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