Rules and Properties

by Osama M. Khaled last modified 2022-06-24T23:08:48+01:00

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

Questions #: 13
Pass Score: 80.0%

    Area equation is a clear manifestation of using variables

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

    True
    False

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

    True
    False

    Multiplication sign (x) is used in algebraic equations

    True
    False

    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

    True
    False

    In the notation 2b

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

    True
    False

    The Commutative Property of Addition

    Changing the order when adding does not affect the answer

    a + b = b + a

    True
    False

    The Associative Property of Addition

    Changing the grouping when adding does not affect the answer

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

    True
    False

    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 

    True
    False

    The Commutative Property of Multiplication

    Changing the order when multiplying does not affect the answer

                 ba = ab

    True
    False

    The Associative Property of Multiplication

    Changing the grouping when multiplying does not affect the answer

    (ab)c = a(bc)

    True
    False

    Multiplication Property of 0

    The product of 0 and any number is 0

    0 . a = 0       and         a . 0 = 0

    True
    False

    Multiplication Property of 1

    The product of 1 and any number is that number

    1 . a = a               and               a . 1 = a

    True
    False

    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

    True
    False