Division with Remainders • Topic 1 of 3

Divide 3-Digit by 1-Digit (Long Division)

Division means splitting a number into equal groups. When we divide a 3-digit number by a 1-digit number, we use long division with the D-M-S-B-R method:

  • D = Divide
  • M = Multiply
  • S = Subtract
  • B = Bring down
  • R = Repeat (or Remainder)

The dividend is the number being divided. The divisor is what we divide by. The quotient is the answer. The remainder is what is left over.

Check: (Divisor x Quotient) + Remainder = Dividend

Long Division: 847 / 7 = 121D-M-S-B-R MethodDivide: 8/7 = 1 (with 1 left)Multiply: 7 x 1 = 7Subtract: 8 - 7 = 1Bring down 4 to get 14Repeat with 14/7=2 and 47/7=6 R5? No: 7x121=847 exact1217 x 121 = 847
Solved Examples
1
Worked Example
Divide 847 by 7.
SolutionDivide 8 by 7: quotient 1, remainder 1. Bring down 4 -> 14. Divide 14 by 7: quotient 2, remainder 0. Bring down 7 -> 7. Divide 7 by 7: quotient 1, remainder 0. Answer: 847 / 7 = 121. Check: 7 x 121 = 847.
2
Worked Example
Find 453 / 6.
SolutionDivide 4 by 6: cannot, so use 45. 45/6=7, remainder 3. Bring down 3 -> 33. 33/6=5, remainder 3. Answer: Quotient 75, Remainder 3. So 453 = (6 x 75) + 3. Check: 450 + 3 = 453.
3
Worked Example
A school has 756 books to be arranged equally on 9 shelves. How many books per shelf?
SolutionDivide 756 by 9. 7/9: cannot, use 75. 75/9=8 R3. Bring down 6 -> 36. 36/9=4 R0. Answer: 84 books per shelf. Check: 9 x 84 = 756.

Key Points

  • D-M-S-B-R: Divide, Multiply, Subtract, Bring down, Repeat
  • The remainder must always be less than the divisor
  • Check: Divisor x Quotient + Remainder = Dividend
  • If a digit is smaller than the divisor, bring down the next digit
Quick Check — 4 MCQs
Tap an option to check your answer0 / 4
Q1.The number being divided is called the:
Explanation: Dividend.
Q2.The answer to a division is the:
Explanation: Quotient.
Q3.$125\div5=$
Explanation: $25$.
Q4.The remainder is always ___ the divisor.
Explanation: Less than.
Practice more MCQs → 📝 Assignment · 35 marks