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Common Math Mistakes Students Make (and Fixes)

Diterbitkan 2 November 2026 · Oleh Sumzo team

The most common math mistakes students make — signs, brackets, fractions, exponents and equations — with the correct version and a quick fix for each.

The most common math mistakes aren’t about hard ideas — they are small slips with signs, brackets, fractions and exponents that turn a correct method into a wrong answer. Knowing the usual suspects, and checking your answers, prevents most of them.

Sign mistakes

Distributing a minus sign. $-(x - 4)$ is $-x + 4$, not $-x - 4$. The minus applies to every term inside the bracket. Likewise $-2(x - 3) = -2x + 6$.

Subtracting negatives. $5 - (-3) = 8$. Subtracting a negative adds.

Squaring negatives. $(-3)^2 = 9$, but $-3^2 = -9$: without brackets, only the 3 is squared. On a calculator, type the brackets.

Bracket mistakes

Squaring a sum. $(x + 3)^2$ is $x^2 + 6x + 9$, not $x^2 + 9$. Write it as $(x + 3)(x + 3)$ and expand all four products.

Forgetting to multiply every term. $3(2x + 5) = 6x + 15$ — the 3 multiplies the 5 too.

Fraction mistakes

Adding tops and bottoms. $\frac{1}{2} + \frac{1}{3}$ is $\frac{5}{6}$, not $\frac{2}{5}$. Use a common denominator: $\frac{3}{6} + \frac{2}{6}$.

Cancelling terms instead of factors. $\frac{x + 6}{3}$ is not $x + 2$; only whole factors cancel. But $\frac{3x + 6}{3} = x + 2$, because $3x + 6 = 3(x + 2)$.

Dividing by a fraction. Multiply by its reciprocal: $6 \div \frac{2}{3} = 6 \times \frac{3}{2} = 9$.

Exponent mistakes

Multiplying exponents instead of adding. $x^2 \cdot x^3 = x^5$, not $x^6$.

Splitting a power over a sum. $(a + b)^2 \neq a^2 + b^2$ — see brackets above.

Negative exponents. $2^{-3} = \frac{1}{8}$, not $-8$.

Equation mistakes

Doing something to one side only. Whatever you do, do it to the whole of both sides.

Dividing by $x$. From $x^2 = 5x$, dividing by $x$ gives $x = 5$ and loses $x = 0$. Factor instead: $x(x - 5) = 0$, so $x = 0$ or $x = 5$.

Forgetting the second root. $x^2 = 16$ gives $x = 4$ or $x = -4$.

Flipping inequalities. Multiplying or dividing an inequality by a negative number reverses the sign: $-2x < 6$ gives $x > -3$.

Percentage mistakes

Percent change from the wrong base. From 50 to 65 is a 30% increase ($\frac{15}{50}$), not about 23% ($\frac{15}{65}$).

Adding successive percentages. A 20% rise then a 20% fall is a 4% fall overall: $1.2 \times 0.8 = 0.96$.

Order of operations

$2 + 3 \times 4 = 14$, not 20: multiply before adding. And $8 \div 2 \times 4 = 16$ — multiplication and division are done left to right.

Careless mistakes

• Copying a number wrong from the question or between lines.
• Dropping units, or mixing cm and m.
• Rounding too early, then carrying the rounded value forward.

How to catch mistakes before they cost marks

• Substitute back. If $x = 7$ solves $3(x - 2) = 2x + 1$, both sides should be equal: $15 = 15$.
• Estimate first. A quick estimate makes wrong answers stand out.
• Write every step. Mistakes hide in steps done in your head.
• Keep a mistakes list. Most people repeat the same two or three slips.

The math answer checker shows the first step where your working went wrong, and each lesson in the Learning Center — such as equations and simplifying expressions — has a section on the mistakes for that topic.

Mistakes with units

Area and volume units. 1 m is 100 cm, but 1 m² is $100 \times 100 = 10{,}000$ cm², and 1 m³ is 1,000,000 cm³. Convert lengths before calculating area, or convert with the squared factor.

Time. 1 hour 15 minutes is 1.25 hours, not 1.15 hours, because 15 minutes is a quarter of an hour.

Mixing units in one calculation. Change everything to the same unit first.

Mistakes with graphs

• Reading the wrong scale — check what each square is worth before reading a value.
• Swapping coordinates: $(x, y)$ means across first, then up.
• Getting the sign of a slope wrong: a line falling from left to right has a negative slope.
• Joining points of a curve with straight lines.

Mistakes in word problems

• “5 less than $x$” is $x - 5$, not $5 - x$.
• “Twice the sum of $x$ and 3” is $2(x + 3)$, not $2x + 3$.
• Answering a different question — the problem may ask for the total, not one part.
• Forgetting to answer in words, with units.

A checklist before you hand in

• Did I answer exactly what was asked?
• Did I substitute my answer back where I could?
• Are the units there, and do they match the question?
• Is the size of the answer sensible?
• Are signs and brackets correct in every line?

Working through this list takes a minute and catches most of the mistakes above.

Frequently asked questions

What is the most common math mistake? Sign errors — especially forgetting that a minus sign in front of a bracket changes every term inside it.

What are common algebra mistakes? Squaring a sum as $a^2 + b^2$, cancelling terms instead of factors, dividing by $x$ and losing a solution, and forgetting to flip an inequality when dividing by a negative.

How can I stop making math errors? Write every step, check answers by substitution, estimate first, and keep a list of the mistakes you personally make most often.

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