Up

Order of operations

Sometimes you will see a calculation written in the form  \({\text{8 - (2 x 3)}}\) , where brackets, that is the symbols \((\) and \()\), are put around part of the calculation.
Brackets are  there to tell you to carry out the calculation inside them first. So  \({\text{8  - (2x3 )  =  8 -  6  =  2}}\).
If you had to find the answer to \({\text{8 }} + {\text{ 5 }} - {\text{ 3}}\) , you might wonder whether to do the addition first or  the subtraction first.
If you do the addition first,  \({\text{8 }} + {\text{ 5}} - {\text{ 3 }} = {\text{ 13}} - {\text{ 3 }} = {\text{ 1}}0\).

If you do the subtraction first,  \({\text{8 }} + {\text{ 5}} - {\text{ 3 }} = {\text{ 8 }} + {\text{ 2 }} = {\text{ 1}}0\) .

In this case, it makes no any difference which operation you do first.

If, however, you had to find the answer to  \({\text{3 }} + {\text{ 4x2}}\) , your answer will depend on whether you do the  addition first or the multiplication first.
If you do the addition first,  \({\text{3 }} + {\text{ 4x 2 }} = {\text{ 7x 2 }} = {\text{ 14}}\).

If you do the multiplication first,  \({\text{3 }} + {\text{ 4x 2 }} = {\text{ 3 }} + {\text{ 8 }} = {\text{ 11}}\).

To avoid confusion, mathematicians have decided that, if there are no brackets, multiplication and  division are carried out before addition and subtraction.

Such a rule is called a convention: clearly the opposite decision  could be  made,  but  it  has  been  agreed  that the  calculation \({\text{3 }} + {\text{ 4x 2}}\)  should be carried out as  \({\text{3 }} + {\text{ 4x 2 }} = {\text{ 3 }} + {\text{ 8 }} = {\text{ 11}}\).

There are  a  number of these conventions, often  remembered by  the word 'BoDMAS', which stands for:

  • Brackets
  • Divide
  • Multiply
  • Add
  • Subtract

This  is  the order  in  which arithmetic operations must be carried out.
Most  calculators  have  the  'BoDMAS '  convention  programmed into them, and so automatically carry out operations in the correct order.

Below you can download some free math worksheets and practice.


Downloads:
4215 x

Evaluate each expression.

This free worksheet contains 10 assignments each with 24 questions with answers.

Example of one question:

Beginning-Algebra-Order-of-operations-easy

Watch bellow how to solve this example:

 

Downloads:
2469 x

Evaluate each expression.

This free worksheet contains 10 assignments each with 24 questions with answers.

Example of one question:

Beginning-Algebra-Order-of-operations-medium

Watch bellow how to solve this example:

 

Downloads:
2201 x

Evaluate each using the values given.

This free worksheet contains 10 assignments each with 24 questions with answers.

Example of one question:

Beginning-Algebra-Order-of-operations-hard

Watch bellow how to solve this example:

 
 
 

Facebook PageGoogle PlusTwitterYouTube Channel

Algebra and Pre-Algebra

Beginning Algebra
Adding and subtracting integer numbers
Dividing integer numbers
Multiplying integer numbers
Sets of numbers
Order of operations
The Distributive Property
Verbal expressions
Beginning Trigonometry
Finding angles
Finding missing sides of triangles
Finding sine, cosine, tangent
Equations
Absolute value equations
Distance, rate, time word problems
Mixture word problems
Work word problems
One step equations
Multi step equations
Exponents
Graphing exponential functions
Operations and scientific notation
Properties of exponents
Writing scientific notation
Factoring
By grouping
Common factor only
Special cases
Linear Equations and Inequalities
Plotting points
Slope
Graphing absolute value equations
Percents
Percent of change
Markup, discount, and tax
Polynomials
Adding and subtracting
Dividing
Multiplying
Naming
Quadratic Functions
Completing the square by finding the constant
Graphing
Solving equations by completing the square
Solving equations by factoring
Solving equations by taking square roots
Solving equations with The Quadratic Formula
Understanding the discriminant
Inequalities
Absolute value inequalities
Graphing Single Variable Inequalities
Radical Expressions
Adding and subtracting
Dividing
Equations
Multiplying
Simplifying single radicals
The Distance Formula
The Midpoint Formula
Rational Expressions
Adding and subtracting
Equations
Multiplying and dividing
Simplifying and excluded values
Systems of Equations and Inequalities
Graphing systems of inequalities
Solving by elimination
Solving by graphing
Solving by substitution
Word problems