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 dividend before the division bracket and place the divisor over it. The digits of the quotient must be written below the divisor.
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.
156794|386
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.
156794|386
4
Multiply the 4 by 386 and place the result (1544) below the partial dividend 1567.
156794|386
1544 4
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.
156794|386
1544 4
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.
156794|386
1544 40
239
Multiply the 0 by 386 and place the result (0) below the 239.
156794|386
1544 40
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.
156794|386
1544 40
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.
156794|386
1544 406
239
0
2394
Multiply the 6 by 386 and place the result (2316) below the 2394.
156794|386
1544 406
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.
156794|386
1544 406
239
0
2394
2316
78
Final answer
156794|386
1544 406 R 78
239
0
2394
2316
78