Divide by 1- and 2-Digit Numbers

Division is the inverse of multiplication. When you divide, you split a number into equal groups. The number being divided is the dividend, the number you divide by is the divisor, and the result is the quotient. Sometimes there is a remainder — the amount left over when the dividend cannot be divided exactly.

Division as the Inverse of Multiplication

• 48 ÷ 6 = 8 because 8 × 6 = 48.
• To check a division: quotient × divisor + remainder = dividend.
• If the remainder is 0, the division is exact (no remainder).

Short Division (Bus-Stop Method): No Remainder

1. Write the divisor to the left of the bracket and the dividend under the bracket.
2. Divide the first digit (or first two digits) by the divisor. Write the quotient above the bracket.
3. 84 ÷ 4: divide 8 by 4 = 2 (write 2 above). Divide 4 by 4 = 1 (write 1 above). Quotient: 21.
4. Check: 21 × 4 = 84. Correct.

Short Division: With Remainder

1. 85 ÷ 4: divide 8 by 4 = 2 remainder 0. Bring down 5. Divide 5 by 4 = 1 remainder 1.
2. Write the remainder after R: quotient is 21 R1.
3. Check: 21 × 4 + 1 = 84 + 1 = 85. Correct.

2-Digit Divisor: Estimate First

• 96 ÷ 12: think of a multiple of 12 close to 96. 12 × 8 = 96 — exact!
• Use trial: try 12 × 7 = 84 (too small), 12 × 8 = 96 (exact). Quotient: 8.
• For larger dividends, estimate to narrow down the trial digit.

Interpreting Remainders

• Round up when you need enough groups: 27 items in boxes of 4 — 27 ÷ 4 = 6 R3 → need 7 boxes.
• Round down when you use only full groups: 27 people in cars of 4 — 6 full cars (3 people wait).
• The context of the problem tells you whether to round up or down.