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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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User Guide   

To make best use of nubtrek, understand what is available.

nubtrek is designed to explain mathematics and science for young readers. Every topic consists of four sections.

  nub,

  trek,

  jogger,

  exercise.

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User Guide    

nub is the simple explanation of the concept.

This captures the small-core of concept in simple-plain English. The objective is to make the learner to think about. continue

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trek is the step by step exploration of the concept.

Trekking is bit hard, requiring one to sweat and exert. The benefits of taking the steps are awesome. In the trek, concepts are explained with exploratory questions and your thinking process is honed step by step. continue

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jogger provides the complete mathematical definition of the concepts.

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User Guide    

exercise provides practice problems to become fluent in the concepts.

This part does not have much content as of now. Over time, when resources are available, this section will have curated and exam-prep focused questions to test your knowledge. continue

summary of this topic

Algebra: Variables and Expressions

Algebra: Variables and Expressions

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Introduction to Variables


 »  variable means "that varies or changes in value".
    →  eg: number of cars `= x`
    →  in this `x` is a variable.


 »  variable is a quantity represented with a symbol
    →  eg: number of cars `= x`
    →  If there are `2` cars, then `x=2`
    →  If there are `400` cars, then `x=400`


 »  variables are used in expressions
    →  eg: number of wheels in `x` cars `= 4x`
    →  If there are `2` cars, then number of wheels `=4 xx 2 = 8`

Introduction to Variables

plain and simple summary

nub

plain and simple summary

nub

dummy

a variable is a quantity that can assume different numerical values.

simple steps to build the foundation

trek

simple steps to build the foundation

trek

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In this page, it is explained that a variable is a symbol that represents a number.


Keep tapping on the content to continue learning.
Starting on learning "Introduction to Variables". ;; In this page, it is explained that a variable is a symbol that represents a number.

How many yellow flowers are shown in the figure?one flower with 8 petals

  • `1`
  • `2`

The answer is '`1`'

How many petals does the yellow flower have?one flower with 8 petals

  • `4`
  • `8`

The answer is '`8`'

How many yellow flowers are shown in the figure?four flower with 8 petals

  • `1`
  • `4`

The answer is '`4`'

How many petals do all the four yellow flowers have?four flower with 8 petals

  • `8xx4`
  • `8`

The answer is '`8xx4`'

If a person has `2` yellow flowers of the kind shown in the figure, how many petals do those `2` flowers have?one flower with 8 petals

  • `8`
  • `8 xx 2 = 16`

The answer is '`8xx2= 16`'

A person has `x` yellow flowers of the kind shown in the figure. The `x` can be any number.

The number of petals from `x` flowers is `8x`.

 •  if `x` is `2` then the number of petals is `8 xx 2 = 16`.

 •  if `x` is `6` then the number of petals is `8xx6 = 48`

 •  etc. one flower with 8 petals In this, the number of flowers is considered as a symbol `x` and the number of petals is derived as a formula `8x`.

The letter `x` in the formula is called a variable.

How many cherry flowers are shown in the figure?one flower with 5 petals

  • `1`
  • `2`

The answer is '`1`'

How many petals does the cherry flower have?one flower with 5 petals

  • `4`
  • `5`

The answer is '`5`'

How many cherry flowers are shown in the figure?3 flower with 5 petals

  • `1`
  • `3`

The answer is '`3`'

How many petals do all the three cherry flowers have?3 flower with 5 petals

  • `5xx3`
  • `5`

The answer is '`5xx3`'

If a person has `y` cherry flowers of the kind shown in the figure, how many petals do those `y` flowers have?one flower with 5 petals

  • `5`
  • `5y`

The answer is '`5y`'.

If a person has `2` yellow blossom flowers and `3` cherry flowers of the kinds shown in the figure, how many petals do all the flowers have?two different flowers

  • `8+5 = 13`
  • `8xx2 + 5xx3`

The answer is '`8xx2 + 5xx3`'

If a person has `x` yellow blossom flowers and `y` cherry flowers of the kinds shown in the figure, how many petals do all the flowers have?two different flowers

  • `8+5 = 13`
  • `8xx x + 5xx y`

The answer is '`8xx x + 5xx y`'. `x` and `y` are two variables.

In the examples, it is clearly given that

 •  an unknown number can be represented using a symbol. eg: `x` flowers.

 •  a symbol, which is used in place of a number, can take a value based on the problem. eg: the number of flowers is taken as `x` and in a particular basket the number of flowers is `3`; then `x=3` for that basket.

The symbol is called a variable.

Which of the following is a meaning for the word 'variable'?

  • that varies or changes in value
  • that easily gets angry

The answer is 'that varies or changes in value'.

What is the term used to refer to quantities represented with a letter?

  • Practice Saying the Answer

The answer is 'variable'.

comprehensive information for quick review

Jogger

comprehensive information for quick review

Jogger

dummy

Variable: is a representation of a numerical quantity with a letter or a symbol.
example: number of dogs `x` and number of cats `y`.



           

practice questions to master the knowledge

Exercise

practice questions to master the knowledge

Exercise

How many legs will a group of dogs have?dog Note: The number of dogs in the group is not given, so take the number of dogs as a variable.

  • `4`
  • if the group has x dogs, the number of legs ` = 4x`

The answer is 'if the group has x dogs, the number of legs ` = 4x`'

your progress details

Progress

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Progress

How many yellow flowers are shown in the figure?
1
1
2
2
The answer is ' 1 '
How many petals does the yellow flower have?
4
4
8
8
The answer is ' 8 '
How many yellow flowers are shown in the figure?
1
1
4
4
The answer is ' 4 '
How many petals do all the four yellow flowers have?
4
8 multiplied 4
8
8
The answer is 8 multiplied 4
If a person has 2 yellow flowers of the kind shown in the figure, how many petals do those 2 flowers have?
8
8
2;times;equals;16
8 times 2 equals 16
The answer is "8 times 2 equals 16"
A person has x yellow flowers of the kind shown in the figure. The x can be any number. The number of petals from x flowers is 8 x. ;; if x is 2, then the number of petals is 8 times 2 equals 16. ;; if x is 6, then the number of petals is 8 times 6 equals 48. ;; In this the number of flowers is considered as a symbol x and the number of petals is derived as a formula 8x. The letter x in the formula is called a variable.
How many cherry flowers are shown in the figure?
1
1
2
2
The answer is ' 1 '
How many petals does the cherry flower have?
4
4
5
5
The answer is ' 5 '
How many cherry flowers are shown in the figure?
1
1
3
3
The answer is ' 3 '
How many petals do all the three cherry flowers have?
3
5 multiplied 3
5
5
The answer is 5 multiplied 3
If a person has y cherry flowers of the kind shown in the figure, how many petals do those y flowers have?
5
5
5;times;why;y
5 times y
The answer is "5 times y"
If a person has 2 yellow blossom flowers and 3 cherry flowers of the kinds shown in the figure, how many petals do all the flowers have?
13
8 plus 5 = 13
2;3;31;times
8 times 2 plus 5 times 3 equals 31
The answer is "8 times 2 plus 5 times 3 equals 31"
If a person has x yellow blossom flowers and y cherry flowers of the kinds shown in the figure, how many petals do all the flowers have?
13
8 plus 5 = 13
x;why;y;times
8 times x plus 5 times y
The answer is "8 times x plus 5 times y". x and y are two variables.
In the examples, it is clearly given that ; an unknown number can be represented using a symbol. Example x flowers. ;; a symbol, which is used in place of a number, can take a value based on the problem. For example, the number of flowers is taken as x and in a particular basket the number of flowers is 3; then x equals 3 for that basket. ;; The symbol is called a variable.
Which of the following is a meaning for the word 'variable'?
varies;changes;in;value
that varies or changes in value
easily;gets;angry
that easily gets angry
The answer is 'that varies or changes in value'.
What is the term used to refer to quantities represented with a letter?
variable
The answer is 'variable'.
a variable is a quantity that can assume different numerical values.
Variable is a representation of a numerical quantity with a letter or a symbol.
How many legs will a group of dogs have?
4
4
2
if the group has x dogs, the number of legs equals 4 x
The answer is "if the group has x dogs, the number of legs equals 4 x"

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