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Thought-Process to Discover Knowledge

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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.

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Sequence in Arithmetic Operations of Same Precedence

In this page, the sequence in arithmetic operations of same precedence in a numerical expression is explained. That is, multiple operations of same precedence are evaluation from left to right.



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Consider `20-4-3`.

It is wrong to do `20-4-3` `!=20-1` `=19`.

The correct order of simplification is `20-4-3` `= 16-3` `=13`

The two subtractions are in the same precedence level. This is to be handled from left to right sequence.

Consider `36-:6-:3`

It is wrong to simplify as `36-:6-:3` `!=36-:2` `=18`

The correct order of simplification is `36-:6-:3` `=6 -:3` `= 2`.

The two divisions are in same precedence level. This is to be handled from left to right sequence. .

Sequence in Arithmetic Operations of Same Precedence: To simplify multiple arithmetic operations of same precedence, the operations are carried out in left to right sequence.

Consider `20-4+3`.

It is wrong to do `20-4+3` `!=20-7` `=13`.

The correct order of simplification is `20-4+3` `= 16+3` `=19`

The subtraction and addition are in the same precedence level. This is to be handled from left to right sequence.

Consider `36-:6xx3`

It is wrong to simplify as `36-:6xx3` `!=36-:18` `=2`

The correct order of simplification is `36-:6xx3` `=6 xx3` `= 18`.

The division and multiplication are in same precedence level. This is to be handled from left to right sequence.

Solved Exercise Problem:

Simplify `4+6-:3xx2`

  • `8`
  • `8`
  • `5`

The answer is "`8`".

The division and multiplication are higher in precedence over addition. so `6-:3xx2` is to be simplified first.

In that, the division and multiplication are of same precedence, so it is simplified from left to right.

`4+6-:3xx2`

`=4+2xx2`

`=4+4`

`=8`.

Solved Exercise Problem:

Simplify `10-3-2xx3`.

  • `1`
  • `1`
  • `15`

The answer is "`1`". The multiplication is higher in precedence over subtraction and so `2xx3` is to be simplified first. Then the two subtraction are in the same precedence level and so they are simplified in the left to right sequence.

`10-3-2xx3`

`=10-3-6`

`=7-6`

`=1`

                            
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