Remainders

• When division is not exact, we get a quotient and remainder.
• Remainder must be less than the divisor.
• Real stories: leftover sweets, extra seats.
• Check: (quotient × divisor) + remainder = dividend.

Level 1 — Core idea

Verbal: 17 ÷ 5: make groups of 5 from 17 — three groups of 5, 2 left over.

Symbolic: 17 ÷ 5 = 3 remainder 2; write 17 = 5 × 3 + 2.

Visual: 17 dots → circle three 5s; 2 dots outside → remainder 2.

Level 2 — Going deeper

Rule: remainder < divisor. If remainder equals divisor, you can make one more group.

NCERT anchor

NCERT Math Mela, Class 3 — Chapter 7 shares objects that do not split evenly. Always say "3 remainder 2," not "3 point something" at this level.

17 ÷ 5 = ?

Step 1 — 5 × 3 = 15 (largest multiple of 5 below 17)
Step 2 — 17 − 15 = 2 left
Step 3 — 17 ÷ 5 = **3 remainder 2**
Check: 5×3 + 2 = 17 ✓

22 children, 5 per team. How many full teams? Any left?

Step 1 — 22 ÷ 5 = 4 × 5 = 20, remainder 2
Step 2 — **4 full teams**, **2 children** without a full team
Answer: 4 teams, 2 remainder

• 14 ÷ 3 = ? and remainder?
• Check 11 = 3×3 + 2 — true or false?
• Can remainder be 6 when dividing by 5?
• Stretch: 29 ÷ 4 = ? Write the check equation.

Revision tip: Always multiply back and add remainder — if you don't get the start number, recheck.

Open the Practice tab for graded questions on Remainders.