Division Calculator

Division Calculator – Quotient & Remainder Framework

Use this compact structure: choose output (decimal vs integer+remainder), compute, verify, move on.

Core Relationships

• a = bq + r
• 0 ≤ r < |b| (Euclidean)
• Decimal q = a / b
• r = a − bq
• a ÷ (c/d) = a × d / c
• Scale decimals to clear divisor

Decision Steps

1. Validate divisor ≠ 0.
2. Pick mode: decimal or int+remainder.
3. Compute q = a / b.
4. Integer mode: q_int = trunc(a/b); r = a − b q_int.
5. Check: b q_int + r = a.

Guardrails

• Remainder magnitude must be < |b|.
• Round only at display.
• Beware floating drift on repeating decimals.

Pitfalls

• Negative remainder (decide convention).
• Off‑by‑one quotient when |r| ≥ |b|.
• Decimal misplacement after scaling.

Quick Checks

• b ≠ 0
• |r| < |b|
• Rebuild: bq + r
• Sign logic consistent

Action Tip

Always finish by reconstructing the dividend—fastest correctness test.