# Math Mistakes, the Eleven Most Common Ones

## Math mistakes made over and over again

I once watched a YouTube video by someone who had been teaching high school math for 10 years. These are the top 11 mistakes that students consistently made:

1.  Confusing the base of a power

-32 = ? The students think it is (-3)x(-3).   wrong

In reality it is -32 = -(3)*(3) -9

2. Incorrect cancelling of terms in a fraction.

The students might write =      x – 8  wrong
I should have been =   x – 4

3. Forgetting double negative signs create a positive.

E.g., 9 – 5(x – 8) = 9 – 5x – 40 is wrong.

It should be 9 – 5(x – 8) = 9 – 5x + 40.

4. BEDMAS — Forgetting the order of operations. Operations should be done in this order: brackets, exponents, division, multiplication, addition & subtraction. That can be abbreviated to BEDMAS.

E.g., 22 -3(10 – 6) = 22 -3 * 4 = 4 – 3 * 4 = 4 – 12 = -8

5. Multiplying the base of a power.

E.g., 3(2x) = 6x    wrong.

6. Multiplying the number outside the parentheses by the denominator.

E.g., ½ + 3(15) = ½ + 315  wrong.

Is should be ½ + 3(15) = ½ + 35 = 5⁄10 + 6⁄10 = 11⁄10 = 1 1⁄10

7. Using inverse operations.

E.g., 3x  = 6 becomes x = 63  wrong.

Multiply each side by x.  Then 3 = 6x and 3⁄6 = x = ½

8. Treating a function lik e a number.

E.g., Sin (x + y) = sin x + sin y    wrongIt should be

Sin (x + y) = sinx cosy+ cosxsiny

Log(x + 4) = log x + log 4  wrong. Log(x + 4) can’t be simplified.

E.g., X5 + X3 = X15    wrong.

It should be X5 + X3 = X8

10. Forgetting the plus and minus signs when giving a square root.

E.g., X2  = 9. Therefore √9=3.  wrong.

It should be X = ±√9.

11. Expanding a binomial that is squared.

E.g., (x + 3)2 = x2 +  32= x2 + 9  wrong.

To expand that binomial it should be (x + 3)2 = (x + 3)(x + 3) = x2 +  3x +3x  + 32 = x2 + 6x + 9 