Long Division — Fixing "Place, Multiply, Subtract, Bring Down"
Have you ever looked at a long division problem and wondered where to even start explaining "place, multiply, subtract, bring down"?
Most children who stumble on long division aren't struggling with their times tables. There are four steps — place, multiply, subtract, bring down — and every time, they're just skipping one of them somewhere.
Long division is "place, multiply, subtract, bring down," repeated
Japan's Ministry of Education, in its commentary on the national curriculum guidelines for elementary mathematics (2017), lists this as something a child should be able to do by grade 4: "understand that calculations where the divisor is a 1- or 2-digit number and the dividend is a 2- or 3-digit number can be done building on basic calculations. Also, understand how to write these as column calculations." (Grade 4, Numbers and Calculation)
This column form is built out of a repeated cycle of four steps: place, then multiply, then subtract, then bring down. The procedure is to work through this set of four, one place at a time, all the way down to the ones place. The same commentary states: "In grade 4, teach the method of column calculation for division of whole numbers, and have children understand that division with many digits can be done building on basic calculations." No matter how many digits are added, the same cycle handles it.
Pattern 1: skipping "bring down"
After finishing the hundreds place, if a child moves on to the next calculation without bringing down the tens digit, the quotient ends up one digit short. If 618 ÷ 3 comes out as small as 26, suspect this pattern.
Pattern 2: forgetting to write a 0 in the quotient
Sometimes a 0 belongs at a place partway through the quotient. If, say, a 0 belongs at the tens place but a child moves on to the next place without writing it, every place after that is thrown off.
Pattern 3: the placed quotient is off (dividing by a 2-digit number)
Once a child moves on to dividing by a 2-digit number, the "place" step gets harder: instead of settling the quotient almost automatically by working backward through the times tables, as happens with a 1-digit divisor, a child now has to start from a rough "about this much" guess rather than an exact answer. It feels like the same procedure, but it's easy to get stuck here. Place the quotient too high, and there won't be enough left to subtract. Place it too low, and the remainder ends up equal to or bigger than the divisor. Either way shows up right there on the page once the answer is written out.
How to teach it at home
Step 1: Say the four steps out loud, one digit at a time
Say "place, multiply, subtract, bring down" out loud, and don't move on until one place is finished. Saying the names of the steps out loud lets a child check for themselves how far they've gotten.
Step 2: Check the placed quotient with multiplication (when dividing by a 2-digit number)
Once a quotient digit is placed, multiply it by the divisor before writing it down, to check whether it can actually be subtracted. Asking one question at a time — "if we put down 7, what's 7 times 24? Can we subtract that?" — helps a child notice on their own when a placed digit is too high.
Step 3: Check the work with the verification equation
The same commentary gives this equation: dividend = divisor × quotient + remainder. Once an answer is written, build the habit of calculating divisor × quotient + remainder and checking that it comes back to the original number. A skipped "bring down" or a missing 0 means this equation won't come back to the original number. The mismatch itself is the signal that a step got skipped somewhere.
What to avoid
Don't have a child redo a wrong long division from scratch. Check, one at a time, where among the four steps things stopped — usually there's only one spot to fix. Repeating the whole thing just repeats the one step that was never fixed, unchanged.
I used to think a stumble in long division always came down to weak times tables. Looking into it, that wasn't the only cause. Where a child gets stuck usually isn't the times tables — it's one of the four steps.
How to practise
- Division (÷ 1-Digit Number) practises column form and calculation from 2-digit ÷ 1-digit up to 3-digit ÷ 1-digit, both with and without a remainder
- Moving on to Division by 2-Digit Numbers, placing the quotient becomes the central skill. Use the checking method from Step 2 here
- If working backward through the times tables to place a quotient still feels shaky, check the grade 3 article "Why Division with Remainders Trips Kids Up" first — long division goes faster afterward. That article covers the idea that "the remainder is smaller than the divisor"; this one covers how that idea gets used inside column form
Frequently asked questions
Q. Placing the quotient takes so long that tests don't get finished
A. Being slow to place the quotient usually comes down to a slow reverse lookup of Times Tables: 6 to 9 and 1 — "what's the biggest times-table fact in the 6 times table that doesn't go over 40?" Before adding more long division practice, do 5 reverse lookups a day on their own, spoken aloud — it pays off faster. Once a reverse lookup takes under 2 seconds, the step of settling on a quotient speeds up by itself, and the whole column calculation gets faster too.
Q. Should they check their work every single time?
A. While it's still new, yes, every time is a good idea. But if the checking itself becomes a burden and your child starts disliking long division, limit it to just the problems they got wrong. The goal isn't checking the answer — it's learning to notice for themselves which step got skipped.
If your child is stalling in the same spot every time among the four steps, you already know where to fix it. Repeating just that one step is enough.
This article is written by a parent who builds diglabo. I am not a teacher or an education specialist. The general guidance here is based on how the topic is taught in Japanese primary schools, checked against Japan's national curriculum guidelines.
diglabo's worksheets follow the Japanese curriculum. What that means if you are outside Japan