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Door 5 · Grade 4

🔢 Division with Remainders

D-M-S-B-R: Divide, Multiply, Subtract, Bring down, Repeat

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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

Worked example

Problem: Divide 847 by 7.

  1. Divide 8 by 7: quotient 1, remainder 1.
  2. Bring down 4 -> 14.
  3. Divide 14 by 7: quotient 2, remainder 0.
  4. Bring down 7 -> 7.
  5. Divide 7 by 7: quotient 1, remainder 0.

Answer: 847 / 7 = 121.

Interpreting Remainders in Word Problems

When solving word problems with division, the remainder can mean different things depending on the context. There are three rules:
• Rule 1 — Ignore: When the question asks for 'full groups' or 'complete sets'. The remainder is not counted. E.g. how many full boxes?
• Rule 2 — Round Up: When the question asks 'how many needed for everyone'. Even one extra person needs one more group. E.g. how many buses/taxis?
• Rule 3 — Keep: When the question asks 'how much is left over' or 'how much does each get'. E.g. how many rupees each? How much left?

Worked example

Problem: A farmer has 175 apples. He packs them in bags of 8 each. How many full bags can he make? How many apples are left?

  1. 175 / 8 = 21 remainder 7.
  2. Full bags = 21 (Rule 1 - ignore the 7 leftover apples for the bag count).
  3. Apples left over = 7 (Rule 3 - keep the remainder).

Answer: 21 full bags with 7 apples left.

Divisibility and Finding Quotient Patterns

A number is exactly divisible by another when the remainder is 0. Knowing divisibility rules helps you divide quickly.
Quick Divisibility Rules:
• Divisible by 2: last digit is 0,2,4,6,8
• Divisible by 5: last digit is 0 or 5
• Divisible by 9: sum of digits is divisible by 9
• Divisible by 10: last digit is 0

The relationship between division and multiplication: if A / B = C, then B x C = A.

Worked example

Problem: Is 648 divisible by 9? Verify by division.

  1. Sum of digits: 6+4+8=18.
  2. 18 is divisible by 9.
  3. So 648 is divisible by 9.
  4. Verify: 648 / 9 = 72 with remainder 0.
  5. Check: 9 x 72 = 648.

Answer: Check: 9 x 72 = 648.