CHAPTER 1 Summary^77
5.Anintegeris
A.a positive or negative number
B.a natural number, its opposite, or
zero
C.any number that can be graphed
on a number line
D.the quotient of two numbers.
6.Theabsolute valueof a number is
A.the graph of the number
B.the reciprocal of the number
C.the opposite of the number
D.the distance between 0 and the
number on a number line.
7.Atermis
A.a numerical factor
B.a number, a variable, or a product
or quotient of numbers and
variables raised to powers
C.one of several variables with the
same exponentsD.a sum of numbers and variables
raised to powers.
8.Anumerical coefficientis
A.the numerical factor of the
variable(s) in a term
B.the number of terms in an
expression
C.a variable raised to a power
D.the variable factor in a term.ANSWERS
1.D;Example:Since the numbers 2 and 5 are factors of 10. Other factors of 10 are 1, and 10. 2.C;Examples:2, 3,
11, 41, 53 3.C;Example:In the number 3 is the exponent (or power), so 2 is a factor three times, and 4.A;Examples:
a,b,c 5.B;Examples: 0, 6 6.D;Examples: and 7.B;Examples:6, 8.A;Examples:The term 3 has numerical
coefficient 3, 8zhas numerical coefficient 8, and - 10 x^4 yhas numerical coefficient -10.
- 9, | 2 |= 2 |- 2 |= 2 2 x,- 4 ab^2
23 , 23 = 2 # 2 # 2 =8.
2 * 5 =10, -10,-5,-2,-1,1.1 Fractions
Operations with Fractions
Addition/Subtraction
1.Same denominator: Add/subtract the numerators
and keep the same denominator.
2.Different denominators: Find the LCD, and write
each fraction with this LCD. Then follow the
procedure above.
Multiplication: Multiply numerators and multiply
denominators.
Division: Multiply the first fraction by the reciprocal of
the second fraction.
Perform each operation.or6 is the LCD.oror 44
5
6
5
,
1
4
=
6
5
#^4
1=
24
5
,
1
1
9
4
3
#^5
6=
20
18
=
10
9
,
=
4 - 3
6
=
1
6
2
3
-
1
2
=
4
6
-
3
6
1
4
5
2
5
+
7
5
=
2 + 7
5
=
9
5
,
QUICK REVIEW
CONCEPTS EXAMPLES
1.2 Exponents, Order of Operations, and
Inequality
Order of Operations
Simplify within any parentheses or brackets and above
and below fraction bars first. Always follow this order.
Step 1 Apply all exponents.
Step 2 Do any multiplications or divisions from left to
right.
Step 3 Do any additions or subtractions from left to
right.
SimplifyApply the exponent.
Add inside the parentheses.
Multiply.
= 8 Subtract.= 36 - 28
= 36 - 4172
= 36 - 414 + 32
36 - 4122 + 32
36 - 4122 + 32.
1.3 Variables, Expressions, and Equations
Evaluate an expression with a variable by substituting a
given number for the variable.
Evaluate for andSubstitute.
Multiply. Apply the exponent.
= 22 Add.= 6 + 16
= 2132 + 1 - 422
2 x+y^22 x+y^2 x= 3 y=- 4.(continued)