Multiplication of Two and Three Digit Numbers

How to multiply a three digit number by a two digit number (e.g. 529 * 67).

  • Place one number above the other so that the hundreds', tens' and ones' places are lined up. Draw a line under the bottom number.
  • 
     529
      67
    
    
  • Multiply the two numbers in the ones' places. (9 * 7 = 63). This number is larger than 9 so place a 6 above the tens' place column and place 3 below the line in the ones' place column.
  • 
      6
     529
      67
       3
    
  • Muliply the digit in the top tens' place column (2) by the digit in the lower ones' place column (7). The answer (2*7=14) is added to the 6 above the top tens' place column to give an answer of 20. The 0 of 20 is placed below the line and the 2 of the 20 is placed above the hundreds' place column.
  • 
     26
     529
      67
      03
    
  • The hundreds' place of the top number (5) is multiplied by the ones' place of the multiplier (5*7=35). The two that was previously carried to the hundreds' place is added and the 37 is placed below the line.
  • 
     26
     529
      67
    3703
    
  • After 529 has been multiplied by 7 as shown above, 529 is multiplied by the tens' place of the multiplier which is 6. The number is moved one place to the left because we are multiplying by a tens' place number. The result would be 3174:
  • 
      15
      529
       67
     3703
    3174
    
    
  • A line is drawn under the lower product (3174) and the products are added together to get the final answer of 35443.
    
      15
      529
       67
     3703
    3174
    35443
    
    

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