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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.

In this lesson properties of equations are explained.

•  equations are statement of equality between two expressions

•  the statement of equality remains unchanged when the expressions are modified per PEMA / CADI

•  the statement of equality remains unchanged for arithmetics between two equations

It is very important to go through this once to understand in-equalities in algebra.

click on the content to continue..

What is an equation?

• statement of two quantities being equal
• statement of two quantities being equal
• an imaginary line between north and south pole

The answer is "statement of two quantities being equal".

Consider the equation 2+3 = 11//2 - 0.25xx2.

The left hand side of the equation is 2+3.

The right hand side of the equation is 11//2 - 0.25xx2.

The equation 2+3 = 11//2 - 0.25xx2 states that the left hand side equals the right hand side.

Consider the equation 2+3 = 11//2 - 0.25xx2.

Can the left hand side be modified without affecting the statement of equality?

• Yes, the left hand side is a numerical expression which can be modified as per PEMA Precedence / CADI Laws and Properties of Arithmetics
• Yes, the left hand side is a numerical expression which can be modified as per PEMA Precedence / CADI Laws and Properties of Arithmetics
• No, the left hand side is not a numerical expression.

The answer is "Yes, the left hand side is an numerical expression which can be modified".

Consider the equation 2+3 = 11//2 - 0.25xx2.

The left hand side 2+3 can be modified into 2+3-1+1 as per the additive identity and inverse properties. The value of the expression is not changed, so the equation holds true for 2+3-1+1 = 11//2 - 0.25xx2

Note: the left hand side 2+3 cannot be modified into 2+3+2, as this changes the value of the expression. That is, the equation will not be true with this modified expression.

Consider the two equations 2=3-1 and 4=2+2. Which of the following is true?

• The equations can be added into a new equation. 2+4 = (3-1) + (2+2)
• The equations can be multiplied into a new equation. 2xx4 = (3-1) xx (2+2)
• both the above
• both the above

The answer is "both the above"

Consider two equations 2=3-1 and 4=2+2. Multiple equations can be used to arrive at equations derived from them as per the following.

•  Equations can be added or subtracted. eg: 2+4 = (3-1) + (2+2)

•  Equations can be multiplied or divided (except for expressions evaluating to 0). eg: 2xx4 = (3-1) xx (2+2)

•  Equations can be taken exponent of (when expressions evaluate to integers). 2^4 = (3-1)^(2+2)

Numerical Equations :

An equation is a statement of equality between left hand side and right hand side.

Equation consists of expressions on the LHS and RHS. These expressions may be modified as per PEMA precedence / CADI Laws and Properties of Arithmetics.

Multiple equations can be used to arrive at equations derived from them as per the following.
•  Equations can be added or subtracted
•  Equations can be multiplied or divided (except for expressions evaluating to 0)
•  Equations can be taken exponent of (when expressions evaluate to integers)

Note 1: For expressions evaluating to fractions or decimals, the exponent should be worked out with details. This will be explained in higher classes.

Note 2 : The inverses of exponent, that is root and logarithm are explained in higher classes.

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