Exercise 1 Page 29

The pilot charges 25 dollars for each passenger, without regard to whether the passenger is an adult or a child. This means that to find the total amount of money they pilot will charge, we need to multiply $25 by the total number of passengers. $25 (12adults+15children) 25(12+15) To evaluate this function, we will start by applying the Distributive Property.

25(12+15)

Distr

Distribute 25

25 * 12 + 25 * 15

Multiply

Multiply

300 + 375

AddTerms

Add terms

675

Altogether, the passengers will pay 675 dollars.

Extra

Other Important Properties of Operations

When we want to manipulate an expression for any reason, there are a number of a properties that we can use to legally rewrite it. Besides the Distributive Property, there are four main properties to consider.

Properties of Operations
Property	Algebraic Rule	Explanation
Associative Property of Addition	( a+ b)+ c= a+( b+ c)	The way that three or more terms are grouped when being added does not change the sum.
Commutative Property of Addition	a+ b= b+ a	The order does not matter when adding terms.
Associative Property of Multiplication	( a* b)* c= a*( b* c)	The way that three or more terms are grouped when being multiplied does not change the product.
Commutative Property of Multiplication	a* b = b* a	The order does not matter when multiplying terms.