# Understanding BODMAS

Struggling with a new explained concept called BODMAS? Well, look no further. In Grade 9 the concept of understanding BODMAS is explained.

**In simple terms, it is how mathematical affairs should take place in a set order.** Without any order, mathematical answers would differ from one person to the next. ‘BODMAS’ is a mnemonic – a system such as a pattern of letters, ideas, or associations which assists in remembering something.

**BODMAS stands for…**

**(B)rackets – Sums in brackets should be completed first****(O)rders – Powers, square roots, cube roots etc****(D)ivision – Left to right****(M)ultiplication – Left to right****(A)ddition – Left to right after the division/multiplication is complete****(S)ubtraction – Left to right**

This is how order takes place in mathematical equations. BODMAS is introduced in grade 9 to pupils remember what order mathematical equations should be completed in. This is also how scientific calculators and programs like Microsoft Excel work out their equations/sums.

It is believed that BODMAS was introduced by **Achilles Reselfelt** to help in solving the mathematical problem involving operational signs. Whenever an operation is introduced in a sum, ‘BODMAS’ rule is applicable. The BODMAS rule determines the order of operations.

In mathematics and computer programming, the **order of operations** (or **operator precedence**) is a collection of rules that reflect conventions about which procedures to perform first in order to evaluate a given mathematical expression.

In Layman’s terms, BODMAS is the order of operations used throughout mathematics, science, technology and many computer programming languages so that the end result of evaluation agrees with the way in which evaluation of expressions is in agreement with standard conventions.

As it is been tried and tested it is the sequence of mathematical equations and this rule is applied from grade 9 through to Grade 12.

**Example** 1 – Understanding BODMAS

*For example:*

*Let us look at the following sum. 8 + 2*5 =??*

*If we look at that sum and work, it out from left to right we may state our answer is 50.*

*8+2*5= 10*5 = 50 however, that answer is INCORRECT.*

*The BODMAS rule must be applied to the following sum. Which based on the rule, tells us to work out the multiplication part of the sum before we can add it together.*

*Therefore 8+2*5= * *(begin with the multiplication).*

*8+10 = 18 Is the CORRECT answer.*

*If we had to change up the same question, how would you answer…*

*(8+2)*5 =? Using the BODMAS rule we need to first start with the BRACKETS*

*(10)*5 = 50 After the brackets are completed we can arrive at the correct answer.*

**Example 2** – Understanding BODMAS

*For example:6 + 3 of 7 – 5= 6 + 3 × 7 – 5 (start with the multiplication)= 6 + 21 – 5 (then the addition)= 27 – 5 (then the subtraction)Answer = 22*

**Example 3** – Understanding BODMAS

*For example:20 +*

**21 ÷ 3**× 2 (concentrate on the division first)= 20 +

**7**× 2 (then move on to the multiplication)= 20 +

**14**(now you are free to add your sum)Answer= 34

## Example 4

*For Example:*

*78 – [5 + 3 of (25 – 2 × 10)]*

*= 78 – [5 + 3 of ( 25 – 20)], (Simplifying ‘multiplication’ 2 × 10 = 20)*

*= 78 – [5 + 3 of 5], (Simplifying ‘subtraction’ 25 – 20 = 5)*

*= 78 – [5 + 3 × 5], (Simplifying ‘of’)*

*= 78 – [ 5 + 15], (Simplifying ‘multiplication’ 3 × 5 = 15)*

= 78 – 20, (Simplifying ‘addition’ 5 + 15 = 20)

*= 58, (Simplifying ‘subtraction’ 78 – 20 = 58)*

*Answer: 58*

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