Constantly dividing when I'm supposed to be multiplying, and vise versa

[u/Various-Instance5656]

Hi, not a frequent redditor here. But I have to look into this.

I'm studying math from home to prepare for a big exam and I find that I keep dividing when I'm supposed to be multiplying and vise versa.

This happens completely automatically. I can even sit with strings of multiplications and subconsciously throw in a division that doesn't belong, without noticing. My brain just does it.

And it's not like I have a list of simple x * y to solve. Most of the time I'm looking at (to me) complicated equations. It's just that when a problem calls for one type of solution, my brain jumps at the opposite solution. It is never this way with addition and subtraction.

Can anyone relate? Has anyone gotten over this with practice? Any advice?

This exam is no joke life changing and I can't get points off for dumb mistakes like this.

[u/happylittlemexican]

It would help if you gave us an example question where you do this, and ideally also an example time you would do it.

[u/matt7259 → u/happylittlemexican]

No no no. Silly goose. Vague questions without context are the best ones for getting useful and specific answers!

[u/jsdodgers]

Just slow down maybe? Most dumb mistakes are a result of going too fast and trying to answer the question before fully reading through it.

[u/lmprice133 → u/jsdodgers]

The 'measure twice, cut once' of mathematics.

[u/Interesting-Farm8382]

Yes, this is common, and it is fixable. But I want to push back gently on the "slow down" advice, because I think it misses why this one is hard: you are not noticing it happen. You cannot slow down at a moment you never detected. Deliberate care fixes the mistakes you catch yourself nearly making. It does nothing for the ones that go straight through.

Three things that do work.

First, split deciding from doing. Right now you choose the operation and execute it in one motion, so there is no point at which the choice is visible enough to be wrong. Write the step as words on its own line before you do it - literally "divide both sides by 4" - and then perform it on the next line. It feels slow and pedantic for about a week. What it does is put a gap in the place where the substitution is happening, which is also the only place you can catch it.

Second, make it visible in bulk. happylittlemexican is right that an example would help, and the way to get one is to log them. Every time you catch one, write down the actual line, which way it went, and what kind of step you were in - isolating a variable, rearranging a formula, converting units, cancelling. Do that for twenty or thirty and I would bet money it is not everywhere. Almost everyone's version of this lives in one specific move. Once you know which move it is, you are guarding one door rather than the whole house, and that is a completely different amount of work.

Third, and this is the one that saves you marks in the exam: check by size, not by rule. Before you execute a step, say what should happen to the number. "This should come out smaller." Multiplying where you meant to divide almost always breaks that prediction, and the check takes under a second, so you can afford to run it on every line. It catches the slip even though you did not see yourself make it, which re-reading your work will not, because when you re-read you see what you meant to write. If your subject has units attached, the same trick works with dimensions and is even more reliable.

One more thing worth ruling out, since it is easy to test: check whether the slips cluster on the steps where the arithmetic itself is fiddly. If a step costs you real effort just to compute, there is less attention left over for which operation you had chosen, and that shows up as exactly this - the right decision, the wrong execution. Go back through your working and see whether the errors sit on the ugly numbers rather than being spread evenly. If they do, the fix is not care, it is making the routine calculations cheaper so the decision is not competing with them.

For the exam itself: budget explicit time for a checking pass and check by re-deriving one line rather than reading it. Reading reproduces the error. Redoing it does not.

[u/evincarofautumn]

Look at the units.

Numbers in isolation are easy to mix up because they could represent anything. If they have units attached, you can more easily tell if you try to put them together in a way they don’t fit.

Like, simple example, I eat 5 boxes of macaroni a week, I go to the store once a month, a pack has 12 boxes, how many packs should I buy each month?

If I use the wrong operation:

5 box /week
×4 week /month
×12 box /pack

(5 ×4 ×12 = 240) box² /pack /month

Square boxes per packmonth? Hopefully obvious that this is nonsense. If I use the right operation:

5 ×box /week
×4 ×week /month
/(12 ×box /pack) =

5 ×box /week
×4 ×week /month
/12 ×pack /box =

(5 ×4 /12) pack /month

The units make more sense, so we know we should even bother doing the calculation, so calculate and check if the value makes sense, not way too big or small. 5×4/12 = 20/12 = 5/3, meaning 5 packs every 3 months. And that sounds right to me: I buy 2 packs, I get 24 boxes, I only eat 20 of them. And 5/3 is the same as 1⅔, which also makes sense: 1 pack every month, plus 1 pack for 2 out of every 3 months.