How to stop mixing up numbers

Question

I'm in my final year in school and for the past three or four years it has not been uncommon for me to get my answers slightly off because of a random mistake. It's not every question but I mess up a single digit or 2 on 20%-60% of the questions I do. Even when I slow down I oftentimes end up mixing up a minus with a plus, using the wrong number, or sometimes just randomly pulling a number out of nowhere (It happens fairly rarely). For example, just now I've been doing the quadratic formula and when doing 3x\^2 - 21x + 20 I randomly decided to use the 20 instead of the 3 for the 2(a) denominator. There have also been times when I multiplied or divided an expression by two and randomly left one of the numbers untouched.

Any tips for dealing with this?

Answer 1

The two best defenses are going to be diligently writing out your work, step by step, and finding methods to double check answers.

I’m guessing you’re already pretty diligent about writing out your work, so that you can look back over it.

By the second point, I mean coming up “sanity checks” or other things you can use to double check an answer makes sense. Like if you try two slightly different methods to do something, and they agree, then it’s less likely you made a mistake. Exactly how to apply this depends on the problem though. In some cases, perhaps you can make a small sketch to visually check that something makes sense. Or plugging your answer back into the original equation.

And of course, practice should still help, though I can understand how this would be frustrating if it feels like progress is slow.

Answer 2

These are what we call "silly mistakes". There is technically no specific cause for it but they mostly occur due to either trying to quickly solve the problem, negligence, or not paying attention while solving. The only thing to fix this is, well, practice.

As for the quadratic equation one, write down the values of a, b and c before solving. Like, if the question is 5x^(2) + 2x + 15 = 0, let the first line be a = 5, b = 2, c = 15. That way, while using the quadratic formula, you can directly refer this first line instead of the question itself.

I've personally followed this in questions involving multiple variables (there are formulae having a heck ton of a, b, c, a1, b1, c1, a2, b2 c2 and God know what!) as even though my Math is pretty good, I make mistakes too. So yeah, the more you take your time and write down the given stuff properly, the less likely you are to make a mistake!

Answer 3

Practice. Check your answers when you're done. That's it.