Everyone makes math mistakes. The difference between good and great isn't making fewer errors - it's catching them before they cost you points.

1. Sign Errors

The most common mistake in all of mathematics. Negative signs get lost, flipped, or ignored.

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

Fix: Circle every negative sign before you start computing. When multiplying or dividing, count the negatives: odd count = negative result, even count = positive.

2. Order of Operations Mistakes

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

Most people know PEMDAS/BODMAS, but still trip up with nested expressions or when exponents are involved.

Fix: When in doubt, add parentheses to make the order explicit. 2 + (3 x 4) removes all ambiguity.

3. Decimal Point Drift

Example: 0.3 x 0.7 = 0.21, not 2.1 or 0.021.

Fix: Count total decimal places in the factors (1 + 1 = 2), then place that many decimal places in the answer. Two places → 0.21.

4. Off-by-One Errors

"How many numbers from 5 to 12?" The answer is 8, not 7. People subtract (12 - 5 = 7) and forget to add 1 for inclusive counting.

Fix: Use the formula: last - first + 1. Or just remember: "fence posts, not gaps."

5. Distribution Errors

Forgetting to distribute to ALL terms inside parentheses.

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

Fix: Draw arrows from the outside term to each inside term. Every term gets multiplied.

6. Fraction Addition Without Common Denominators

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

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

Fix: Never add numerators unless the denominators match. Finding a common denominator must happen first, every time.

7. Percentage Reversal

"A is what percent of B?" versus "What is A percent of B?" - these are completely different questions.

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

Fix: Identify which number is the "whole" and which is the "part." The whole always goes in the denominator.

Building Error-Proof Habits

The best way to eliminate mistakes isn't to "be more careful" - that's vague and unhelpful. Instead:

1. Always estimate first. If your estimate says ~100 and you got 1000, recheck.
2. Check the last digit. Quick parity/unit digit checks catch most arithmetic errors.
3. Work backwards. Plug your answer back into the original problem.
4. Practice under time pressure. Errors increase when you're rushed. Training under pressure builds resilience.

Math Gym's speed drills are designed to build exactly this kind of accuracy-under-pressure muscle memory.