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BODMAS board for 3 plus 4 times 5 minus 2
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7 Common Math Mistakes and How to Avoid Them

Catch the error type before it repeats.

April 1, 2026Math Gym Team1 min read

Error check

Handle operation order before speed

A fast answer is only useful after multiplication and division are placed correctly.

BODMAS board for 3 plus 4 times 5 minus 2
  1. 1Mark multiplication and division first.
  2. 2Evaluate those pieces.
  3. 3Return to addition and subtraction from left to right.
Common slip

Do not run left to right until the higher-priority operations are already simplified.

Sign check

Compute size first, then apply the sign

For one negative factor, the product is negative after the positive size is known.

Signed multiplication level board for negative times positive
  1. 1Ignore the sign for one breath.
  2. 2Compute 8 x 6 = 48.
  3. 3Apply one negative sign.
Fast check

One negative makes a negative answer; two negatives make a positive answer.

Most errors are repeatable. That is good news: once you can name the error type, you can build a check for it.

1. Sign Errors

Negative signs get lost or flipped.

Example: -3 x (4 - 7) = -3 x (-3) = 9, not -9.

Check: count negatives before multiplying or dividing. Odd count gives a negative result. Even count gives a positive result.

2. Order of Operations

Example: 2 + 3 x 4 = 14, not 20.

Check: add parentheses around the operation that must happen first.

3. Decimal Drift

Example: 0.3 x 0.7 = 0.21, not 2.1.

Check: count decimal places in the factors, then place that many decimal places in the answer.

4. Off-by-One Counts

"How many numbers from 5 to 12?" The answer is 8, not 7.

Check: for inclusive ranges, use last - first + 1.

5. Distribution Errors

Example: 3(x + 4) = 3x + 12, not 3x + 4.

Check: every term inside the parentheses must receive the outside factor.

6. Fraction Addition

Wrong: 1/3 + 1/4 = 2/7

Right: 1/3 + 1/4 = 4/12 + 3/12 = 7/12

Check: only add numerators after the denominators match.

7. Percentage Reversal

"30 is what percent of 200?" and "What is 30% of 200?" are different.

  • 30 is what percent of 200? 30 / 200 = 15%
  • What is 30% of 200? 0.30 x 200 = 60

Check: identify the whole first. The whole goes in the denominator.

Build the Habit

Before another timed set, choose one check:

  • estimate first
  • check the last digit
  • plug the answer back in
  • repeat the exact missed pattern

Speed improves when errors become easier to catch.