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Real Numbers
Algebra 5
Casa Grande Union High School
MATHO
TERMS
On the MATHO card from the center table, fill in each blank (in pen) with one of the
terms below. Do not use the terms more than once. Fill in all blanks.

<
>
Absolute value
Add
Associative
Binomial
Coefficient
Commutative
Composite Number
Constant
Degree
Denominator
Distance
Distributive
Exponent
Factors
Multiply
Negative
Nonterminating
Numerator
Polynomial
Positive
Prime
Rational
Root
Scientific
Subtract
Terminating
Terms
Trinomial
Variable
MATHO Clues
Parts of an algebraic expression.
3x2 + 5x + 2 has 3 of these
The number in front of a variable
The value that changes, usually represented
by a letter
Infinity Symbol
The value indicating the number of times a
base is multiplied. In 35, 5 is the ___.
Greater Than Symbol
MATHO Clues
Radical symbol
The top number in a fraction
The bottom number in a fraction
A number that can be written as a
fraction or ratio
A polynomial with 3 terms
To simplify (a5)6, you ___ 5 and 6.
MATHO Clues
The distance a number is from 0
The magnitude or difference in values
Property shown: 3 + a = a + 3
Property shown: (a + b) + c = a + (b + c)
8 x 105 is called ____ notation
Property shown:
a(b + c) = ab + ac
8
a
To simplify a 3 , you ____ the exponents.
Absolute value is always what type of number?
MATHO Clues
An integer that has exactly 2 positive factors: itself and
1.
An integer that has more than 2 positive factors.
A polynomial with 2 terms.
To simplify a5 * a6, you ___ 5 and 6.
1
x
What type of exponent (positive or negative) is x to turn 5 into 5 ?
A decimal that ends, such as 3.571
The greatest exponent is the ___ of the polynomial.
A decimal that continues to infinity, such as 5.333…
A polynomial with many terms
MATHO Clues
Less than symbol
8 is the square _____ of 64
2 and 3 are ____ of 6…another word for divisor
Real Numbers
What is a real number?
What is a rational number?
What is an irrational number?
Rational, Irrational or Neither?
5
-½
¾
0.17
Square root of 15
3i
|7.3|
Square of 15
|-4.25|
Square root of 7
3.25
Square root of 16
-i
|85|*|32|
Absolute Value
You’re at the Florence Boulevard exit
off I-10 and travel to the Pinal exit.
How far did you travel?
Define absolute value.
Evaluate.
|10|
|-5|
|5 – 8|
-|5|
-|-15|
|0|
|4 - |
-3|4|
2|33|
|-1| - |-2|
-5/|-5|
|-1/2|
-|-7|
-(-6)
Interval Notation
You go to the store. What is the
amount of money (interval) that you
must have to purchase a $15 gift for
your teacher?
You have a checking account. What is
the amount of money (interval)
possible for your current balance for
an account in good standing?
Bounded Intervals
Notation
[a,b]
Interval Type
closed
Inequality
a<x<b
(a,b)
open
a
x
b
[a,b)
half-open
a
x
b
a
x
b
(a,b]
half-open
Graph
[
]
(
)
Unbounded Intervals
from here to infinity…
Notation
Interval Type
Inequality
[a,)
half-open
x>a
(a, )
open
x>a
(- , b]
half-open
x b
(- , b)
(- ,  )
half-open
entire real line
x b
Graph
Words to Symbols
c is at most 2
You have to be at least 18 to vote.
F is between 3 and 7
I need at least $5 to buy lunch.
I’m leaving at 6 and can’t stay out past
12 midnight.
m is nonnegative
The legal driving age is Arizona
Algebraic Expressions
An algebraic expression is a collection of
letters (called ____________) and real
numbers (called __________) combined
using the operations of __________,
__________, _______, __________, and
____________.
3x + 5 versus 3x + 5 = 187
Identify:
terms
coefficients constant variable
Evaluate Algebraic Expressions
4x – 6 for x = -1
9 – 7x for x = 2
6x + x2 for x = ½
f(2) given f(x) = 3x
g(-1) given g(m) = m2 + 2m – 5
m(0) given m(t) = 5t2 + 3t + 7
Exercises
Describe the subset of real numbers
represented by the inequality and sketch on
a number line.
1. x < 5
6. -5 < h < -3
2. -3 < m < 7
7. 4 < y < 5
3. 0 < p < 17
8. x is negative
4. All real numbers 9. y is no more than 5
5. x > -2
10. z is at least -6
Evaluate the expression.
11.
12.
13.
14.
15.
16.
|-15|
|3 - |
2|33|
-5|- 9|
|-3| - |-5|
-|16.25| + 20
17. f + 9 for f = 15
18. 2(u – 7) for u = 5
19. n  (-3) for n = 12
m 1
for m  2
20.
m  (3  1)
Assignment
Pg. 10-12: 19-25(odd) 42-66 (x3),84,
85, 97-100