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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 divisor before the division bracket and place the dividend under it. The digits of the quotient must be written over the dividend.
Proceed with the division as you normally would when dividing whole numbers except put the decimal point in the quotient directly above the decimal point in the dividend.
Quotient will be find to 3 decimal place(s).
Add 2 trailing zero(es) on the dividend to complete 3 decimal place(s).
Remember that you can write zeroes to the right of the last decimal place and not change the value of the decimal.
 
               
9365)348746.100
 
From the left of the dividend (348746100), 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.
 
               
9365)348746.100
 
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.
Place the answer (3) above the division bracket and directly above the last digit of the partial dividend (34874).
 
         3     
9365)348746.100
 
Multiply the 3 by 9365 and place the result (28095) below the 34874 of the dividend.
 
         3     
9365)348746.100
     28095
 
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.
 
         3     
9365)348746.100
     28095
      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.
Put the decimal point just above the decimal point in the dividend.
 
         37.   
9365)348746.100
     28095
      67796
 
Multiply the 7 by 9365 and place the result (65555) below the 67796.
 
         37.   
9365)348746.100
     28095
      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.
 
         37.   
9365)348746.100
     28095
      67796
      65555
       2241 1
 
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.
 
         37.2  
9365)348746.100
     28095
      67796
      65555
       2241 1
 
Multiply the 2 by 9365 and place the result (18730) below the 22411.
 
         37.2  
9365)348746.100
     28095
      67796
      65555
       2241 1
       1873 0
 
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.
Bring down the next digit of the dividend (0) and place it to the right of the difference (3681), making it 36810.
 
         37.2  
9365)348746.100
     28095
      67796
      65555
       2241 1
       1873 0
        368 10
 
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.
 
         37.23 
9365)348746.100
     28095
      67796
      65555
       2241 1
       1873 0
        368 10
 
Multiply the 3 by 9365 and place the result (28095) below the 36810.
 
         37.23 
9365)348746.100
     28095
      67796
      65555
       2241 1
       1873 0
        368 10
        280 95
 
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 the next digit of the dividend (0) and place it to the right of the difference (8715), making it 87150.
 
         37.23 
9365)348746.100
     28095
      67796
      65555
       2241 1
       1873 0
        368 10
        280 95
         87 150
 
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).
 
         37.239
9365)348746.100
     28095
      67796
      65555
       2241 1
       1873 0
        368 10
        280 95
         87 150
 
Multiply the 9 by 9365 and place the result (84285) below the 87150.
 
         37.239
9365)348746.100
     28095
      67796
      65555
       2241 1
       1873 0
        368 10
        280 95
         87 150
         84 285
 
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
 
         37.239
9365)348746.100
     28095
      67796
      65555
       2241 1
       1873 0
        368 10
        280 95
         87 150
         84 285
          2 865
 
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