**COMMON
ERRORS WHICH SHOULD BE AVOIDED**

**When
Working With Operations of Subtraction and Division**

**It
is incorrect to speak or write of the quotient of a and b.
When speaking or writing about division, statements must make it clear which
is the divisor and which is the dividend.**

**It
is incorrect to speak or write of the difference of a and b.
When speaking or writing about subtraction, statements must make it clear
which is the subtrahend and which is the minuend.**

**When
Working With Operation Symbols**

**It
is incorrect to write 3 + - 4. Correct syntax is 3 + (- 4)**

**It
is incorrect to write 3
- 4. Correct syntax is 3
(- 4) **

**It
is incorrect to write 3 - ^{-} 4. Correct
syntax is 3 - (- 4)**

**When
Working With Square Roots and Exponents**

**It
is incorrect to write (a + b) ^{2 } = a^{2} + b^{2}. It
is correct to write (a + b)^{2 } = a^{2} + 2ab
+ b^{2}**

**It
is incorrect to write .
They are not equal.**

**When
Working With Fractions**

**It
is incorrect to write .
They are not equal.**

**It
is incorrect to write .
They are not equal.**

**It
is incorrect to write . They
are not equal.**

**It
is incorrect to expand fractions in this manner:
**

**When
Working With Equations**

**It
is correct to write:
divide both sides of the equation by 10**

It
is **incorrect** to write:

divide 10 to both sides of the equation

It
is **incorrect** to write:

divide 10 by both sides of the equation

It
is **incorrect** to write (or do)

divide the right side of the equation by 10

eg. Faced with 10x = 20 it is incorrect
to claim that dividing 20 by 10 gives the equation x = 2

**It
is correct to write:
subtract 5x from both sides of the equation**

It
is **incorrect** to write:

subtract 5x to both sides of the equation

It
is **incorrect** to write:

subtract both sides by 5x

It
is **incorrect** to write:

minus 5x from both sides of the equation

It
is **incorrect** to write:

- 5x from both sides of the equation

It is incorrect to write or speak of moving variables or numbers from one
side of the equation to the other.

**When
Tempted to Cancel**

**Do
NOT do the following:
**

**Do
NOT do the following:**

**Do
NOT do the following:
**