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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.
 
156794 ÷ 386
 
Place the divisor before the division bracket and place the dividend under it. The digits of the quotient must be written over the dividend.
From the left of the dividend (156794), take as many digits as necessary to form a number (1567) that will contain the divisor (386) at least once, but less than ten times.
 
          
386)156794
 
Determine how many times the divisor 386 is contained into the partial dividend 1567, and obtain the first digit of the quotient.
The answer is 4 (4 × 386 = 1544) but not 5 because 5 × 386 = 1930.
 
Place the answer (4) above the division bracket and directly above the last digit of the partial dividend (1567).
 
       4  
386)156794
 
Multiply the 4 by 386 and place the result (1544) below the partial dividend 1567.
 
       4  
386)156794
    1544
 
Draw a line under the 1544 and subtract it from 1567 (1567 - 1544 = 23). 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 (9) and place it to the right of the difference (23), making it 239.
 
       4  
386)156794
    1544
      239
 
Determine how many times the divisor 386 is contained into 239 and place the answer to the right of the existing digits of the quotient.
The answer is 0 (0 × 386 = 0) but not 1 because 1 × 386 = 386.
 
       40 
386)156794
    1544
      239
 
Multiply the 0 by 386 and place the result (0) below the 239.
 
       40 
386)156794
    1544
      239
        0
 
Draw a line under the 0 and subtract it from 239 (239 - 0 = 239). 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 (4) and place it to the right of the difference (239), making it 2394.
 
       40 
386)156794
    1544
      239
        0
      2394
 
Determine how many times the divisor 386 is contained into 2394 and place the answer to the right of the existing digits of the quotient.
The answer is 6 (6 × 386 = 2316) but not 7 because 7 × 386 = 2702.
 
       406
386)156794
    1544
      239
        0
      2394
 
Multiply the 6 by 386 and place the result (2316) below the 2394.
 
       406
386)156794
    1544
      239
        0
      2394
      2316
 
Draw a line under the 2316 and subtract it from 2394 (2394 - 2316 = 78). The difference can never be greater than the divisor, if so, you selected an incorrect value, and must select a bigger one.
There are no digits in the dividend to bring down so 406 is the quotient and 78 is the remainder.
 
       406
386)156794
    1544
      239
        0
      2394
      2316
        78
 
Final answer
 
       406 R 78
386)156794
    1544
      239
        0
      2394
      2316
        78
 
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