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Basic Math Decoded
 

Basic Math Decoded Example

Basic Math Decoded
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This example has been taken directly from the solution given by Basic Math Decoded to the formulated problem.
 
65984 × 736
 
Place one number beside the other with the multiplication symbol between them. Draw a line under the numbers.
 
 65984×736
 
Multiply the number 65984 by the digit 7 and place the answer below the line. Write the answer in such way that the last digit be lined up with the digit being multiplied in the second number.
There are 2 blank spaces to the last column of the second number; this is because you are really multiplying the number by 700, which is the same that multiplying by 7 and by 100. Some books suggest writing zeroes instead of blank spaces, but it is the same when you add all the partial multiplications, at the end.
 
Multiply the digits 7 and 4 (7 × 4 = 28).
This number is larger than 9, so place the 2 above the column on the left to be added in the next step and place the 8 below the line.
 
    2     
 65984×736
       8  
 
Multiply the digits 7 and 8 (7 × 8 = 56). Add the 2 to the answer which equals 58.
This number is larger than 9, so place the 5 above the column on the left to be added in the next step and place the 8 below the line and to the left of the other digits.
 
   52     
 6598736
      88  
 
Multiply the digits 7 and 9 (7 × 9 = 63). Add the 5 to the answer which equals 68.
This number is larger than 9, so place the 6 above the column on the left to be added in the next step and place the 8 below the line and to the left of the other digits.
 
  652     
 65984×736
     888  
 
Multiply the digits 7 and 5 (7 × 5 = 35). Add the 6 to the answer which equals 41.
This number is larger than 9, so place the 4 above the column on the left to be added in the next step and place the 1 below the line and to the left of the other digits.
 
 4652     
 65984×736
    1888  
 
Multiply the digits 7 and 6 (7 × 6 = 42). Add the 4 to the answer which equals 46.
This number is larger than 9, but there are no more columns, so place the answer below the line and to the left of the other digits.
 
 4652     
 65984×736
  461888  
 
Multiply the number 65984 by the digit 3 and place the answer in a new row below the last one, moving one place to the right.
This is because you are really multiplying the number 65984 by 30, which is the same that multiplying by 3 and by 10, the power of ten immediately inferior at the previous multiplication.
 
Multiply the digits 3 and 4 (3 × 4 = 12).
This number is larger than 9, so place the 1 above the column on the left to be added in the next step and place the 2 below the line in the corresponding row.
 
    1     
 65984×736
  461888
        2
 
Multiply the digits 3 and 8 (3 × 8 = 24). Add the 1 to the answer which equals 25.
This number is larger than 9, so place the 2 above the column on the left to be added in the next step and place the 5 below the line in the corresponding row, and to the left of the other digits.
 
   21     
 65984×736
  461888
       52
 
Multiply the digits 3 and 9 (3 × 9 = 27). Add the 2 to the answer which equals 29.
This number is larger than 9, so place the 2 above the column on the left to be added in the next step and place the 9 below the line in the corresponding row, and to the left of the other digits.
 
  221     
 65984×736
  461888
      952
 
Multiply the digits 3 and 5 (3 × 5 = 15). Add the 2 to the answer which equals 17.
This number is larger than 9, so place the 1 above the column on the left to be added in the next step and place the 7 below the line in the corresponding row, and to the left of the other digits.
 
 1221     
 65984×736
  461888
     7952
 
Multiply the digits 3 and 6 (3 × 6 = 18). Add the 1 to the answer which equals 19.
This number is larger than 9, but there are no more columns, so place the answer below the line in the corresponding row, and to the left of the other digits.
 
 1221     
 65984×736
  461888
   197952
 
Multiply the number 65984 by the digit 6 and place the answer in a new row below the last one, moving one place to the right.
This is because you are multiplying the number by the one's place, and in the previous multiplication you were multiplying by the ten's place.
 
Multiply the digits 6 and 4 (6 × 4 = 24).
This number is larger than 9, so place the 2 above the column on the left to be added in the next step and place the 4 below the line in the corresponding row.
 
    2     
 65984×736
  461888
   197952
         4
 
Multiply the digits 6 and 8 (6 × 8 = 48). Add the 2 to the answer which equals 50.
This number is larger than 9, so place the 5 above the column on the left to be added in the next step and place the 0 below the line in the corresponding row, and to the left of the other digits.
 
   52     
 65984×736
  461888
   197952
        04
 
Multiply the digits 6 and 9 (6 × 9 = 54). Add the 5 to the answer which equals 59.
This number is larger than 9, so place the 5 above the column on the left to be added in the next step and place the 9 below the line in the corresponding row, and to the left of the other digits.
 
  552     
 65984×736
  461888
   197952
       904
 
Multiply the digits 6 and 5 (6 × 5 = 30). Add the 5 to the answer which equals 35.
This number is larger than 9, so place the 3 above the column on the left to be added in the next step and place the 5 below the line in the corresponding row, and to the left of the other digits.
 
 3552     
 65984×736
  461888
   197952
      5904
 
Multiply the digits 6 and 6 (6 × 6 = 36). Add the 3 to the answer which equals 39.
This number is larger than 9, but there are no more columns, so place the answer below the line in the corresponding row, and to the left of the other digits.
 
 3552     
 65984×736
  461888
   197952
    395904
 
Final answer
 
Add all the rows together, and write the answer.
 
 65984×736
  461888
   197952
    395904
  48564224
 
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