MathKnights™

How to do long division - the steps, the why, and the burger question

Divide, Multiply, Subtract, Bring down - taught with the sharing-in-chunks meaning underneath, plus remainders, partial quotients, and the four mistakes that cause most of the tears.

By Erika Nagy · mom of two, founder of MathKnights · Updated July 2026

Long division is where "I'm bad at math" gets born. Not because the math is hard — because it's the first time kids must run a four-step procedure over and over without losing their place, and most of them were handed the steps with no idea why they work. This guide fixes both: the steps, the why, and the famous mnemonic — honestly reviewed.

Before the steps: what long division actually is

Long division is just sharing out a big number in chunks, biggest chunks first. 672 ÷ 4 asks: share 672 among 4 groups. You share out the hundreds first, trade what's left for tens, share those, trade again, share the ones. The written algorithm is only a bookkeeping system for that sharing. Kids who see it once with real objects — 6 dimes and pennies, base-ten blocks, even LEGO studs — stop treating the steps as magic spells.

The four steps (and the burger question)

Divide → Multiply → Subtract → Bring down — then repeat.

The classic mnemonic: "Does McDonald's Sell Burgers?" Our honest review: it genuinely works for remembering the order, and there's no shame in using it. Its limit is that it can't tell your kid what to do at each step or why — a kid chanting burgers can still be completely lost. Use the mnemonic as the checklist, and the tortilla-sharing meaning as the understanding. You need both.

Worked example: 672 ÷ 4

1. Divide: How many 4s in 6 (hundreds)? One. Write 1 above the 6.

2. Multiply: 1 × 4 = 4. Write it under the 6.

3. Subtract: 6 − 4 = 2. (That's 2 hundreds left over.)

4. Bring down: the 7 comes down → now you have 27 (tens).

Repeat: 4s in 27? Six (6×4=24). Write 6 up top; 27−24=3; bring down the 2 → 32. 4s in 32? Eight, exactly. Answer: 168.

Sense-check (always!): 168 × 4 should rebuild 672. It does. Teach the check as part of the routine, not an extra.

Remainders: the leftover pizza slices

Example: 125 ÷ 4

Run the steps: 4s in 12? Three (12). Subtract → 0, bring down 5. 4s in 5? One (4). Subtract → 1 left over. Answer: 31 R1 — thirty-one each, one slice left on the table.

Later, that R1 grows up to become 31 1/4 or 31.25 — remainders, fractions, and decimals are the same leftover wearing three outfits. Planting that idea early pays off for years.

The gentler on-ramp: partial quotients

If the standard algorithm produces tears, try partial quotients first — the "friendly chunks" method. For 672 ÷ 4: take out 100 groups of 4 (400), then 50 more (200), then 18 more... kids subtract easy chunks until nothing's left and add up the chunks: 100+50+18 = 168. It's slower but transparent — every step is a choice they understand. Many kids who learn partial quotients first slide into the standard algorithm a month later without drama, because now they know what the compact version is abbreviating.

The four mistakes to watch for

When is a kid ready?

Long division typically lands in 4th grade with one-digit divisors and grows through 5th–6th. The honest prerequisites: reasonably quick multiplication facts and comfortable multi-digit subtraction. If facts aren't automatic yet, drilling long division mostly drills frustration — build fluency first (our multiplication chart guide covers the "stubborn eight" strategy), then this procedure gets dramatically easier.

How to practice without tears

Two problems done carefully with the sense-check beat ten done sloppily. Real-life division is everywhere: splitting allowance savings across weeks, sharing 125 LEGO studs among 4 builders, dividing the road-trip miles by driving days. And when the leftover-slices idea clicks, you're already halfway into dividing fractions — same meaning, smaller pieces.

Frequently asked questions

What are the steps of long division?

Divide, Multiply, Subtract, Bring down — repeat until nothing is left to bring down. Any leftover is the remainder.

What does "Does McDonald's Sell Burgers" mean?

It's a mnemonic for the step order: Divide, Multiply, Subtract, Bring down. It works for remembering the sequence, but pair it with the sharing-in-chunks meaning so the steps make sense.

How do you do long division with remainders?

Run the normal steps; whatever is left at the end that's smaller than the divisor is the remainder: 125 ÷ 4 = 31 R1. Later that R1 becomes 1/4 or .25.

What is the partial quotients method?

Dividing by subtracting friendly chunks (100 groups, 50 groups...) and adding up the chunks. Slower but fully transparent — a great on-ramp to the standard algorithm.

What grade do kids learn long division?

Usually 4th grade with one-digit divisors, extending through 5th–6th. Quick multiplication facts and solid subtraction make it far easier.

Division drills, but make them a quest

MathKnights turns division practice - and every other elementary skill - into a knights-and-quests game kids ask to play. Built by a parent, for grades 1-5. Free to start.

Begin the quest - free

This guide reflects one family's teaching experience plus common U.S. grade-level standards as of July 2026. Every child learns differently.