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Chapter 1 – Introduction to Algebra
Name _____________________________
Section 1.1 – Variables
pg. 1-5
Objective: To simplify numerical expressions and evaluate algebraic expressions.
Vocabulary words
Variable – a symbol used to represent one or more numbers
Variable expression – an expression that contains numbers, operations and variables
Simplify each expression.
Evaluate each expression when
and
. Chapter 1 – Introduction to Algebra
Section 1.2 – Grouping Symbols
pg. 6-9
Objective: To simplify expressions with and without grouping symbols
Vocabulary words:
Grouping symbols – a device, such as a pair of parentheses, used to enclose an
expression that should be simplified first
Different types of grouping symbols
Parentheses
Brackets
[
] or
Simplify.
Evaluate if
,
, and
.
Fraction Bar
Evaluate the expression for the given values of the given variable.
Perimeter of a rectangle:
If
and
Chapter 1 – Introduction to Algebra
Section 1.3 – Equations
pg. 10-13
Objective: To find solution sets of equations over a given domain.
Vocabulary words:
Open sentences – sentences containing variables
Domain – the given set of numbers that a variable may represent
Root or solution – a value of the variable that turns an open sentence into a true
statement
Solution set – the set of all solutions of an open sentence
Solve each equation if the domain of x is
Solve over the domain
.
.
Suppose the domain for each equation is the set of all real numbers. Determine the number
of solutions for each equation. Write “none”, “one”, or “more than one”. For those equations
with one solution, determine what the solution is.
Chapter 1 – Introduction to Algebra
Section 1.4 – Translating Words into Symbols
pg. 14-18
Objective: To translate phrases into variable expressions.
Addition
Subtraction
Multiplication
Division
Phrase
The sum of 8 and x
A number increased by 7
5 more than a number
The difference between a number and 4
A number decreased by 8
**5 less than a number **
6 minus a number
The product of 4 and a number
Seven times a number
Translation
One third of a number
The quotient of a number and 8
A number divided by 10
**Less than is special! Any time you see this phrase, you have to flip flop the numbers. So “5
less than a number” translates to
and not
**
Translate each phrase into a variable expression. Let the letter n stand for the number.
Kip has n books. Use n to write an expression for each of the following numbers.
a. The number of books kip has after he buys 3 more books.
b. The number of book sKip has after he gives away 3 books.
Chapter 1 – Introduction to Algebra
Section 1.5 – Translating Sentences into Equations
pg. 19-22
Objective: To translate word sentences into equations.
Translate each sentence into an equation.
Use the figure and the information below it to write an equation.
6
10
5
x
x
Perimeter = 20
x
6
Perimeter = 22
Chapter 1 – Introduction to Algebra
Section 1.6 – Translating Problems into Equations
pg. 23-26
Objective: To translate simple word problems into equations.
Suggested steps when writing an equation for a word problem:
1.
2.
3.
4.
5.
6.
7.
Read the entire problem.
Identify the question.
Find the important information.
Define your variable(s).
Write and solve an equation.
Answer in words.
Check your answer. Does it make sense?
Translate each problem into an equation.
Chapter 1 – Introduction to Algebra
Section 1.8 – Number Lines
pg. 31-35
Objective: To graph real numbers on a number line and to compare real numbers.
Vocabulary words:
Whole numbers – zero and all the positive integers {0, 1, 2, 3…}
Integers – the set whole numbers and their opposites {…-2, -1, 0, 1, 2…}
Real numbers – any number that is either positive, negative, or zero
Write a number to represent each situation. Then write the opposite of that situation and
write a number to represent it.
Graph the numbers
order from least to greatest.
on a number line. Then list them in
State two inequalities, on with > and one with <, for the coordinates of the points shown.
Complete using one of the symbols < or > to make a true statement.
Chapter 1 – Introduction to Algebra
Section 1.9 – Opposites and Absolute Values
pg. 36-39
Objective: To use opposites and absolute values.
Vocabulary words:
Opposite – two numbers that are the same distance from zero, but are on opposite
sides of the number line
Absolute value – a number’s distance from zero on a number line
**Absolute value is always, always, always positive!!!**
Name the opposite and the absolute value of each number.
Simplify.
Complete using one of the symbols >, <, or = to make a true statement.
Translate each statement into symbols.