Base Ten Operations
GradesGrade 4Base Ten OperationsIntroduction to Long Division

Introduction to Long Division

🏛️ Base Ten Operations
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Introduction to Long Division

Long division breaks a big division problem into small, manageable steps!

Long division is an algorithm for dividing larger numbers. We work one digit at a time from left to right: Divide, Multiply, Subtract, Bring Down — and repeat. It is like dividing a number in several small rounds.

The DMSB cycle — 96 ÷ 4:

1DIVIDE: How many times does 4 go into 9? → 2 times. Write 2 above.
2MULTIPLY: 2 × 4 = 8. Write 8 below the 9.
3SUBTRACT: 9 − 8 = 1. Write 1.
4BRING DOWN: Bring down the next digit (6) → now we have 16.
5Repeat DMSB: 4 goes into 16 exactly 4 times. 4 × 4 = 16. 16 − 16 = 0.
6Answer: 24 (with remainder 0).
96÷4=2496 \div 4 = 24
🍬Dividing 135 candy bars among 5 classes
135 ÷ 5 = ?
→ 5 into 13: 2 times (2×5=10). Subtract: 13−10=3. Bring down 5 → 35.
→ 5 into 35: 7 times (7×5=35). Subtract: 35−35=0.
Answer: 27. Each class gets 27 candy bars.
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DMSB: Divide → Multiply → Subtract → Bring down. Repeat until there are no more digits to bring down.

Division with no remainder

84 ÷ 4 = 21 exactlyCheck: 21 × 4 = 84 ✓

Division with a remainder

85 ÷ 4 = 21 remainder 1Check: 21 × 4 + 1 = 85 ✓

Always check with multiplication! quotient × divisor + remainder = dividend.

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Remember This!

Estimate your quotient at each step. If your estimate is too big (the subtraction goes negative), erase and try one less. If too small (remainder ≥ divisor), try one more.

✏️ Try It!

What is 156 ÷ 6?

Practice with CalcVerse
➗Long Division Walkthrough
Take Quiz 📝 — 25 Questions