Always, Sometimes, Never
A rational number is a real number.
Always True
((15)(2))/(1^2+2+2)
6
For all real numbers b, b*0=0
The Zero Property of Multiplication
One cell phone plan costs $39.93 per month. The first 500 minutes of usage are free. Each minute thereafter costs $0.35. For a bill of $69.70, how many minutes over 500 minutes was the cell phone in use?
The cell phone was used 85.057 minutes over.
n+m/2+5
; use m=10, and n=12
32
All integers are rational numbers.
Always True
(2^2+5)*9
81
For all real numbers x, x+0=x and x*1=x
The Identity Properties
The Library of Congress in Washington D.C. is the largest library in the world. It contains nearly 125 million items! The library adds about 10,000 items to its collection daily. How many days will it take the library to reach about 150 million items?
It will take 2500 days to reach 150 million items in the library.
(11)(a+10-c)
; use a=15, and c=14
121
Negative numbers are integers.
Sometimes True (Counter-example: -0.1)
8(5*11-7^2)
48
For all real numbers a, -1*a=-a
Multiplication Property of -1
Spectrum charges $24.95 a month for basic cable services and $6.95 a month for each additional premium channel. If Sami’s monthly bill is $45.80, how many premium channels is he receiving?
Sami is receiving 3 premium channels.
14+y+z2
; use y=10, and z=3
33
A whole number is an irrational number.
Never True
16/(14(7-6)-10)
4
Let a, b, and c be any real numbers.
a+b+c=c+a+b
c*b*a=b*a*c
Commutative Properties
Alicia and Travis are selling tickets for a school talent show. Bleacher seats cost $3.00 and floor seats cost $4.00. Alicia sells 30 bleacher seat tickets and 25 floor seat tickets. Travis sells 65 bleacher seat tickets. How much money have they collected for the talent show?
They have collected 385 dollars for the talent show.
2-(c-(a-7))
; use a=12, and c=6
1
Square root numbers are integers.
Sometimes True (Example:
sqrt4)
8x+3-(2x-3y)+7y
6x+3+10y
Let a, b, and c be any real numbers.
(a+b)+c=a+(b+c)
c*(b*a)=(c*b)*a
Associative Properties
The price of a computer dropped $34.95 each month for 7 consecutive months. If the starting price was $1450, what was the price after 7 months?
The price after 7 months is $1,205.35.
b2+ca
; use a=11, b=4, and c=12
148