In every subject, there are common errors students make. Mathematics is no different. Here I’ve listed 10 common mistakes students make when solving mathematics problems.

#### (1) Incorrect order of operations

**Example**

Calculate 5 + 3×2

Correct is 11 as multiplication must be done before addition.

**Common error **

would be to add 5 and 3 first then multiply by 2.

If that error is made then the wrong answer is 16.

#### (2) Forgetting what power notation means

**Example**

Calculate 2^{3} + 7

**Correct**

2^{3} = 2×2×2 = 8

8 + 7 = 15

**Common error **

Not knowing what 2^{3} means and either thinking it is 23 or 2×3 = 6.

If these errors were made the answers would be 30 or 13.

#### (3) Forgetting that two brackets side by side should be multiplied.

**Example**

(5 + 4)(2 + 7)

Correct

(5 + 4)(2 + 7) = (5 + 4)×(2 + 7) = 9×9 = 81.

**Common error**

Use =, – or ÷ to connect the brackets so the calculation becomes

(5 + 4)+(2 + 7) = 18

(5 + 4)-(2 + 7) = 0

(5 + 4)÷(2 + 7) = 1

#### (4) Adding and subtracting fractions incorrectly

**Example**

Do this calculation

**Correct**

**Incorrect**

Common error is to just add or subtract the numerators and denominators.

This would be incorrect.

#### (5) Thinking 1 is prime

A prime number has exactly two factors. 1 has only one factor.

#### (6) Finding the original price from a sale price

**Example**

In a sale all prices were reduced by 10%. What was the pre-sale price of something that sold for $90 in the sale?

**Correct**

Let the pre-sale price be p.

p – 10%p = 90

0.9p = 90

p = 90÷0.9

p = 100

Pre-sale price was $100.

**Incorrect**

Pre-sale was 90 + 10%90 = 99

**Common error**

Adding instead of dividing

#### (7) Cancelling incorrectly

**Example**

Calculate

**Correct**

Incorrect

**Common error**

Splitting the fraction prematurely

Cancelling should only be done when there is multiplication

**Example**

As in the above example

#### (8) Confusing multiples with factors

**Example **

Write down the factors of 14 and the first 4 multiples of it.

**Correct**

The factors of 14 are those whole numbers which divide into it without a remainder. They are 1,2, 7, 14.

Multiples of 14 are numbers which arise by multiplying other whole numbers apart from 0 by 14. The first 4 multiples of 14 are 1×14 = 14, 2×14 = 28, 3×14 = 42 and 4×14 = 56.

#### (9) Interpreting the algebraic expression *xy* wrongly.

**Correct**

*xy* = *x* × *y*

*xy **≠ x *+* y*

*xy **≠ x – y*

*xy **≠ x *÷* y*

* *

#### (10) Using the √ in trying to solve a quadratic equation

Example

Solve *x*^{2} = 3*x* + 4

**Correct**

*x*^{2} = 3*x* + 4

hence *x*^{2} – 3*x* – 4 = 0

hence (*x* – 4)(*x* + 1) = 0

*x* = 4 or *x* = -1

**Incorrect**

*x*^{2} = 3*x* + 4

hence *x* = √(3*x* + 4)

All sorts of errors then follow.

How to avoid these errors? Practice, practice and more practice!! There may be some tricks to help such as remembering the order of mathematical operations by the mnemonic (word) BEDMAS

which means Brackets first, Exponents(powers) next, Division and Multiplication next then Addition and Subtraction. However in the end basic mistakes are avoided by a lot of practice.

Sharleen Hanson says

Great set of tips! This article is bound to help lots of budding mathematicians!

Patricia Fowler says

I appreciate you creating Student Shed. I am looking forward to assisting my son prepare for his B.J.C exams come 2019. I just hope and pray he stays the cause. Your explanation of common errors that students make is meaningful. Our kids need to pay attention to what the question is asking them to solve, look carefully at how the numbers are written and pay attention to how they prepare their step by step explanation for their answers. I would appreciate you explaining the quadratic equation a little more. Break it down or give several examples please. Thank you so much for your kind assistance.

Patricia