Long division

What is this skill?

In fifth grade, children divide by two-digit numbers, such as 1,248 ÷ 24. The question is the same as always: how many groups of 24 fit into 1,248? The difference is that the divisor is too big to know from a times table, so children need a way to build up to the answer.

The usual route is estimate, test and adjust. 24 is close to 25, and four 25s make 100, so 1,248 holds roughly 50 of them. Checking, 24 × 50 = 1,200, which leaves 48, and 48 is two more 24s. The answer is 52. Many classrooms write this as partial quotients, taking big friendly chunks first (a chunk of 50, then a chunk of 2) and adding the chunks. The long division layout does the same job in a tidier column.

When the numbers do not divide evenly, there is a remainder. For 1,000 ÷ 36, 36 × 27 = 972, with 28 left over. The remainder must always be smaller than the divisor; if it is not, another group still fits. In the practice here, remainder questions ask only for the whole-number part of the answer (27 in this example), and the prompt says so.

Why it matters

Division with larger divisors is where many children lose confidence in math, because it needs estimating, multiplying, subtracting and place value all at once. It is also what makes later topics possible: dividing decimals, working out unit rates, and simplifying fractions by finding common factors.

Because every step of the method is multiplication or subtraction, trouble with long division often turns out to be trouble with one of those, not with division itself. That makes it a good diagnostic. If your child gets stuck, watch which step slows down.

Common mistakes

• Placing the first digit of the answer in the wrong spot. Estimating how big the answer should be (hundreds, tens or ones) first prevents this.
• Choosing a quotient digit that is too big, so the subtraction goes negative, or too small, so the remainder is larger than the divisor. Both are signals to adjust and try again, not to start over.
• Dropping a zero in the answer when a step does not divide at all. A column that holds no groups still gets a 0.
• Subtracting carelessly. Most errors in long division are small subtraction slips, so slowing down on that step pays off.
• Treating a remainder as part of the answer, or ignoring it when the question asks for it.

How to help at home

• Help your child write out the first few multiples of the divisor (×1, ×2, ×3, ×5, ×10) on the side. This one habit turns most long division problems into quick lookups.
• Practice friendly rounding: 24 is close to 25, 49 is close to 50. Estimating the answer first shows what size to expect.
• Check every answer by multiplying back and adding the remainder: 36 × 27 + 28 should return 1,000.
• Use real sharing: 1,260 trading cards into 35 binders, or 500 pages read at 24 pages a day.
• If your child is stuck, ask what they would do with an easier divisor like 20. The method is the same.

Worked examples

These are real questions from the Tutorsaurus long division practice, with the answers worked out.

1. Example 1

   77 ÷ 11 = ?

   Answer: 7. 11 × 7 = 77, so 77 ÷ 11 = 7.

2. Example 2

   1080 ÷ 36 = ?

   Answer: 30. 36 × 30 = 1080, so 1080 ÷ 36 = 30.

3. Example 3

   1215 ÷ 23 = ? (whole number only, drop the remainder)

   Answer: 52. 23 × 52 = 1196, and 1215 − 1196 = 19 is left over. The whole number part of the answer is 52 (52 R19).