The Order Of Operations & BEDMAS

It should be Brackets not Bracets. Source: http://mlcs8z.wikispaces.com/file/view/bedmas.JPG/34411439/bedmas.JPG

Hi. This page will be about the order of operations and BEDMAS in algebra. The reader should be familiar with exponents, brackets (parantheses), multiplication, subtraction, addition and subtraction.


Table Of Contents

What Is The Order Of Operations and BEDMAS?

Examples

Practice Questions

Solutions


What Is The Order Of Operations and BEDMAS?

The order of operations is a mathematical and algebraic rule in which we follow when we have a combination of addition, subtraction, multiplication, division, exponents and brackets. The term and memory aid BEDMAS stands for brackets, exponents, division, multiplication, addition and subtraction.

    \[Brackets\]

    \[Exponents\]

    \[Division\]

    \[Multiplication\]

    \[Addition\]

    \[Subtraction\]

Brackets have the highest priority and should be dealt with first. We go from left to right in BEDMAS/PEDMAS (or from top to bottom as displayed above).


Examples

Example One

    \[8 - 9 + 6 = -1 + 6 = 5\]


Example Two

    \[(11 - 3) + 7 = 8 + 7 = 15\]

Because of the bracket, we compute 11 - 3 to get 8 first and then add 7.


Example Three

    \[5^2 + (7 - 8) = 5^2 - 1 = 25 - 1 = 24\]

We have a bracket and an exponent. The bracket is computed first before dealing with 5^2. We subtract 1 from 5^2 = 25 to get 24.


Example Four

    \[(\dfrac{1}{2} \times 5) - 1 + 4 = \dfrac{5}{2} -1 + 4 = \dfrac{5}{2} + 3 = \dfrac{5}{2} + \dfrac{6}{2} = \dfrac{5 + 6}{2} = \dfrac{11}{2}\]

The bracket is evaluated first where the 5 is multiplied by the half. After adding and subtraction (with fractions), we get the answer of \dfrac{11}{2} = 5.5.


Example Five

    \[(2 \times 10 \div 5) - (3^2 - 4) + 1 - 3 = (20 \div 5) - (9 - 4) - 2 = 4 - 5 - 2 = -1 - 2 = -3\]

This example features a combination of BEDMAS components. We first deal with each of the two brackets. In the first bracket, one can do either multiplication or division first. Either way, the first bracket computes to 4. In the second bracket, the term with the exponent is evaluated first. After evaluating the brackets, we add and subtract the terms to obtain the answer of -3.


Example Six

There are case where there are embedded brackets.We deal with the most inside bracket first.

    \[((2 \times 4) - 2 + 3) + 5 = (8 - 2 + 3) + 5 = 9 + 5 = 14\]


Practice Questions

Here are some practice questions to build understanding of BEDMAS and the order of operations.

1) 1 - 4 \div 2

2) (5 - 3 \div 3) + 2 - 2^2

3) 2^2 \div 4 + 1 - 7 \times 2

4) 1 + 7 - (2^2 \times 3)

5) (5 - 3 + 2)^2

6) 9 \div 3 \times 2 - (2 \times 10 \div 5)

7) 5 \times 2 \div 2 - (3^2 + 1 - 3 \times 2)

8) 1 - \dfrac{25}{5^2} + 3 - (2^3 + 1 - 4)


Solutions

1) -1

2) 2

3) -12

4) -4

5) 16

6) 2

7) 1

8) -2

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