How to avoid arithmetic and sign errors

[hackedagainanda]

I find most of the errors I make are related to arithmetic or using the wrong sign. (Note: This applies to mainly algebra and trigonometry for me.)

I've tried writing slower and neater, and have been structuring my operations linearly on the paper step by step.

Do any of you have some tried and true methods for avoiding simple errors?

I feel a bit ashamed that the arithmetic is still tripping me up while I have the algebra down.

 

[jedishrfu]

Sometime just going back to baby steps helps ie do each step of your solution changing one thing at a time.

Also do a post-mortem on your work look back at what you specifically did wrong when and where you lost the sign.

I know one common reason is moving a term from one side to the other and forgetting to subtract it:

x = y + 3   --->   x + 3 = y (wrong)   --> x - 3 = y (right)

baby steps:

x = y + 3
-3 = -3
x - 3 = y + 3 - 3 
x - 3 = y + 0
x - 3 = y

 

[DaveC426913]

Some techniques I use:

1. Do the problem a second time, ideally from the bottom up - if possible - but at least changing the order of as many operations as you can manage (i.e. the commutable ones).
2. Do a sanity check. Is the answer near what it's supposed to be? Should it be positive? Should it be about the size you got?
3. Estimate. If you round the numbers enough so you can do it in your head, do you get about the right answer?

 

[jedishrfu]

I would like to add that it’s important to understand exactly where and when you make your mistakes.

Years ago, my brother was frustrated in an algebra course because he couldn’t stop making mistakes. Upon investigation, I saw that many of them occurred not in his solution but in the rush to check his answers. He would then go back and change things because of the check mistake.

The solution was simple look for errors in the check before you believe it and go back to change things. The other lesson was don’t rush and always have a solid reason for each step you take. Don’t take big expansive steps just moderate sized ones so you can see what you did in review.

 

[fresh_42]

I like to say: Writing is faster than thinking!
see https://www.physicsforums.com/insights/10-math-tips-save-time-avoid-mistakes/

It might be a bit over the top, but it points to a simple truth. To write many small steps might be a bit annoying, but it's faster and less uncertain than to perform them by thought and only write the results. In the article above is an example (point 3).

 

[gmax137]

Whenever possible, check that the "answer" makes sense. If you're doing a circuit powered by a 1.5 volt flashlight battery and you show a resistor dissipating 15 kilowatts, then something is probably wrong.

Many problems are too abstract for this approach.

 

[symbolipoint]

Common enough, that parts of some steps get lost and then further steps will not compensate for mistakes in the earlier steps. Also, do not try to combine too many steps in your head; but like earlier poster said, make some more small steps on paper.