Order Of Operations BODMAS|Playing with Numbers|Simplification of Brackets|Solved Examples|LearnMath

Hello students !
Welcome to Crash Course 2.0 Mathematics Middle School
Today, we shall learn about Order Of Operations (ODMAS), Simplification of Brackets (BODMAS) | Class 5 - Class 8 |
Chapter name : Playing with Numbers ( Middle School Mathematics )
Educator : Saraswoti Karki
Contact: [email protected]
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EXTRA NOTES APART FROM THE VIDEO FOR REFERENCE :
Order of Operations BODMAS

Operations
"Operations" mean things like add, subtract, multiply, divide, squaring, etc. If it isn't a number it is probably an operation.

But, when you see something like...

7 + (6 × 52 + 3)

... what part should you calculate first?

Start at the left and go to the right?
Or go from right to left?

Warning: Calculate them in the wrong order, and you can get a wrong answer !

So, long ago people agreed to follow rules when doing calculations, and they are:

Order of Operations
Do things in Brackets First

yes 4 × (5 + 3) = 4 × 8 = 32

not 4 × (5 + 3) = 20 + 3 = 23 (wrong)

Exponents (Powers, Roots) before Multiply, Divide, Add or Subtract

yes 5 × 22 = 5 × 4 = 20

not 5 × 22 = 102 = 100 (wrong)

Multiply or Divide before you Add or Subtract

yes 2 + 5 × 3 = 2 + 15 = 17

not 2 + 5 × 3 = 7 × 3 = 21 (wrong)

Otherwise just go left to right

yes 30 ÷ 5 × 3 = 6 × 3 = 18

not 30 ÷ 5 × 3 = 30 ÷ 15 = 2
(wrong)

How Do I Remember It All ... ? BODMAS !

B
Brackets first
O
Orders (i.e. Powers and Square Roots, etc.)
DM
Division and Multiplication (left-to-right)
AS
Addition and Subtraction (left-to-right)

What is an Expression?
An expression is a sentence with a minimum of two numbers and at least one math operation. This math operation can be addition, subtraction, multiplication, and division. The structure of an expression is:

Expression = (Number, Math Operator, Number)

For example,

= 7 + 9

= 23 × 4

= 37 – 6

= 25 + 9 – 4 ÷ 2

In all the given expressions, a math operator is used between the two numbers.

A math expression is different from a math equation. An equation will always use an equivalent (=) operator between two math expressions.

For example,

= 25 + 7 = 64 ÷ 2

= 20 × 5 = 102

The structure of defining math expression advances in different grades. In early grades, children are expected to write math expressions using numbers and operators. Later on, words help students to form a math expression.



Let’s consider a word problem.

Tom has to fill a box with oranges and apples. The number of apples should be 5 more than oranges. Tom picks 3 oranges each time and repeats it 5 times. Count the total number of oranges and apples.

To solve this, formulate the math expressions as follows:

= Number of oranges = 3 × 5

= Number of oranges = 15

Number of apples = Number of oranges + 5

= Number of apples = 15 + 5

= Number of apples = 20

Total number of fruits = Number of oranges + Number of apples

Third math expression will be:

= 15 + 20

= 35

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