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.
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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.
Where Long Division: Beyond Single Digits takes you
- 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.
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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