  (★5)²=y25 ].

        Look at this picture to know more easily:-

∴  (★5)²=y25

Example-1

 

        For the number 35. It will be :-

∴ (35)²=1225

Example-2

        For the number 105. It will be :-

∴ (105)²=11025

(2) Tricks–2 :-

       In this trick, we will calculate the square of any two-digit number. Remember, this trick will only work for any two-digit number. So let's consider that "xy" is a two-digit number, where x & y are the two digits of the number "xy".

        Now, we will calculate the value of (xy)².

        Suppose, x²=ab, y²=cd 

& x×y×2=efg  [ Here we have taken the total numbers seen in (xy)² for multiplication. ]

        Here a, c, e & f can sometimes be zero or not.

        Now look at the image, where we have to write these values :-

∴ (xy)² = summation result (R).

Example-1

        For (43)²

          Here 4²=16, 3²=09 & 4×3×2=024

∴ from above (43)²=1849

Example-2

        For (21)²

          Here 2²=04, 1²=01 & 2×1×2=004

∴  (21)²=441

Example-3

        For (97)²

           Here 9²=81, 7²=49 & 9×7×2=126

∴  (97)²=9409

        With the help of the above trick, we can calculate the square of any two-digit number within 5 to 10 seconds.

N.B :- We have written many things here, by which this trick looks big, because we want you to understand this trick easily. Therefore, when you apply the trick, you should not write simple calculations like 4²=16, 3²=09 and 4×3×2=024, which are seen in Example-1. So you should do these calculations in your mind and put them directly and then add them to get the result.

(3) Trick–3 :-

        This trick works for any number, multiplied by the largest number of any digit, such as 99, 999, 9999, 99999, 99999, etc. [ i.e :- One is any number, while the other is a number with 9 each digit ].

N.B :- This trick works when the second number ( the number whose every digit is 9 ) contains more digits than the first number.

        See the examples to know more easily:-

Example-1

          Let us consider that the numbers are 7 and 9999. See these steps for calculating multiplication:-

Step–1 :- Take equal number of digits from each side. Such as 9 from 9999 and 7 from the other side.

Step–2 :- Multiply 7 with 9. i.e :- 7×9=63.

Step–3 :- Take 6 from the number 63 and write this after the 'equal' (=) sign.

Step–4 :- Now after 6, write these ninas, which are in the circle.

Step–5 :- Now take 3 from 63 and write this after nines. Here the trick is completed. So 7×9999=69993.

See more other examples:-

Example–2

Example–3

Example–4

N.B :- It is very easy to calculate the multiplication of the 1st one digit number with the 2nd larger number, but it is difficult to calculate the multiplication of the 1st number with the 2nd larger number when they contain two or more digits, like Example-3 and 4. So look the next trick for this.

(4) Trick–4 :-

        To calculate hard multiplication of Trick-3 (Like example-3 & 4) in an easy way, look here:-

        Look the steps of this trick.

(5) Trick–5 :-

          See again trick-4 If two numbers contain the same number of digits, then we have a trick to calculate multiplication. Look at this trick:-

(6) Trick–6 :-

        See here to calculate hard multiplication in an easy way. Here you have to calculate multiplication by using your own mind, or you have to know the situation and use these tricks. We have given some examples here, look these:-

Example-1

                   208×9999998

                 =208×(10000000–2)

                 =2080000000–416
                 =2079999584

Example-2

                   6507×71

                 =(6000+500+7)×71

                 =(426000+35500+497)

                 =461997

Example-3

                    507×493

                  =(500+7)(500–7)      [ By using the algebraic formula (a+b)(a–b)=a²–b² ]

                  =(500)²–(7)²

                  =250000–49

                  =249951

Example-4

                     200003×200003

                   =(200003)²

                   =(200000+3)²         [ By using the algebraic formula (a+b)²=a²+b²+2ab ]

                   =40000000000+9+1200000

                   =40001200009

Example-5

                      697×697

                    =(697)²
                    =(700–3)²             [ By using the algebraic formula (a–b)²=a²+b²–2ab ]
                    =490000+9–4200
                    =490009–4200
                    =485809

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