Hi! I'm Vidi. Let's learn Division with Remainders together — read with me, then play the games to win a ⭐!
🔵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
👀 See a worked example
Divide 847 by 7.
Divide 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.
Find 453 / 6.
Divide 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.
A school has 756 books to be arranged equally on 9 shelves. How many books per shelf?
Divide 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.
🤖 Vidi's 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
🟢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?
👀 See a worked example
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?
175 / 8 = 21 remainder 7. Full bags = 21 (Rule 1 - ignore the 7 leftover apples for the bag count). Apples left over = 7 (Rule 3 - keep the remainder). Answer: 21 full bags with 7 apples left.
175 people need to cross a river. Each boat carries 8 people. How many boat trips are needed?
175 / 8 = 21 remainder 7. Since all 175 people must cross, the 7 extra people need one more trip. Apply Rule 2 (round up): 21 + 1 = 22. Answer: 22 boat trips.
Rs.1,000 is shared equally among 6 friends. How much does each get? How much is left?
1000 / 6 = 166 remainder 4. Each friend gets Rs.166 (quotient). Rs.4 is left over (Rule 3 - keep remainder). Answer: Rs.166 each, Rs.4 remaining.
🤖 Vidi's Key Points
- Rule 1 (Ignore): Use when question asks for 'full' or 'complete' groups
- Rule 2 (Round up): Use when everyone must be included (buses, taxis, rows)
- Rule 3 (Keep): Use when question asks what is left over
- The same division can have different answers depending on context!
🟣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.
👀 See a worked example
Is 648 divisible by 9? Verify by division.
Sum of digits: 6+4+8=18. 18 is divisible by 9. So 648 is divisible by 9. Verify: 648 / 9 = 72 with remainder 0. Check: 9 x 72 = 648.
A number when divided by 7 gives quotient 58 and remainder 4. Find the number.
Using the formula: Number = (Divisor x Quotient) + Remainder = (7 x 58) + 4 = 406 + 4 = 410.
Find the smallest 3-digit number exactly divisible by 8.
100 / 8 = 12 R4. So 100 is not divisible by 8. To find the next: 8 x 13 = 104. Check: 104 / 8 = 13 R0. Answer: 104.
🤖 Vidi's Key Points
- A number with remainder 0 is exactly divisible by the divisor
- Divisibility by 2: even last digit; by 5: last digit 0 or 5; by 9: digit sum divisible by 9
- Formula: Number = (Divisor x Quotient) + Remainder
- Division and multiplication are inverse operations
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