__maths__>__Whole Numbers__>__Numerical Expressions with Whole Numbers__### Brackets Or Parenthesis in Precedence Order

In this page, handling of brackets or parenthesis in a numerical expression is explained. That is brackets have the highest precedence order and expressions inside brackets are evaluated first.

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Multiplication is higher in precedence to addition. In some expressions, addition has to be carried out before multiplication.

For example: Result of `2+4` has to be multiplied by `3`. This cannot be given as `2+4xx3` as the result of this expression does not equal the example.

Which of the following helps to define such expressions?

- parenthesis or brackets are used
- parenthesis or brackets are used
- the precedence is fixed and cannot be modified with parenthesis

The answer is "Parenthesis or brackets are used". *Parenthesis or brackets are higher in precedence.*

Simplify `4+6-:(3xx2)`

- `8`
- `5`
- `5`

The answer is "`5`".

`4+6-:(3xx2)`

The expression inside bracket is simplified first.

`=4+6-:6`

The division is higher in precedence over addition.

`=4+1`

Then addition is simplified.

`=5`.

Simplify `(10-3-2)xx3`.

- `1`
- `15`
- `15`

The answer is "`15`".

The expression inside bracket is simplified first.

`(10-3-2)xx3`

the two subtraction are in the same precedence level and so they are simplified in the left to right sequence.

`=(7-2)xx3`

`=(5)xx3`

Then, the multiplication is simplified.

`=15`

What is the symbol `(` or `)`called?

- brackets
- parentheses
- both the above
- both the above

The answer is "both the above"

**Arithmetics Precedence ** : Precedence Order in arithmetics is BODMAS* It is also called as PEMDAS*

The order is as follows

• Parentheses or Brackets

• Exponents or Order

• Multiplication and Division

• Addition and Subtraction

For a number of operations of same precedence level, the operations are carried out from left to right in sequence.

*Solved Exercise Problem: *

Simplify `(1+3-1)xx2+2-1`

- `7`
- `7`
- `11`
- `9`

The answer is "`7`"

*Solved Exercise Problem: *

What is the value of `7-2xx2`?

- `7-2xx2``= 5xx2=10`
- `7-2xx2``=7-4``=3`
- `7-2xx2``=7-4``=3`

The answer is "`3`". Multiplication is higher in precedence than subtraction. So multiplication, `2xx2`, is carried out first.

*Solved Exercise Problem: *

What is the value of `3-1-1`?

- `3-1-1``= 3-0`=3`
- `3-1-1``=2-1``=1`
- `3-1-1``=2-1``=1`

The answer is "`1`". The two subtractions are in the same precedence level and in such a case, the operations are carried out in the left to right order.

**Simplification of Expressions** : BODMAS

• B - Brackets

• O - Order (exponents, roots, logarithm)

• D - Division

• M - Multiplication

• A - Addition

• S - Subtraction

• And Left to Right sequence for multiple operations of same precedence. * PEMDAS • P - Parentheses • E - Exponents (roots and logarithm) • M - Multiplication • D - Division • A - Addition • S - Subtraction • And Left to Right sequence for multiple operations of same precedence. *

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