Mathematical+Reflections,+p.+52+0910

April 26, 2010 CS Notes: None __ Mathematical Reflections #3 __ Q1. Explain how the distributive and commutative property can be used to write equivalent expressions. Use examples to illustrate your explanations. A1. The distributive property is a mathematical property, which is used to rewrite expressions involving addition and multiplication. If an expression is written in factored form, we can use the distributive property to write the expression in expanded form. If an expression is written as a factor multiplied by a sum, we can use the distributive property to multiply each term in parenthesis to get an equivalent expression. For example: § 4(5+ x ) = 4(5)+4( x )=20+4 x  Another important mathematic property is the commutative property. It states that the order in which quantities are added or multiplied does not mater. Thus, addition and multiplication are said to be commutative. For example: § 2x + 3x = 3x+ 2x = 5x § 5*6x = 6x*5 = 30x Q2.a Give an example of a real-life situation that can be represented by at least two equivalent expressions. Explain how each expression represents the situation. A2.a An expression the represents a real life situation is 2(a+a) or 2a+2a. The situation would be: There were 2 boys. One of the boys ate two apples and the other ate two apples as well. How many apples eaten in total? The explanation: the 2 in the expression represents the number of fruits eaten and the two a’s in the parenthesis represent the two boys. Whereas in the other expression, 2a is the number of fruits eaten by each boy. Q2.b Use the distributive and commutative properties to show that the expressions are equivalent. A2.b **__ Distributive method __** 2(a+a) 2(a) + 2(a) 2a+2a 4a 2(a+a) 2(a) + 2(a) 2a+2a (using commutative property and swapping places, we get,) 2a+2a 4a In this investigation I used the distributive and commutative properties to write equivalent expressions. I also learned how to use expressions in daily life
 * __ Big Idea __**** : Equations can be used to model real things. **
 * __ Essential Question __**** : What are the distributive and commutative properties used for? **
 * __ Commutative method __**
 * __ Summary: __**