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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.
 
58.378 × 0.396
 
Place one number above the other aligned to the right. Draw a line under the bottom number. Temporarily disregard the decimal points and multiply the numbers like you would multiply integer numbers.
 
     58.378
   ×  0.396
 
Multiply the number 58378 by the digit 6 and place the answer below the line aligned to the right.
 
Multiply the digits 6 and 8 (6 × 8 = 48).
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 8 below the line.
 
         4
     58.378
   ×  0.396
          8
 
Multiply the digits 6 and 7 (6 × 7 = 42). Add the 4 to the answer which equals 46.
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 6 below the line and to the left of the other digits.
 
        44
     58.378
   ×  0.396
         68
 
Multiply the digits 6 and 3 (6 × 3 = 18). Add the 4 to the answer which equals 22.
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 2 below the line and to the left of the other digits.
 
      2 44
     58.378
   ×  0.396
        268
 
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 and to the left of the other digits.
 
     52 44
     58.378
   ×  0.396
       0268
 
Multiply the digits 6 and 5 (6 × 5 = 30). Add the 5 to the answer which equals 35.
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.
 
     52 44
     58.378
   ×  0.396
     350268
 
Multiply the number 58378 by the digit 9 and place the answer in a new row below the last one, moving one place to the left.
 
Multiply the digits 9 and 8 (9 × 8 = 72).
This number is larger than 9, so place the 7 above the column on the left to be added in the next step and place the 2 below the line in the corresponding row.
 
         7
     58.378
   ×  0.396
     350268
         2
 
Multiply the digits 9 and 7 (9 × 7 = 63). Add the 7 to the answer which equals 70.
This number is larger than 9, so place the 7 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.
 
        77
     58.378
   ×  0.396
     350268
        02
 
Multiply the digits 9 and 3 (9 × 3 = 27). Add the 7 to the answer which equals 34.
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 4 below the line in the corresponding row, and to the left of the other digits.
 
      3 77
     58.378
   ×  0.396
     350268
       402
 
Multiply the digits 9 and 8 (9 × 8 = 72). Add the 3 to the answer which equals 75.
This number is larger than 9, so place the 7 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.
 
     73 77
     58.378
   ×  0.396
     350268
      5402
 
Multiply the digits 9 and 5 (9 × 5 = 45). Add the 7 to the answer which equals 52.
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.
 
     73 77
     58.378
   ×  0.396
     350268
    525402
 
Multiply the number 58378 by the digit 3 and place the answer in a new row below the last one, moving one place to the left.
 
Multiply the digits 3 and 8 (3 × 8 = 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
     58.378
   ×  0.396
     350268
    525402
        4  
 
Multiply the digits 3 and 7 (3 × 7 = 21). Add the 2 to the answer which equals 23.
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 3 below the line in the corresponding row, and to the left of the other digits.
 
        22
     58.378
   ×  0.396
     350268
    525402
       34  
 
Multiply the digits 3 and 3 (3 × 3 = 9). Add the 2 to the answer which equals 11.
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 1 below the line in the corresponding row, and to the left of the other digits.
 
      1 22
     58.378
   ×  0.396
     350268
    525402
      134  
 
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 22
     58.378
   ×  0.396
     350268
    525402
     5134  
 
Multiply the digits 3 and 5 (3 × 5 = 15). Add the 2 to the answer which equals 17.
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.
 
     21 22
     58.378
   ×  0.396
     350268
    525402
   175134  
 
Final answer
 
Add all the rows together and write the answer.
 
     58.378
   ×  0.396
     350268
    525402
   175134  
   23117688
 
We must now count up the decimal places of both numbers and move the decimal place to its proper location. We have 3 decimal place(s) in the first number and 3 in the second one, so we move the decimal point 6 place(s) to the left to give the final answer.
 
  23.117688
 
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