# Math Equations

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## Teaching Math Equations

An equation is a statement of equality.

When we write,  A = B,  we mean that A is equal to B. Since these letters represent numbers, we are saying, the magnitude of A is equal to the magnitude of B.

Example:     25  =  25

True enough, 25 does equal 25.  But, what is more important, is the operations we can perform to the equation, maintaining equality at all times, allowing us to "solve" for an unknown.

In this example A is 25, and B is 25.   (Note: A = B can be written B = A)

Addition:     say we add 10 to A.   Well, 25 + 10 is 35.  To maintain equality, we must also add 10 to B.

This equation becomes:    35  =  35

In other words, if we add 10 to A, we must ALSO add 10 to B, if we do not, our equation becomes  35 = 25,  which we know is incorrect, we would say 35 does not equal 25 and we would write this fact this way:  35 ≠  25.

Adding 10 to our equation ( A = B ) is shown:

A  +  10  =   B  +  10

Adding the same quantity to both sides of the equation maintains equality.

Subtraction:   suppose we subtract 5 from the equation 25 = 25. We'd have 25 - 5  which is 20.  To maintain equality, we must subtract 5 from both sides of the equation.

The equation then becomes:  20  =  20

Subtracting 5 from our equation ( A = B) is shown:

A  -  5  =   B  -  5

Subtracting the same quantity to both sides of the equation maintains equality.

Multiplication:   Let's multiple by 3.  25 * 3 is 75.

The equation 25 = 25 then becomes:  75  =  75

This operation to our equation A = B is shown:

3 * A    =  3 * B

Multiplying the same quantity to both sides of the equation maintains equality.

Side note:  A student once remarked: "I can solve all my problems, just multiply the equation by 0 and all my problems vanish!"  True enough.

Division:   First of all, division by 0 is undefined, therefore we will not allow division by 0.  We will allow division by all numbers except 0.  (If we divide by a variable, we must also state that at that step, that variable cannot be 0.)

So, let's divide by 5.  25 divided by 5 is 5.

The equation 25 = 25 becomes 5 = 5

This operation to the equation A = B is shown:

A / 5   =  B / 5

Dividing the same non-zero quantity to both sides of the equation maintains equality.

Note:  many attempts using algebra to prove one number equals another number of different magnitude are done by dividing by the unknown and NOT considering the case when that unknown is 0.

So, IN GENERAL, whatever mathematical operation you do to one side of an equation, you must also do to the other side.

This is another FREE Equations PRINTABLE presented to you from the Math Concepts section ofK12math.com

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