Order of Operations

When entering mathematical expressions, it is important to follow the correct order of operations. Expert TA follows standard mathematical rules, similar to calculators and programs like Microsoft Excel. 

Implied Multiplication

In Expert TA, the multiplication symbol (*) is not always shown, but it is still applied. This allows equations to appear more natural and closer to how they are written by hand.

For example:

• f = 2.5 x cos(3yz) – xyz
  is equivalent to
• f = 2.5*x*cos(3*y*z) – x*y*z

Multiplication is implied between numbers and variables:

• y = 1/2a is interpreted as y = (1/2)*a

Common Order of Operations Examples

1/2a vs 1/(2a)
Multiplication and division have equal precedence and are evaluated from left to right.

• 1/2a is interpreted as (1/2)*a → 0.5a
• 1/(2a) places 2a in the denominator

Similarly:

• 1/ab is interpreted as (1/a)*b → b/a
• To include both variables in the denominator, use 1/(ab)

√a + b vs √(a + b)

• √a + b → only a is under the square root
• √(a + b) → the entire expression is under the square root

ab² vs (ab)²

• ab² → only b is squared
• (ab)² → the entire expression ab is squared

Example:

• 2*4² = 2*16 = 32
• (2*4)² = 64

a/b² vs (a/b)²

• a/b² → only b is squared
• (a/b)² → the entire fraction is squared

Important

• Always use parentheses to make your intended calculation clear
• Do not assume the system will interpret expressions the way you expect
• When in doubt, add parentheses to control the order of operations