# Arithmetic properties

May 29th, 2015
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The associative property-In addition and multiplication, terms may be arbitrarily associated with each other through the use of parentheses:The commutative property-In addition and multiplication, terms may be arbitrarily interchanged, or

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When solving age problems, you need to represent the following in terms of a variable:- the present ages of the people or things involved- the age, at the other specified time, of the people or things involvedThen, form an equation based on these representations.Here are some examples:--------------------------------------------------------------------------------Cary is 9 years older than Dan. In 7 years, the sum of their ages will equal 93.Find both of their ages now.x = Dan's age nowx + 9 = Cary's age now {Cary is 9 yrs older than Dan}x + 7 = Dan's age in 7 yearsx + 16 = Cary's age in 7 yearsx + 7 + x + 16 = 93 {in seven years the sum of their ages will be 93}2x + 23 = 93 {combined like terms}2x = 70 {subtracted 23 from both sides}x = 35 {divided both sides by 35}x + 9 = 44 {substituted 35, in for x, into x + 9}Dan is 35Cary is 44www.algebrahouse.com--------------------------------------------------------------------------------Fred is 4 times as old as his niece, Selma. Ten years from now,he will be twice as old as she will be. How old is each now?x = Selma's age now4x = Fred's age now {Fred is 4 times as old as Selma}

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