Multiplication of a Three Digit by a Two Digit Number

How to multiply a three digit number by a two digit number (e.g. 509 * 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.
  • 
     509
      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
     509
      67
       3
    
  • Muliply the digit in the top tens' place column (0) by the digit in the lower ones' place column (7). The answer (0*7=0) is added to the 6 above the top tens' place column to give an answer of 6. The 6 is placed below the line to the left of the 3.
  • 
      6
     509
      67
      63
    
  • The hundreds' place of the top number (5) is multiplied by the ones' place of the multiplier (5*7=35). The 35 is placed below the line to the left of the 63.
  • 
      6
     509
      67
    3563
    
  • After 509 has been multiplied by 7 as shown above, 509 is multiplied by the tens' place of the multiplier which is 6. The product of 509*6 is moved one place to the left because we are multiplying by a tens' place number. The result would be 3054:
  • 
      15
      509
       67
     3763
    3054
    
    
  • A line is drawn under the lower product (3054) and the products are added together to get the final answer of 34303.
    
      15
      509
       67
     3763
    3054
    34303
    
    






What is the Product of the two numbers?

* =