Lesson 1–2

Example 1  Classify Numbers
Name the sets of numbers to which each number belongs.
a.	–	rationals (Q) and reals (R)	
b.	97	naturals (N), wholes (W), integers (Z), rationals (Q), and reals (R)	
c.	2π	irrationals (I) and reals (R)	
d.	0.5 
	rationals (Q) and reals (R)
The bar over the 6 indicates that the digit repeats forever.	
e.	
 = 19	naturals (N), wholes (W), integers (Z), rationals (Q), and reals (R)	

Example 2  Identify Properties of Real Numbers
Name the property illustrated by 6 + (–3 + 7) = [6 + (–3)] + 7
Associative Property of Addition

The Associative Property says that the way you group three numbers when adding does not change the sum.

Example 3  Additive and Multiplicative Inverse
Identify the additive inverse and multiplicative inverse for –3.75.

Since –3.75 + 3.75 = 0, the additive inverse of –3.75 is 3.75.
Since -3.75 = - and = 1, the multiplicative inverse of –3.75 is –.

Example 4  Use the Distributive Property to Solve a Problem
ENTERTAINMENT  A drama club presented a play for three consecutive nights. There were three different prices for tickets: $2.50 for elementary students, $4.50 for high school students, and $6.50 for adults. The table shows the number of each type of ticket sold each evening. How much did the drama club collect from ticket sales?

	Thursday	Friday	Saturday	
Elementary students	17	32	41	
High school students	50	96	124	
Adults	83	136	186	

There are two ways to find the total amount of money collected from ticket sales.

Method 1
Find the total amount collected for each night by multiplying the ticket sales in each category for that night by the ticket price. Then add the sales for the three nights.
T	=	[17(2.50) + 50(4.50) + 83(6.50)] + [32(2.50) + 96(4.50) +136(6.50)] + [41(2.50) + 124(4.50) + 186(6.50)]	
	=	(807) + (1396) + (1869.50)	
	=	4072.50	

Method 2
Add to find the total number of each type of ticket sold for the three nights. Multiply by the ticket price for each type of ticket. Then add the results.
T	=	2.50[17 + 32 + 41] + 4.50[50 + 96 + 124] + 6.50[83 + 136 + 186]	
	=	2.50(90) + 4.50(270) + 6.50(405)	
	=	225 + 1215 + 2632.50	
	=	4072.50	

The drama club collected $4072.50 from the ticket sales for all three nights.

Notice that both methods result in the same answer. The two methods illustrate the Distributive Property.

Example 5  Simplify an Expression
Simplify 3(a – 7b) – 6(2b – 8a)
3(a – 7b) – 6(2b – 8a)
	=	3(a) + 3(–7b) – 6(2b) – 6(–8a)	Distributive Property	
	=	3a + (–21b) – 12b  + 48a	Multiply.	
	=	3a + 48a – 21b –12b	Commutative Property (+)	
	=	(3 + 48)a + (–21 – 12)b	Distributive Property	
	=	51a – 33b	Simplify.