# Precedence rules for the algebra community

Precedence of operators

In simple algebra, there is a set of precedence (priority) of operations that should be respected in order that everyone evaluates mathematical expressions in the same way. Although these rules have been taught in elementary school or junior high school, they are often overlooked.
Here's a review of operators from highest precedence (to be evaluated firt) to lowest.

1. Brackets (parentheses)
2. Exponentiation & roots
3. Multiplication/division

This set of rules may be abbreviated as BEDMAS for ease of memorization.

When operators of equal precedence are encountered side-by-side, they are evaluated from left to right.

For example, this is how a calculator evaluates the following expression:
2.5+5²*(4+3)/2
=2.5+5²*7/2 ...brackets first
=2.5+25*7/2 ... exponentiation
=2.5+175/2 ... multiplication is to the left of division
=85

Also, note that in square-roots, the expression under the horizontal bar is equivalent to a set of implicit parentheses. For example, if the whole expression 5&sup3+4*7-1/2 were under the square-root sign, it would be interpreted as:
√(5&sup3+4*7-1/2)

Another frequent oversight has to do with fractions.

Fractions in typeset expressions have the numerator and denominator separated by a horizontal line, such as:

5x²+3x-2
-------------
2x²-x+1

When transcribing fractions to a single line, such as evaluating on a calculator, or posting the expression online, we have to recognize that there are implicit parentheses in both the numerator and denominator. The transcribed one-line expression must have parentheses (brackets) around each of the numerator and denominator, such as:
(5x²+3x-2)/(2x²-x+1)
or else it will be incorrectly interpreted using the BEDMAS rule indicated earlier.

Thus the expression
x+5
---
x+3
would be correctly interpreted as (x+5)/(x+3).

A side note for logical expressions:
====================================
The precedence rule for logical expressions are:

Precedence Operator
1 ¬
2 ∧
3 ∨
4 &rightarrow;
5 &leftrightarrow;

For example:
¬p∧q∨p∧¬q&leftrightarrow;T
means
((¬p)∧q)∨(p∧(¬q))&leftrightarrow;T

1. 👍 0
2. 👎 0
3. 👁 270

## Similar Questions

1. ### social studies

What event set precedence that alleviated the problem of having no of succession in the empire roman

asked by glenn on January 9, 2012
2. ### social studies

What event set precedence That alleviated the problem of having no law of succession in the empire

asked by glenn on January 9, 2012
3. ### history

what enent set precedence that alleviated the problem of having no law of succession in the empire

asked by Barbara on January 8, 2012
4. ### history

what event set precedence that alleviated the the problem of having on law of succession in the empire please help

asked by paul on January 8, 2012
5. ### history

what event set precedence that alleviated the problem of having no law of succession in the empire I have no book Please help

asked by paul on January 8, 2012
6. ### math

please help me i need help before tomorrow please help i need help on my homework Post a question and someone will try to help. Be specific about what you don't understand. i need help on greatest common factor What unit would you

asked by Asia on September 5, 2006
7. ### literature (bejamin Franklin)

I have one more confusing question regarding this. And Thank you Ms.Sue for answering the last question! Franklin's humor in Witch Trial at Mt. Holly depends upon the belief that... a)the belief that religion takes precedence over

asked by jason on November 19, 2013
8. ### literature

I have one more confusing question regarding this. And Thank you Ms.Sue for answering the last question! Franklin's humor in Witch Trial at Mt. Holly depends upon the belief that... a)the belief that religion takes precedence over

asked by jason on November 19, 2013
9. ### Boolean Algebra

Let the 6-tuple be a Boolean algebra where B is a set, + and * the sum and the product operators respectively, 0 and 1 the zero and the unit elements respectively and c the complement operator. If b is an element of the set B,

asked by JWalker on November 12, 2019
10. ### computers

Using the operator precedence that excel 2007 follows,which calculation wuld be perfomed first from the following equation?119+7*3/(8-6)-4/2 a)119+7 b)7*3 c)8-6 d)4/2 is a) correct answer thank you

asked by vedrana on September 1, 2011

More Similar Questions