Division • Topic 5 of 6

Long Division (Elementary Level)

Long division is the standard written method for dividing bigger numbers one digit at a time, and at elementary level it is taught as a short loop of steps remembered as DMSB -- Divide, Multiply, Subtract, Bring down (some teachers add a Check step for DMSCB). You look at the leading digit (or first two digits if the first is too small), see how many times the divisor fits, write that in the quotient, multiply back, subtract, then bring down the next digit and repeat until nothing is left to bring down. Two situations trip children up. If the first digit is smaller than the divisor -- as in 156 divided by 6, where 1 is less than 6 -- you take the first two digits, 15, together to start. And if a brought-down number is smaller than the divisor, you put a 0 in the quotient at that place, bring down the next digit, and carry on. Whatever the result, the habit CTET wants children to build is to verify it: Dividend equals Divisor times Quotient plus Remainder, with the remainder less than the divisor. So 96 divided by 4 gives 24 remainder 0, and 4 times 24 plus 0 is indeed 96.

✅ Solved examples

1. Divide 96 by 4 using long division and verify the answer.
Divide 9 by 4: it fits 2 times (4 x 2 = 8); subtract, 9 - 8 = 1. Bring down 6 to make 16. Divide 16 by 4: it fits 4 times (4 x 4 = 16); subtract, 16 - 16 = 0. Quotient = 24, remainder = 0. Check: 4 x 24 + 0 = 96.
2. Divide 745 by 3 using long division.
Divide 7 by 3: fits 2 times (3 x 2 = 6), remainder 1; bring down 4 to make 14. Divide 14 by 3: fits 4 times (3 x 4 = 12), remainder 2; bring down 5 to make 25. Divide 25 by 3: fits 8 times (3 x 8 = 24), remainder 1. Quotient = 248, remainder = 1. Check: 3 x 248 + 1 = 744 + 1 = 745.
3. A school collected Rs 875 equally from 5 classes for a charity event. How much did each class contribute? Use long division.
Divide 8 by 5: fits 1 time, remainder 3; bring down 7 to make 37. Divide 37 by 5: fits 7 times (5 x 7 = 35), remainder 2; bring down 5 to make 25. Divide 25 by 5: fits 5 times exactly, remainder 0. Quotient = 175. Each class contributed Rs 175. Check: 5 x 175 = 875.

✏️ Practice — try these, take hints as needed

1. Use long division to find 84 / 6.
Start with 8 / 6, then bring down 4.
Verify with Divisor x Quotient.
14 remainder 0 (6 x 14 = 84)
2. Divide 156 by 6. (Note: the first digit is smaller than the divisor.)
1 is less than 6, so begin with 15.
6 x 26 = 156.
26 remainder 0
3. Find 425 / 4 by long division and state the remainder.
4 / 4, then 2 / 4 gives a 0 in the quotient, then 25 / 4.
Check Divisor x Quotient + Remainder.
106 remainder 1 (4 x 106 + 1 = 425)

📝 Topic test — 8 questions

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