10 Common Maths Mistakes Students Make (And How to Avoid Them)

Every student makes maths mistakes. But the difference between strong and weak performers is simple: strong students identify their mistakes and prevent repetition.

Let's examine the 10 most common mistakes and concrete strategies to avoid them.

Mistake 1: Sign Errors

The Problem

Working with negative numbers leads to sign confusion:

• -5 - 3 = -2 (WRONG! It's -8)
• -4 × -3 = -12 (WRONG! It's +12)
• 2 - (-5) = -3 (WRONG! It's +7)

Why It Happens

Sign rules aren't always taught with clear understanding. Students "memorize" rules without intuitive understanding.

How to Avoid It

For addition and subtraction with negatives: Think of a number line. Start at the first number, then move.

5 - 8: Start at 5, move 8 steps left → -3 ✓

-5 - 3: Start at -5, move 3 steps left → -8 ✓

For multiplication:

Positive × Positive = Positive (happy)

Negative × Negative = Positive (sad × sad = happy)

Positive × Negative = Negative (one sad ruins it)

Negative × Positive = Negative

Memory trick: "Two negatives make a positive" applies only to multiplication and division, NOT to subtraction!

Mistake 2: Order of Operations (BODMAS/PEMDAS)

The Problem

2 + 3 × 4 = 14 (WRONG! It's 14, but students calculate 5 × 4 = 20) 10 - 2 × 3 = 24 (WRONG! It's 4)

How to Avoid It

BODMAS/PEMDAS (Brackets, Orders, Division/Multiplication, Addition/Subtraction): Steps:

1. Simplify inside Brackets first
2. Calculate Orders (powers, roots)
3. Division and Multiplication (left to right, same priority)
4. Addition and Subtraction (left to right, same priority)

Example: 2 + 3 × 4 - 6 ÷ 2

Step 1: Multiplication and Division first (left to right)

- 3 × 4 = 12 - 6 ÷ 2 = 3 - Now: 2 + 12 - 3

Step 2: Addition and Subtraction (left to right)

- 2 + 12 = 14 - 14 - 3 = 11 ✓ Strategy: Write intermediate steps. Rushing causes order-of-operations mistakes.

Mistake 3: Fraction Errors

The Problem

1/2 + 1/3 = 2/5 (WRONG! It's 5/6) (1/2) / (1/3) = 1/6 (WRONG! It's 3/2)

How to Avoid It

Addition/Subtraction: Find common denominator

1/2 + 1/3 = 3/6 + 2/6 = 5/6 ✓

Multiplication: Multiply numerators and denominators

1/2 × 1/3 = (1×1)/(2×3) = 1/6 ✓

Division: Invert and multiply

(1/2) ÷ (1/3) = (1/2) × (3/1) = 3/2 ✓

Strategy: Say the rule aloud while solving. "I need a common denominator... 6 is the LCD... convert both fractions..."

Mistake 4: Distributing Incorrectly

The Problem

2(3 + 4) = 6 + 4 = 10 (WRONG! It's 14) 3(x - 2) = 3x - 2 (WRONG! It's 3x - 6) -(a + b) = -a + b (WRONG! It's -a - b)

How to Avoid It

Distributive Property: a(b + c) = ab + ac

You must multiply EVERY term inside the brackets.

Example 1: 2(3 + 4) = 2(3) + 2(4) = 6 + 8 = 14 ✓ Example 2: 3(x - 2) = 3(x) + 3(-2) = 3x - 6 ✓ Example 3: -(a + b) = -1(a + b) = -1(a) + -1(b) = -a - b ✓ Strategy: Use different colors for each distribution. Visually separate which term is being multiplied.

Mistake 5: Unit Conversion Errors

The Problem

2 km = 2 m (WRONG! It's 2,000 m) 5 hours = 5 minutes (WRONG! It's 300 minutes) 100 cm² = 1 m² (WRONG! It's 0.01 m²)

Why It's Tricky

Units for area and volume convert differently than linear units:

1 meter = 100 centimeters (multiply by 100)

1 square meter = 10,000 square centimeters (multiply by 100²)

1 cubic meter = 1,000,000 cubic centimeters (multiply by 100³)

How to Avoid It

Linear conversions (length, distance, time):

1 km = 1,000 m

1 m = 100 cm

1 hour = 60 minutes

1 minute = 60 seconds

Area conversions (multiply by conversion factor squared):

1 m² = 100 × 100 = 10,000 cm²

1 km² = 1,000 × 1,000 = 1,000,000 m²

Volume conversions (multiply by conversion factor cubed):

1 m³ = 100 × 100 × 100 = 1,000,000 cm³

1 km³ = 1,000 × 1,000 × 1,000 = 1,000,000,000 m³

Strategy: Draw conversion charts. Post them above your study desk. Refer to them.

Mistake 6: Rounding Errors

The Problem

3.67 rounded to 1 decimal place = 3.6 (WRONG! It's 3.7) 0.0456 rounded to 1 significant figure = 0.04 (WRONG! It's 0.05)

How to Avoid It

Rounding rule: Look at the digit you're rounding to, then look at the NEXT digit.

If the next digit is 5 or more: round UP

If the next digit is 4 or less: round DOWN

Example 1: 3.67 rounded to 1 decimal place

Look at tenths place (6)

Next digit is 7 (≥ 5)

Round up: 3.7 ✓

Example 2: 0.0456 rounded to 1 significant figure

First significant figure is 4

Next digit is 5 (≥ 5)

Round up: 0.05 ✓

Strategy: Circle the digit you're rounding to. Draw an arrow to the next digit. This visual reminder prevents errors.

Mistake 7: Algebra Errors - Moving Terms

The Problem

x + 5 = 12, solved as x = 12 + 5 = 17 (WRONG! It's 7) 3x = 15, solved as x = 15 - 3 = 12 (WRONG! It's 5)

How to Avoid It

Golden Rule: Whatever operation moved the term to the other side, that's the OPPOSITE operation. Term moved (+5 to the right): Subtract 5 from both sides

x + 5 = 12

x = 12 - 5 = 7 ✓

Term moved (multiplication by 3): Divide both sides by 3

3x = 15

x = 15 ÷ 3 = 5 ✓

Strategy: Don't "move" terms. Instead, perform the same operation on both sides. This prevents flip-flopping operations.

Mistake 8: Exponent Errors

The Problem

2³ × 2² = 2⁶ (WRONG! It's 2⁵) (2³)² = 2⁵ (WRONG! It's 2⁶) 2³ + 2² = 2⁵ (WRONG! It's 12)

How to Avoid It

Rules:

Same base, multiplication: Add exponents: aᵐ × aⁿ = aᵐ⁺ⁿ

Power of a power: Multiply exponents: (aᵐ)ⁿ = aᵐⁿ

Addition of powers: You CAN'T combine. Calculate separately: 2³ + 2² = 8 + 4 = 12

Example 1: 2³ × 2² = 2³⁺² = 2⁵ = 32 ✓ Example 2: (2³)² = 2³×² = 2⁶ = 64 ✓ Example 3: 2³ + 2² = 8 + 4 = 12 ✓ (NOT 2⁵) Strategy: Write out the rule above your working. This keeps the rule visible while solving.

Mistake 9: Percentage Errors

The Problem

"25% of 80 is 105" (WRONG! It's 20) "80 increased by 25% is 80 + 25 = 105" (WRONG! It's 100)

How to Avoid It

Percentage of a number: 25% of 80 = (25/100) × 80 = 0.25 × 80 = 20 ✓ Percentage increase: 80 increased by 25% = 80 + (25% of 80) = 80 + 20 = 100 ✓ (NOT: 80 + 25) Percentage decrease: 80 decreased by 25% = 80 - (25% of 80) = 80 - 20 = 60 ✓ Strategy: Always calculate the percentage amount first, then add or subtract from the original number.

Mistake 10: Misreading the Question

The Problem

Question: "What is the remainder when 47 is divided by 5?" Student answers: "9" (which is the quotient) Correct answer: "2" (the remainder)

How to Avoid It

Read the question twice slowly

Identify exactly what's being asked

Circle or underline the key words: "find," "calculate," "how many," "what is," "how much"

Before answering, restate what you're finding: "I'm looking for the remainder, not the quotient"

Quick Reference Checklist

Before submitting an exam, verify:

✓ Did I use the correct signs throughout?

✓ Did I follow BODMAS/PEMDAS?

✓ Did I find a common denominator for fractions?

✓ Did I distribute to all terms?

✓ Did I check my units?

✓ Did I apply exponent rules correctly?

✓ Did I understand what the question is asking?

✓ Does my answer make logical sense?

Practice on The Practise Ground

Our quizzes highlight common errors with detailed feedback:

Mistake identification

Step-by-step corrections

Conceptual explanations

Progressive difficulty

Every mistake is a learning opportunity!

FAQ