Divide by 1- and 2-Digit Numbers
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What you will learn
- 1Divide 2- and 3-digit numbers by a 1-digit divisor with no remainder
- 2Divide 2- and 3-digit numbers by a 1-digit divisor with a remainder
- 3Divide 3-digit numbers by a 2-digit divisor using estimation and trial
- 4Interpret remainders in the context of a word problem
Mini Lesson
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: No Remainder
- Write the divisor to the left of the bracket and the dividend under the bracket.
- Divide the first digit (or first two digits) by the divisor. Write the quotient above the bracket.
- 84 ÷ 4: divide 8 by 4 = 2 (write 2 above). Divide 4 by 4 = 1 (write 1 above). Quotient: 21.
- Check: 21 × 4 = 84. Correct.
Short Division: With Remainder
- 85 ÷ 4: divide 8 by 4 = 2 remainder 0. Bring down 5. Divide 5 by 4 = 1 remainder 1.
- Write the remainder after R: quotient is 21 R1.
- 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 first: 156 ÷ 12 → 12 × 10 = 120 is too small, 12 × 13 = 156. Quotient: 13.
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 cookies in packs of 4 — 27 ÷ 4 = 6 R3 → 6 full packs (3 cookies left over).
- The context of the problem tells you whether to round up or down.
Words to know
Dividend
The number being divided
e.g. In 96 ÷ 12, 96 is the dividend.
Divisor
The number you divide by
e.g. In 96 ÷ 12, 12 is the divisor.
Quotient
The answer to a division problem
e.g. The quotient of 96 ÷ 12 is 8.
Remainder
What is left over when a number cannot be divided exactly
e.g. 85 ÷ 4 = 21 with a remainder of 1.
Inverse
The opposite operation — division undoes multiplication
e.g. Multiplication is the inverse of division.
Tip: always check your division by multiplying the quotient by the divisor and then adding the remainder. The result should equal the original dividend.
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