Two Common Math Mistakes

(1) Forgetting the Pythagorean theorem:

Here is an example with numbers:

There are two possible answers because the square of a negative number is positive:

Conceptually, the reason that the squareroot of (a² + b²) doesn’t equal (a + b) relates to right triangles.  According to the Pythagorean theorem, a right triangle with sides a and b has a hypotenuse, c, equal to the squareroot of (a² + b²).

(2) Forgetting a common denominator:

Here is an example with numbers:

You can’t just ignore the numerators.  The way to add fractions is to first find a common denominator.  In the above example, 1/2 and 1/4 have a common denominator of 4, since 1/2 can be expressed as 2/4.  Once both fractions have a common denominator, you can add the numerators together.

Chris McMullen, author of the Improve Your Math Fluency Series