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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   

Welcome to nubtrek.

The content is presented in small-focused learning units to enable you to
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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

User Guide    

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

User Guide    

jogger provides the complete mathematical definition of the concepts.

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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 Equations


 »  numerical equation is a statement equating two numerical expressions.

    →  eg: `2+4-1 = 5`
Note that `2+4-1` is evaluated to `6-1` which equals `5`.

    →  eg: `4xx3-7 = 2+4-1`
Note that both sides can be evaluated to `5`

Numerical equations are not studied in detail, as the arithmetic can be performed to a number as result.


 »  Algebraic Equation

    →  a statement equating one algebraic expression to a numerical expression. eg: `2x+7=9`

    →  OR a statement equating two algebraic expressions. eg: `3x-1 = 7-x`

Introduction to Equations

plain and simple summary

nub

plain and simple summary

nub

dummy

Algebraic equation is a statement that two quantities, represented with one or more variables, are equal.

simple steps to build the foundation

trek

simple steps to build the foundation

trek

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In this page, algebraic equation is introduced as a statement of two algebraic expressions, or a statement of equating an algebraic expression to a number.


Keep tapping on the content to continue learning.
Starting on learning "Introduction to Equations". ;; In this page, algebraic equation is introduced as a statement of two algebraic expressions, or a statement of equating an algebraic expression to a number.

Numerical equation is a statement equating two numerical expressions.

    →  eg: `2+4-1 = 5`
Note that `2+4-1` is evaluated to `6-1` which equals `5`.

    →  eg: `4xx3-7 = 2+4-1`
Note that both sides can be evaluated to `5`

Numerical equations are not studied in detail, as the arithmetic can be performed to a number as result. Connecting Numerical equations to Algebraic equation helps to understand.

In this pattern of squares using crayons, if the number of squares in a row is `x`, the number of crayons forming the squares `=3x+1`. square using crayons one row Someone used 22 crayons to create such a pattern. How many squares will be made?

  • given number of crayons, the number of squares cannot be calculated
  • equate the number of crayons to the algebraic expression

The answer is 'equate the number of crayons to the algebraic expression'. This is explained in the next page.

The number of crayons forming `x` squares `=3x+1`. Someone used `22` crayons to create a similar pattern. square using crayons one row The question provides that the "number of crayons used `= 22`"

We know that "the number of crayons forming squares `= 3x+1`"

Both the above are number of crayons and so can be equated.

`3x+1=22`.

This is an example of algebraic equation.

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

  • an imaginary line along the center of the Earth
  • a statement that two quantities are equal

The answer is 'a statement that two quantities are equal'.

What is the word or phrase used to refer a statement that two quantities are equal?

  • Practice Saying the Answer

The answer is 'algebraic equation'.

An algebraic equation has the following.

 •  an equal symbol `=`

 •  a quantity on the left hand side (LHS) of the equal symbol.

 •  another quantity on the right hand side (RHS) of the equal symbol.

 •  One of the quantities on LHS or RHS is an algebraic expression.

 •  The other is in the form of algebraic expression or numerical expression or a number.

What is the terms used to refer either side of equation?

  • Practice Saying the Answer

The answer is 'left hand side (LHS) and right hand side (RHS)'.

comprehensive information for quick review

Jogger

comprehensive information for quick review

Jogger

dummy

Algebraic Equation : A statement equating two expressions is an algebraic equation.

`text(expression1) = text(expression2)`

expression1 is the left hand side of the equation.

expression2 is the right hand side of the equation.



           

practice questions to master the knowledge

Exercise

practice questions to master the knowledge

Exercise

your progress details

Progress

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Progress

Numerical equation is a statement equating two numerical expressions. Some examples are given. Numerical equations are not studied in detail, as the arithmetic can be performed to a number as result. Connecting Numerical equations to Algebraic equation helps to understand.
In this pattern of squares using crayons, if the number of squares in a row is x, the number of crayons forming the squares equals 3 x + 1. Someone used 22 crayons to create such a pattern. How many squares will be made?
given;cannot;calculated;squares
given number of crayons, the number of squares cannot be calculated
equate;algebraic
equate the number of crayons to the algebraic expression
The answer is 'equate the number of crayons to the algebraic expression'. This is explained in the next page.
The number of crayons forming x squares = 3 x+1. Someone used 22 crayons to create a similar pattern.;; the question provides that the number of crayons used = 22 ;; We know that the number of crayons forming squares equals 3 x + 1. ;; Both the above are number of crayons and so can be equated. 3x + 1 = 22. This is an example of algebraic equation.
Which of the following is a meaning for the word 'equation'?
imaginary;line;along;earth
an imaginary line along the center of the Earth
statement;that;2;equal
a statement that two quantities are equal
The answer is 'a statement that two quantities are equal'.
What is the word or phrase used to refer a statement that two quantities are equal?
equation
The answer is 'algebraic equation'.
Algebraic equation is a statement that two quantities, represented with one or more variables, are equal.
An algebraic equation has the following. An equal symbol equals. ;; a quantity on the left hand side - called LHS - of the equal symbol. ;; another quantity on the right hand side - called RHS - of the equal symbol. ;; One of the quantities on LHS or RHS is an algebraic expression. ;; The other is in the form of algebraic expression or numerical expression or a number.
What is the terms used to refer either side of equation?
left;right;hand;side
The answer is 'left hand side (LHS) and right hand side (RHS)'.
Algebraic Equation: A statement equating two expressions is an algebraic equation. Example format is expression 1 equals expression 2. Expression 1 is the left hand side of the equation. Expression 2 is the right hand side of the equation.

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