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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.

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Numerical Expressions

In this page, numerical expressions are introduced as statement of a number using multiple numbers and arithmetic operations between the multiple numbers.



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Addition represents "putting-together" two quantities.

Subtraction represents "taking away" part of a quantity.

Multiplication represents "repeated addition" of a quantity.

Division represents "splitting" a quantity into equal parts.

`3+2 = 5`

Addition is one of the arithmetic operations.

`5-2=3`

Subtraction is one of the arithmetic operations.

Subtraction `5-2=3` is the inverse of addition `3+2=5`.

The word "inverse" means: that is opposite or reverse of something

familiarize with the terminology
inverse

`3xx2=6`

Multiplication is one of the arithmetic operations.

Multiplication `3xx2` is repeated addition `3+3`, that is `3` repeated `2` times.

`6-:2=3`.

Division is one of the arithmetic operations.

Division `6-:2=3` is inverse of multiplication `3xx2 = 6`

Consider `2+4+3`. This can be evaluated to `9`.

This is an example of a numerical expression.

The word "expression" means: collection of numbers and arithmetic operations between them, which together represent a quantity.

familiarize with the terminology
expression

Numerical Expression : A numerical expression is a statement of a value using numbers and arithmetic operations between them.

eg: `3+4xx2-6-:3 is a numerical expression involving addition, multiplication, subtraction, and division.

The expression in the given example evaluates to `3+4xx2-6-:3 = 9`

`2xx4xx3` is an example of a numerical expression. It is evaluated to `24`.

`a+3x` is not a numerical expression. It is not entirely numbers and arithmetic operations. It has letters a and x.

Solved Exercise Problem:

Is `3-2` a numerical expression

  • Yes, the subtraction of two numbers
  • Yes, the subtraction of two numbers
  • No, simple subtraction is not a numerical expression

The answer is "Yes, the subtraction of two numbers"

Solved Exercise Problem:

Is `3+4-2+1` a numerical expression?

  • No, it has both addition and subtraction
  • Yes, addition and subtraction can be part of a numerical expression
  • Yes, addition and subtraction can be part of a numerical expression

The answer is "Yes, addition and subtraction can be part of an expression".

Solved Exercise Problem:

Is `3+4xx2-6-:3` a numerical expression?

  • No, as it has the addition, subtraction, multiplication, division
  • Yes, all arithmetic operations can be part of a numerical expression
  • Yes, all arithmetic operations can be part of a numerical expression

The answer is "Yes, all arithmetic operations can be part of a numerical expression"

Solved Exercise Problem:

is `3` a numerical expression?

  • No. 3 is only a number. Not a numerical expression
  • Yes. technically a number can also be considered a numerical expression
  • Yes. technically a number can also be considered a numerical expression

The answer is "Yes. technically a number can also be considered a numerical expression".

Consider `1+2` and `3xx1`. Note that when evaluated, both result in identical numerical value `1+2=3` and `3xx1 = 3`.

They are two different expressions, evaluating to equal values.

                            
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