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  =  a2 + b2.  It is correct to write (a + b)2  =  a2 + 2ab + b2

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: