Long Division: Beyond Single Digits
Bridge the gap between basic arithmetic and complex division. Tackle multi-digit divisors, master tricky zero placeholders, conquer decimals, and understand the algebraic mechanics behind the algorithm.
Like Duolingo, but for Long Division: Beyond Single Digits. Tomo turns the whole topic into a game you play five minutes a day, until it actually sticks.
21 levels across 4 sections, about 42 minutes end to end, roughly 8 days at five minutes a day. It moves through Conquering Multi-Digit Divisors; Beyond Whole Numbers: Decimals and Remainders; Speed, Efficiency, and Auditing; and The Underlying Mechanics. It assumes you already know the basics.
Free forever · No credit card · iPhone & Android
Key ideas in Long Division: Beyond Single Digits
- Rounding 28 up to 30 lets you estimate quotient digits via the simpler 3-times table.
- Dividing 18 tens by 3 tens predicts a trial quotient digit of 6 with minimal risk of wild guessing.
- Every subtraction step in long division must yield a remainder strictly smaller than the divisor.
- A remainder larger than the divisor signals another whole group can be extracted by increasing the quotient digit.
- If the divisor exceeds the dividend's first two digits, zero tens can be formed.
- Comparing the divisor directly to the dividend's leading pair dictates where the first quotient digit sits.
- Multiplying candidate digit 8 by the divisor's leading 6 tens gives 48 tens, which instantly exceeds 43 tens.
- Checking the product of the candidate digit and the tens column detects overshoots without full scratch work.
- An overshoot reveals the candidate digit is at most one or two units too generous.
- Stepping down the candidate digit by exactly one salvages the existing scratch setup quickly.
- Every brought-down digit creates a distinct quotient position that must be filled.
- When the divisor exceeds the partial dividend, write 0 in the quotient to hold place.
- Skipping the 0 and pulling the next digit immediately collapses 205 into 25.
- A zero in the quotient records a digit fit, not the completion of the algorithm.
- Division only halts when no dividend digits remain and the final remainder is assessed.
- Confusing a step quotient of 0 with remainder 0 causes premature termination.
You've tried the other tabs
Thirty open tabs. Four facts you actually kept.
You watched. You nodded. By Sunday it was gone.
One answer, then back to scrolling.
Eight weeks. You meant to finish. You didn't.
Tomo gives Long Division: Beyond Single Digits the Duolingo treatment: levels, streaks, and quick quizzes that test what you just learned. That game loop is what the tabs above never had, so it's the one you actually finish.
Here's what playing it feels like
A real question from this course. Take your best guess.
When you want to divide 184 by 28, what friendlier number should you round 28 to?
Get it right to open this lesson and 20 more in the app.
How to learn Long Division: Beyond Single Digits, step by step
Go in order. 21 short levels across 4 sections, about 42 minutes in all, five minutes a day.
- 1
Conquering Multi-Digit Divisors
- Tackling Two-Digit Divisors
- Preventing Quotient Zero Traps
- 2
Beyond Whole Numbers: Decimals and Remainders
- Turning Remainders into Decimals and Fractions
- Dividing by Decimals
- 3
Speed, Efficiency, and Auditing
- Compact Division and Partial Quotients
- Auditing and Verifying Division Results
- 4
The Underlying Mechanics
- Place Value Deconstruction and Algebraic Parallels
4 sections · 7 units · 21 levels. Built to play, not to enroll.
Questions about Long Division: Beyond Single Digits
How do I learn Long Division: Beyond Single Digits?
Go in order: start with Conquering Multi-Digit Divisors, then Beyond Whole Numbers: Decimals and Remainders, then Speed, Efficiency, and Auditing, then The Underlying Mechanics. On Tomo that's 21 short levels, about 42 minutes in all, played five minutes a day. Start free and play the first level in under a minute.
Is there a Duolingo-style app for Long Division: Beyond Single Digits?
Yes. Tomo works like Duolingo: short daily lessons, streaks and quick quizzes. Long Division: Beyond Single Digits is one of its free courses, and you can type any other topic to get a course of your own.
Is the Long Division: Beyond Single Digits course free?
Yes. Long Division: Beyond Single Digits is playable on Tomo's free plan, which doesn't expire. No credit card, no waitlist. Download the app and start your first lesson.
How long does it take to learn Long Division: Beyond Single Digits?
21 levels across 4 sections, about 42 minutes of play in total. It's built for five minutes a day, so you finish it a little at a time instead of all at once.
Do I need any background to start Long Division: Beyond Single Digits?
No. It's pitched at an intermediate level, so it starts where you are and builds up. If you can tap a phone, you can start.
Tomo is in ChatGPT
Tomo is also a ChatGPT plugin: the same playable courses, built and played inside your chat.
Add Tomo to ChatGPT- What to ask
- “Make me a Tomo course on black holes.” “Turn this chat into a Tomo course.”
- What you get
- Quick questions with instant feedback, hearts and stars, ready to play in about a minute.
- Where it goes
- No sign-up to start. Connect your Tomo account and your streak carries on in the app.
You pick the voice
Long Division: Beyond Single Digits is taught in the Explain Like I'm 5 style: no big words. promise.. Want a different feel? In the app you can spin up the same topic in any of Tomo's teaching styles. Same facts, totally different vibe.
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Start Long Division: Beyond Single Digits today.
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