CLASS-3
MULTIPLICATION OF DOUBLE & TRIPLE DIGIT NUMBER

So, it’s clearly shown before learning multiplication you would learn ‘Time Table’.

Earlier we have learnt multiplication of three digit number with one digit number, Now, we will try to understand the logic or the way of process of Multiplication between three digit number with two digit number and three digit number.

MULTIPLYING 3 (THREE) DIGIT NUMBER 

Q1. MULTIPLY 598 BY 4.

METHOD-

Step.1.- Multiply the ‘Ones’ by 4

8 Ones x 4 = 32 Ones = 3 Tens 2 Ones.   Write 2 in the ‘Ones’ column.

Now carry 3 Tens to the Tens column.

Step 2.- Now multiply the ‘Tens’ by 4.   

 9 Tens x 4 = 36 Tens.

                  Now 3 Tens (Earlier Forwarded) + 36 Tens = 39 Tens.

                                  39 Tens = 3 Hundred 9 Tens

                                  Write 9 in the ‘Tens’ column.

                      Now carry 3 Hundred to the ‘Hundreds’ column.

 Step 3.- Now multiply the ‘Hundreds’ by 4

            5 Hundreds x 4 = 20 Hundreds

   Now 3 Hundred (Earlier Forwarded) + 20 Hundreds = 23 Hundreds

            23 Hundreds = 2 Thousand 3 Hundreds

       Write 3 in ‘Hundreds’ column and 2 in the ‘Thousands’ column.

   Product = 2392 (Two Thousand Three Hundred Ninety Two)   (Ans.)

Q2. MULTIPLY 756 BY 5.

METHOD-

Step 1.- Multiply the ‘Ones’ by 5

6 Ones x 5 = 30 Ones = 3 Tens 0 Ones.

Write 0 in the ‘Ones’ column.

Now carry 3 Tens to the Tens column.

Step 2.- Now multiply the ‘Tens’ by 5 .            

               5 Tens x 5 = 25 Tens.

      Now 3 Tens (Earlier Forwarded) + 25 Tens = 28 Tens.

               28 Tens = 2 Hundred 8 Tens

        Write 8 in the ‘Tens’ column.

   Now carry 2 Hundred to the ‘Hundreds’ column.

Step 3.- Now multiply the ‘Hundreds’ by 5

            7 Hundreds x 5 = 35 Hundreds

 Now 2 Hundred (Earlier Forwarded) + 35 Hundreds = 37 Hundreds

              37 Hundreds = 3 Thousand 7 Hundreds

     Write 7 in ‘Hundreds’ column and 3 in the ‘Thousands’ column.

    Product = 3780 (Three Thousand Seven Hundred Eighty)   (Ans.)

MULTIPLICATION OF BOTH SIDE DOUBLE DIGIT NUMBER

Q1. MULTIPLY 43 BY 35.

METHOD-

Step 1.-  In Multiplier there is double digit that is 3 & 5.  First multiply Multiplicand 43 by 5 Ones of multiplier. Multiply the ‘Ones’ of Multiplicand by 5.

3 Ones x 5 = 15 Ones = 1 Ten 5 Ones. Write 5 in the ‘Ones’ column. Now carry 1 Tens to the Tens column. 

Step 2.-  Now multiply the ‘Tens’ by 5

             4 Tens x 5 = 20 Tens.

             Now 1 Ten (Earlier Forwarded) + 20 Tens = 21 Tens.

             21 Tens = 2 Hundred 1 Ten

             Write 1 in the ‘Tens’ column.

             Now write 2 Hundred to the ‘Hundreds’ column.

Step 3.- In Multiplier there is double digit that is 3 & 5, In Step 1 & 2 we did multiply multiplicand 43 by 5 of multiplier, but now we will multiply by 3 of multiplier to multiplicand 43. Please remember, in that case PRODUCT should be placed one step left from the actual position.  

So, now multiply the ‘Ones’ by 3,  3 Ones x 3 = 9 Ones, Write 9 Ones in the ‘Tens’ column.

Step 4.- Now multiply the ‘Tens’ by 3.   

            4 Tens x 3 = 12 Tens.

           12 Tens = 1 Hundred 2 Tens

           Write 2 Tens in the ‘Hundreds’ column.

          Now write 1 Hundred to the top of ‘Thousands’ column.

Step 5. – Now add the both of the two products

            So, the product is 1505         (Ans.)      

Q2. MULTIPLY 367 BY 28

METHOD-

Step 1.-  In Multiplier there is double digit that is 2 & 8 . First multiply Multiplicand 367 by 8 Ones of multiplier. Multiply the ‘Ones’ of Multiplicand by 8, 

7 Ones x 8 = 56 Ones = 5 Tens 6 Ones.

  Write 6 in the ‘Ones’ column.     

                                   Now carry 5 Tens to the Tens column.

Step 2.- Now multiply the ‘Tens’ of multiplicand by 8

           6 Tens x 8 = 48 Tens.

          Now 5 Tens (Earlier Forwarded) + 48 Tens = 53 Tens.

          53 Tens = 5 Hundreds 3 Tens,Write 3 in the ‘Tens’ column.

          Now write 5 Hundred to the ‘Hundreds’ column.

Step 3.- Now multiply the ‘Hundreds’ of multiplicand by 5

            3 Hundreds x 8 = 24 Hundreds

 Now, 5 Hundred (Earlier Forwarded) + 24 Hundreds = 29 Hundreds

            29 Hundreds = 2 Thousand 9 Hundreds

      Write 9 in ‘Hundreds’ column and 2 in the ‘Thousands’ column.

Step 4.-  In Multiplier there is double digit that is 2 & 8. In Step 1 to 3 we did multiply multiplicand 367 by 8 of  multiplier, but now we will multiply by 2 of multiplier to multiplicand 367. Please remember, in that case PRODUCT should be placed one step left from the actual position. So, now multiply the ‘Ones’ by 2. 7 Ones x 2 = 14 Ones, 

14 Ones = 1 Ten 4 Ones, 

Write 4 Ones in the bottom of ‘Tens’ column. Now write

(carry forward) 1 Ten to the top of ‘Tens’ column. 

Step 5.- Now multiply the ‘Tens’ by 2

           6 Tens x 2 = 12 Tens.

           Now 1 Ten (Earlier Forwarded) + 12 Tens = 13 Tens.

           13 Tens = 1 Hundred 3 Tens.

           Write 3 Tens in the bottom of the ‘Hundreds’ column.

           Now write 1 Hundred to the top of ‘Hundreds’ column.

Step 6. - Now multiply the ‘Hundreds’ by 2

           3 Hundreds x 2 = 6 Hundreds

  Now, 1 Hundreds (Earlier Forwarded) + 6 Hundreds = 7 Hundreds.

            Write 7 Hundreds in the ‘Thousands’ column.

Step 7. – Now add the both of the two products

           So, the product is 10276         (Ans.)

Q3. MULTIPLY 89 BY 326.

METHOD-

Step 1.-  In Multiplier there is double digit that is 8 & 9. First multiply Multiplicand 89 by 6 Ones of multiplier .  Multiply the ‘Ones’ of Multiplicand by 6, 9 Ones x 6 = 54 Ones = 5 Tens 4 Ones.

Write 4 in the ‘Ones’ column. Now carry 5 Tens to the ‘Tens’ column.

Step 2.-  Now multiply the ‘Tens’ of multiplicand by 6,

 8 Tens x 6 = 48 Tens.

Now 5 Tens (Earlier Forwarded) + 48 Tens = 53 Tens.

53 Tens = 5 Hundreds 3 Tens, Write 3 in the ‘Tens’ column. Now write 5 Hundred to the ‘Hundreds’ column.

Step 3.– Now multiply Multiplicand 89 by 2 Tens of. Multiplier. Multiply the ‘Ones’ of multiplicand by 2, Please remember, in that case PRODUCT should be  placed one step left from the actual position. 9 ‘Ones’ X 2 = 18 Ones , but 18 Ones = 1 Ten 8 Ones, write 8 ‘Ones’ at the bottom of   ‘Tens’ column and now write 1 ‘Ten’ (carry forward) at the top of the ‘Tens’ column.

Step.4 – now multiply ‘Tens’ of the multiplicand  by 2

           8 Tens  X 2 = 16 Tens,

           Now 1 Ten (Earlier Forwarded) + 16 Tens = 17 Tens.

           17 Tens = 1 Hundred 7 Tens , write 7 ‘Tens’ at the 

Bottom of the ‘Hundreds’ and write 1 ‘Hundred’ at ‘Thousand’ column.

Step 5.- In Multiplier there is triple digit that is 3,2 & 6. In Step 1 to 4 we did multiply multiplicand 89 by 2 & 6 of multiplier, but now we will multiply by 3 of multiplier to multiplicand 89. Please remember, in that case PRODUCT should be placed two step left from the actual position. So, now multiply the ‘Ones’ by 3 .

9 Ones x 3 = 27 Ones, 

27 Ones = 2 Ten 7 Ones, 

Write 7 Ones in the bottom of ‘Hundreds’ column. 

Now write (carry forward) 2 Ten to the top of ‘Tens’ column. 

Step 6.-   Now multiply the ‘Tens’ by 3                       

          8 Tens x 3 = 24 Tens.

    Now 2 Ten (Earlier Forwarded) + 24 Tens = 26 Tens.

           26 Tens = 2 Hundred 6 Tens.

         Write 6 Tens in the bottom of the ‘Thousands’ column.

   Now write 2 Hundred to the next of the ‘Thousands’ column.

Step 7. – Now add all the three products

           So, the product is 29014             (Ans.)