Rules and Properties

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by Dr. Osama M. Khaled last modified 2022-07-19T05:22:49+01:00

Rules and properties to understand in order to successfully solve an algebraic equation

Questions #: 13
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Pass Score: 80.0%
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Area equation is a clear manifestation of using variables

A = lw  (A is area, l is length, and w is width).

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Arithmetic operations for addition, subtraction, multiplication, and division are still used in algebraic equations

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Multiplication sign (x) is used in algebraic equations

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Raised dot and parantheses

We usually use a raised dot, but not parentheses, for multiplication in order not to confuse readers with symbol which is commonly used in Algebra

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In the notation 2b

The number 2 is an example of a constant because it does not change value

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The Commutative Property of Addition

Changing the order when adding does not affect the answer

a + b = b + a

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The Associative Property of Addition

Changing the grouping when adding does not affect the answer

(a + b) + c = a + (b + c)

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Addition Property of 0 (Identity Property of Addition)

When 0 is added to any number, the result is the same number

a + 0 = a                 or             0 + a = a 

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The Commutative Property of Multiplication

Changing the order when multiplying does not affect the answer

             ba = ab

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The Associative Property of Multiplication

Changing the grouping when multiplying does not affect the answer

(ab)c = a(bc)

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Multiplication Property of 0

The product of 0 and any number is 0

0 . a = 0       and         a . 0 = 0

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Multiplication Property of 1

The product of 1 and any number is that number

1 . a = a               and               a . 1 = a

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Division Properties

Any number divided by 1 is the number itself.  Any number (except 0) divided by itself is 1

a / 1 = a             and          a / a = 1        provided a ≠ 0

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