The Core Idea
Most of us learned subtraction as a borrowing ritual: line up the digits, take from the column on the left when you run short, write the answer underneath. That algorithm is correct, but it was built for paper, not for your head. In your head, holding crossed-out digits and carried tens is exactly the kind of bookkeeping that breaks down.
Mental subtraction works on a different principle. A subtraction like $63 - 28$ is really a question about distance: how far apart are $63$ and $28$ on the number line? Once you see subtraction as distance rather than as column-borrowing, you can move along that line in whatever steps are easiest, and the borrowing disappears. The methods below are all ways of measuring that distance cleanly.
The reasoning matters more than the speed. A child who understands that $900 - 1$ and $899 - 0$ describe the same gap can shift any problem into an easier one on purpose. A child who only memorised borrowing has nothing to fall back on when the digits get awkward. That difference - reasoning you can transfer versus a trick that works in one shape - is the whole point.
Method 1: Left-to-Right by Place Value
The first instinct is to start from the right, the way the written algorithm does. Flip it. Start from the left, subtract the big pieces first, and you carry less in your head.
Take $63 - 28$. Break the $28$ into its place values, $20$ and $8$, then peel them off in order:
$$63 - 20 = 43$$ $$43 - 8 = 35$$
You held one running number the whole time - $63$, then $43$, then $35$ - instead of two columns and a borrow. The answer is $35$.
Why it works: subtraction lets you take away the parts of a number separately, because $63 - 28 = 63 - (20 + 8) = (63 - 20) - 8$. You are not inventing a shortcut; you are using the structure of place value. The left-to-right order helps because the tens give you the rough size of the answer first, and the ones only nudge it.
This method shines when no awkward crossing happens in the tens. When it does - when the ones digit you are subtracting is bigger than the one you have - one of the next two methods is cleaner.
Method 2: Counting Up (Complement Reasoning)
How do you get better at mental subtraction when borrowing keeps tripping you up? Stop subtracting. Add instead.
Subtraction and addition are the same relationship read in two directions. $61 - 47$ asks "what is left after I remove $47$," but it answers the identical question "what do I add to $47$ to reach $61$." Counting up from the smaller number to the larger one measures the same distance without a single borrow.
For $61 - 47$, step up to the friendly number first, then the rest:
$$47 + 3 = 50$$ $$50 + 11 = 61$$ $$3 + 11 = 14$$
The answer is $14$. You hopped to $50$ because round tens are easy resting points, then covered the remaining gap, then added your two hops.
This is exactly how a cashier hands back change - they count up from the price to the cash you gave, never subtracting on paper. Cashiers reach for counting-up first because the number you are subtracting is close to the total; the gap is small, so the hops are few.
Method 3: The Equal-Shift Method (Compensation)
How do you subtract from a round number like $900$ without a chain of borrows? Here is the move that makes "borrowing" cases vanish. The distance between two numbers does not change if you slide both of them by the same amount. So shift both until the subtraction is clean.
Take $900 - 54$. That cluster of zeros forces a chain of borrows in the written method. Instead, subtract $1$ from each number - the gap stays identical:
$$900 - 54 = 899 - 53$$
Now there is nothing to borrow. Subtract by place value: $899 - 53 = 846$. The answer is $846$.
Wait - let me be precise about the direction, because this is where it goes wrong. You must shift both numbers the same way by the same amount. Subtract $1$ from both, or add $1$ to both. If you only change one, you have changed the distance and your answer is off by exactly that amount.
A cleaner everyday case: $452 - 376$. Add $24$ to both to push the second number up to a round $400$:
$$452 - 376 = 476 - 400 = 76$$
The equal-shift method works because subtraction measures a gap, and a gap is unchanged when both endpoints move together. It is the same truth as Method 1, used to engineer an easier problem instead of accepting the one you were handed.
Method 4: Round and Adjust
What is the quickest way to subtract a number like $198$? When a number sits just below a round figure, subtract the round figure and give back the difference. This trades one hard subtraction for one easy subtraction plus a small correction.
Take $345 - 198$. The $198$ is two short of $200$:
$$345 - 200 = 145$$ $$145 + 2 = 147$$
You subtracted $2$ too much, so you add $2$ back. The answer is $147$.
The adjustment direction is the only thing to keep straight: if you subtracted more than you meant to (you rounded the amount being taken away up), you add the surplus back. Picture it on the number line - you overshot, so you walk back the extra steps.
Practice Set
Work each one with the method named, then check against the answers below.
$74 - 31$ (left-to-right by place value)
$52 - 38$ (counting up)
$800 - 47$ (equal-shift)
$263 - 99$ (round and adjust)
$531 - 268$ (your choice - which method fits?)
Answers. 1. $43$. 2. $14$. 3. $753$. 4. $164$. 5. $263$ (counting up or equal-shift both work well here; pure left-to-right forces two awkward crossings).
Common Mistakes With Mental Subtraction
Mistake 1: Borrowing in your head the way you borrow on paper
Where it slips in: On problems with a string of zeros or several crossings, learners try to picture the crossed-out digits and lose track of which columns they have adjusted.
Don't do this: Do not mentally rewrite $900$ as "eight, nine, ten" and carry borrows across three columns - that is the visual the equal-shift method exists to avoid.
The correct way: Shift both numbers to kill the zeros first ($900 - 54 \rightarrow 899 - 53$), then subtract by place value. The single most common source of wrong answers here is starting a borrow chain that the head cannot hold.
Mistake 2: Shifting only one number in compensation
Where it slips in: Using the equal-shift method but adjusting just one side, so the distance silently changes.
Don't do this: Do not turn $452 - 376$ into $452 - 400$ and call it done - you took away $24$ too much.
The correct way: Move both endpoints by the same amount and the same direction, or round one number and adjust the answer at the end. Pick one of those two patterns and do not blend them.
Mistake 3: Adjusting in the wrong direction after rounding
Where it slips in: Round-and-adjust problems, when the learner forgets whether to add or subtract the correction.
Don't do this: Do not subtract the $2$ in $345 - 198$ after you have already subtracted $200$; you would be punishing yourself twice.
The correct way: If you rounded the amount being subtracted up (took away too much), you give the surplus back - you add it. Reading the gap on a number line makes the direction obvious every time.
How Bhanzu Approaches Mental Subtraction
Bhanzu does not teach subtraction as a bag of shortcuts to memorise. The starting point is the idea underneath all four methods: subtraction measures distance, and distance is something you can reshape. Once a student genuinely understands that $899 - 53$ and $900 - 54$ are the same question, they invent the equal-shift move themselves rather than recalling it.
That reasoning-first habit is what transfers. A learner who built mental subtraction on place value and complements carries the same thinking into algebra, where rearranging an expression to make it tractable is the core skill. A learner who only memorised tricks hits a ceiling the moment the numbers stop looking like the examples. Bhanzu trainers teach the why first, on the principle that mental agility comes from understanding number structure - not from speed drills layered on rote rules.
Conclusion
Mental subtraction is about measuring distance, not borrowing column by column - that reframe is what makes every method below possible.
Left-to-right by place value keeps one running number in your head instead of two columns and a borrow.
Counting up turns subtraction into addition, which is why cashiers and quick mental calculators prefer it when the numbers are close.
Equal-shift and round-and-adjust let you reshape an awkward problem into an easy one because the gap stays fixed when you move both endpoints together.
The reasoning transfers - a student who understands why these methods work carries that flexibility into algebra and beyond.
To build mental subtraction on understanding rather than drills, explore Bhanzu's mental maths for kids program or work with a math tutor who teaches the reasoning first. Want a live trainer to walk through these methods with your child? Book a free demo class.
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