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Thought-Process to Discover Knowledge

Welcome to nubtrek.

Books and other education websites provide "matter-of-fact" knowledge. Instead, nubtrek provides a thought-process to discover knowledge.

In each of the topic, the outline of the thought-process, for that topic, is provided for learners and educators.

Read in the blogs more about the unique learning experience at nubtrek.
mathsWhole NumbersNumerical 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

=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

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

•  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