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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.
 
3487.461 ÷ 93.65
 
Multiply both the divisor and dividend by 100 so that the divisor is not a decimal but a whole number. In other words, move the decimal point 2 place(s) to the right in both the divisor and dividend.
 
348746.1 ÷ 9365
 
Place the dividend before the division bracket and place the divisor over it. The digits of the quotient must be written below the divisor.
Proceed with the division as you normally would when dividing whole numbers, except put the decimal point in the quotient exactly when you bring down the digit just after the decimal point.
From the left of the dividend (348746.1), take as many digits as necessary to form a number (34874) that will contain the divisor (9365) at least once but less than ten times.
 
348746.1|9365  
 
Determine how many times the divisor 9365 is contained into the partial dividend 34874, and obtain the first digit of the quotient.
The answer is 3 (3 × 9365 = 28095) but not 4 because 4 × 9365 = 37460.
 
348746.1|9365  
         3
 
Multiply the 3 by 9365 and place the result (28095) below the 34874 of the dividend.
 
348746.1|9365  
28095    3
 
Draw a line under the 28095 and subtract it from 34874 (34874 - 28095 = 6779). The difference can never be greater than the divisor, if so, you selected an incorrect value, and must select a bigger one.
Bring down the next digit of the dividend (6) and place it to the right of the difference (6779), making it 67796.
 
348746.1|9365  
28095    3
 67796
 
Determine how many times the divisor 9365 is contained into 67796 and place the answer to the right of the existing digits of the quotient.
The answer is 7 (7 × 9365 = 65555) but not 8 because 8 × 9365 = 74920.
 
348746.1|9365  
28095    37
 67796
 
Multiply the 7 by 9365 and place the result (65555) below the 67796.
 
348746.1|9365  
28095    37
 67796
 65555
 
Draw a line under the 65555 and subtract it from 67796 (67796 - 65555 = 2241). The difference can never be greater than the divisor, if so, you selected an incorrect value, and must select a bigger one.
Bring down the next digit of the dividend (1) and place it to the right of the difference (2241), making it 22411.
When you bring down the next digit after the decimal point you must place the decimal point in the quotient.
 
348746.1|9365  
28095    37.
 67796
 65555
  22411
 
Determine how many times the divisor 9365 is contained into 22411 and place the answer to the right of the existing digits of the quotient.
The answer is 2 (2 × 9365 = 18730) but not 3 because 3 × 9365 = 28095.
 
348746.1|9365  
28095    37.2
 67796
 65555
  22411
 
Multiply the 2 by 9365 and place the result (18730) below the 22411.
 
348746.1|9365  
28095    37.2
 67796
 65555
  22411
  18730
 
Draw a line under the 18730 and subtract it from 22411 (22411 - 18730 = 3681). The difference can never be greater than the divisor, if so, you selected an incorrect value, and must select a bigger one.
All the digits of the dividend have been exhausted.
Remember that you can write zeroes to the right of the last decimal place and not change the value of the decimal.
Bring down a zero and place it to the right of the difference 3681, making it 36810.
 
348746.1|9365  
28095    37.2
 67796
 65555
  22411
  18730
   36810
 
Determine how many times the divisor 9365 is contained into 36810 and place the answer to the right of the existing digits of the quotient.
The answer is 3 (3 × 9365 = 28095) but not 4 because 4 × 9365 = 37460.
 
348746.1|9365  
28095    37.23
 67796
 65555
  22411
  18730
   36810
 
Multiply the 3 by 9365 and place the result (28095) below the 36810.
 
348746.1|9365  
28095    37.23
 67796
 65555
  22411
  18730
   36810
   28095
 
Draw a line under the 28095 and subtract it from 36810 (36810 - 28095 = 8715). The difference can never be greater than the divisor, if so, you selected an incorrect value, and must select a bigger one.
Bring down a zero and place it to the right of the difference 8715, making it 87150.
 
348746.1|9365  
28095    37.23
 67796
 65555
  22411
  18730
   36810
   28095
    87150
 
Determine how many times the divisor 9365 is contained into 87150 and place the answer to the right of the existing digits of the quotient.
The answer is 9 (9 × 9365 = 84285).
 
348746.1|9365  
28095    37.239
 67796
 65555
  22411
  18730
   36810
   28095
    87150
 
Multiply the 9 by 9365 and place the result (84285) below the 87150.
 
348746.1|9365  
28095    37.239
 67796
 65555
  22411
  18730
   36810
   28095
    87150
    84285
 
Draw a line under the 84285 and subtract it from 87150 (87150 - 84285 = 2865). The difference can never be greater than the divisor, if so, you selected an incorrect value, and must select a bigger one.
 
Final answer
 
348746.1|9365  
28095    37.239
 67796
 65555
  22411
  18730
   36810
   28095
    87150
    84285
     2865
 
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