__maths__>__Foundation of Algebra with Numerical Arithmetics__>__Numerical Arithmetics: Revision for Algebra__### Arithmetic Operations And Precedence

This course is designed for students at 9th and 10th grade level. It assumes the following were introduced.

• Whole numbers, integers, fractions, decimal numbers.

• Addition, subtraction, multiplication, division, exponent, root, logarithm.

• Subtraction is inverse of addition

• Division is inverse of multiplication

• Root and Logarithm are inverses of Exponent

• introduction to variables in algebra

• Numerical expressions

• BODMAS or PEMDAS for precedence order

• BOMA or PEMA The objective of this topic is to *formalize numerical arithmetic as applicable to algebra*.

It is very important to go through these to understand algebra.

*click on the content to continue..*

What is `2+4+3`?

- `9`
- `9`
- `243`

The answer is "`9`". *This is an example of a numerical expression.*

What is `2-4-3`?

• One student did `2-4-3` `= -2-3` `=-5`

• Another student did `2-4-3` `=2-1` =`1`.

Which one is correct?

- `1`
- `-5`
- `-5`

The answer is "`-5`".

Subtraction is to be handled as inverse of addition `2-4-3` `=2+(-4)+(-3)`.

In this case both students will get the correct answer.

• `2+(-4)+(-3)` `= -2-3` `=-5`

• `2+(-4)+(-3)` `=2-7` =`-5`.

What is `2xx4xx3`?

- `24`
- `24`
- `243`

The answer is "`24`". *This is an example of a numerical expression.*

Simplify `2-:4-:3`. Which one of the following is correct?

• `2-:4-:3` `=2/4 -:3` `= 2/12`

• `2-:4-:3` `=2-: 4/3` `=6/4`

- `2/12`
- `2/12`
- `6/4`

The answer is "`2/12`".

Division is to be handled as inverse of multiplication `2-:4-:3` `=2xx 1/4 xx 1/3`.

In this case, both methods will give the correct answer.

• `2xx 1/4 xx 1/3` `= 2/4 xx 1/3` `=2/12`

• `2xx 1/4 xx 1/3` `=2xx 1/12` `=2/12`.

Simplify `2+4xx3`. Which one of the following is correct?

• `2+4xx3` `=6 xx 3` `= 18`

• `2+4xx3` `=2 + 12` `=14`

- `18`
- `14`
- `14`

The answer is "`14`". *Multiplication has higher precedence to addition.* In `2+4xx3`, the multiplication is to be done ahead of addition.

Which one of the following is correct?

• `2xx4^3` `=2 xx 64` `= 128`

• `2xx4^3` `=8^3` `=512`

- `128`
- `128`
- `512`

The answer is "`128`". *Exponent has higher precedence to multiplication.* In `2xx4^3`, the exponent is to be done ahead of multiplication.

Which of the following is a meaning for the word "precedence"?

- priority over another; order to be observed
- priority over another; order to be observed
- preparation required for a task; fundamental requirement

The answer is "priority over another; order to be observed".

In a numerical expression, the precedence order is:

• exponents

• multiplication

• addition.

Multiplication has higher 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 have higher precedence.*

Precedence order is "PEMA" is also known as PEMDAS / BODMAS

**LPA - Precedence ** : Precedence Order in arithmetics is PEMA* PEMDAS or BODMAS *

→ Parenthesis

→ Exponents

→ Multiplication

→ Addition

Note 1: Subtraction is handled as inverse of addition.

Note 2: Division is handled as inverse of multiplication

Note 3: Roots and Logarithm are handled as inverse of exponents

For a number of operations of same precedence, it is prescribed that the operations be carried out from left to right in sequence.

eg: `4-:2xx2` equals `(4-:2)xx2=4` and not `4-:(2xx2)=1`.

With the definition of PEMA, the rule of "left-to-right-sequence" is not required.

eg: `4-:2xx2 = 4xx 1/2 xx 2` and simplify either way and both result in the same correct answer.

`(4xx1/2)xx2 = 4` or

`4xx (1/2 xx 2)= 4`.*this is very important in the context of Algebra, as variables or terms may require to be handled in different order than the prescribed left to right order.*

*Solved Exercise Problem: *

Simplify `(1/2+3.1)xx2+2.1`

- `9.3`
- `9.3`
- `14.76`

The answer is "`9.3`"

*slide-show version coming soon*