Download Ch 1 – The Language of Algebra 1.1 – Writing Expressions and

Ch 1 – The Language of Algebra
1.1 – Writing Expressions and Equations
Variable:
Algebraic Expression:
Numerical Expression:
Multiplication:
Division:
Words for
Addition:
Subtraction:
Multiplication:
Division:
Example: Write an algebraic expression for each verbal expression.
The sum of p and 12
The product of k and q
26 decreased by w
4 more than 8 times k
Example: A python eats 4 pounds of meat each month.
Write a numerical expression to represent the amount it eats in 5 months.
Write an algebraic expression to represent the amount it eats in d months.
Example: Write a verbal expression for each algebraic expression.
37 + s
5(b – 3)
15v
r
t
d
Equation:
Example: Write an equation for each sentence.
The quotient of t and 8 equals 20.
Seven less than three times g is 31.
A number k divided by 4 is equal to 18.
Example: Write a sentence for each equation.
j + 4 = 21
3z – 12 = 11
4b – 5 = 3
1-2: Order of Operations
Order of Operations:
1.
2.
3.
Example: Find the value of each expression.
14  10  2
12  3  5  4
4  (6  7)
6  12
5(3)  13
7  4  7 3
Example: As a 16-year old, Trent Eisenberg ran his own consulting company called F1 Computer. Suppose
he charged a flat fee of $50, plus $25 per hour. One day, Trent worked 1 hour for each of 2 new customers.
Find the value of the expression 2(50) + 2(25) to find the total amount of money he earned.
Substitution Property:
Reflexive Property:
Symmetric Property:
Transitive Property:
Example: Name the property shown by each statement.
If k = 7, then k + 3 = 7 + 3
If a + 4 = 9, then 9 = a + 4
7–c=7–c
If 10 – 3 = 4 + 3 and 4 + 3 = 7, then 10 – 3 = 7
Additive Identity:
Multiplicative Identity:
Multiplicative Property of Zero:
Example: Find the value of [25 + 8(12 – 11) ÷ 11. Identify the property used in each step.
Example: Find the value of (22 – 15) ÷ 7 · 9. Identify the properties used.
Evaluating:
Example: Evaluate each expression if x = 4 and y = 3.
xy + 8
(2y + 10) ÷ x
Example: Evaluate each expression if m = 8 and p = 2.
6·p–m÷p
[m + 2(3 + p)] ÷ 2
1-3: Commutative and Associative Properties
Commutative Property of Addition:
Commutative Property of Multiplication:
Associative Property of Addition:
Associative Property of Multiplication:
Example: Name the property shown by each statement.
8 + (3 + 4) = (3 + 4) + 8
7 · (8 · k) = (7 · 8) · k
4 · 11 · 2 = 11 · 4 · 2
(n + 12) + 5 = n + (12 + 5)
Simplify:
Example: Simplify the expression (4 · m) · 9. Identify the properties used in each step.
Example: Simplify the expression 7 + 2a + 6 + 9. Identify the properties used in each step.
Example: The volume of a box can be found using the expression l x w x
h, where l is the length, w is the width, and h is the height. Find the
volume of a box whose length is 20 inches, width is 12 inches, and height
is 3 inches.
Whole Numbers:
Closure Property of Whole Numbers:
Counterexample:
Example: State whether the statement subtraction of whole numbers is commutative is true or false. If false,
provide a counterexample.
1-4: Distributive Property
Distributive Property:
Example: Simplify each expression.
5(2 + m)
3(4x + 2)
(1 + 3t)9
Term:
Coefficient:
Like Terms:
Equivalent Expressions:
Simplest Form:
Example: Simplify each expression.
8p – 5p
10k + 6m – 5k + 2m
5st + 2st
6 + y + 3z + 4y
Example: Area of a rectangle:
One wing of a building contains three rooms that are identical in size. The floor
of each room is 20 meters in length and width. Find the total floor area of the
wing.
1-5: A Plan for Problem Solving
Problem-Solving Plan:
1.
2.
3.
4.
Formula:
Simple Interest Formula:
Example: Suppose you deposit $350 into an account that pays 2% interest. How much money would ou
have in the account after five years?
Example: How many ways can you make 50¢ using quarters, dimes, and nickels?
Properties of Read Numbers
The following properties are true for any numbers a, b, and c.
Property
Addition
Multiplication
Commutative
Associative
Identity
Zero
Distributive
Substitution
1-6: Collecting Data
Data:
Experiments:
Observational Studies:
Sampling:
Population:
Sample:
Sampling Criteria:
Example: One hundred cable-television subscribers are surveyed to find how much time the average
American spends reading. Is this a good sample? Explain.
Example: Two hundred students at a school basketball game are surveyed to find the students’ favorite
sport. Is this a good sample? Explain.
Example: Every other person leaving a supermarket is asked to name their favorite soap. Is this a good
sample? Explain.
Frequency Table:
Example: Make a frequency table to organize the data in the chart.
Cumulative Frequency Table:
Example: The owners of a bookstore specializing in travel books are looking for a
new location. They counted the number of people who passed by the proposed
location during one afternoon. The frequency table shows the results of their
sampling.
Which group of people passed by the location most frequently?
Is this a good location for the bookstore? Explain.
1-7: Statistics: Displaying and Interpreting Data
Line Graph:
Example: Construct a line graph of the data given in the table. Use the graph to predict the percent of the
labor force in farming in the year 2010.
Histogram:
Example: The table shows the number of people in different age groups who
entered a new store during the first hour of its grand opening. Construct a
histogram of the data.
Cumulative Histograms:
Example: Construct a cumulative frequency histogram of the data.
Stem-and-Leaf Plots:
Example: The table shows the record high temperatures for several states.
Make a stem-and-leaf plot of the temperatures.