Section 3.2 Solving Equations Having Like Terms
and Parentheses
The football team is playing in the championship
game. For the game, the cheerleaders want to buy a
banner that costs $47. They also want to buy small
items to give to the students in the sta
Section 4.1 Factors and Prime Factorization
You want to arrange 24 photos in a rectangular
shape box for your yearbook. We dont want any
more than 10 in a row. What are our options?
Write 24 as a product of two whole numbers in all
possible ways.
Use the
Section 3.3 Solving Equations with Variables on
Both Sides
Solving an equation with the variable on Both Sides:
Step 1) Move the smallest constant first
Step 2) Move the smallest variable next
Step 3) Combine like terms
Step 4) Isolate the variable
Ex) 7n
Section 4.2 Greatest Common Factor
A common factor is a whole number that is afactor
of two or more nonzero whole numbers.
The greatest of the common factors is the greatest
common factor (GCF)
A chorus wants to break into small groups. It
wants to have t
Section 4.3 Equivalent Fractions
Are these fractions the same?
Remember the top is the numerator, and the bottom is the denominator.
0 can not be a denominator.
Two fractions that represent the same number are called equivalent
fractions.
Equivalent Fract
Section 4.4 Least Common Multiple
A multiple of a whole number is the product of the
number and any nonzero whole number.
A multiple that is shared by two or more numbers
is a common multiple.
Multiples of 8 and 12
Find the LCM of 10 and 6
We can just fin
Section 4.5 Rules of Exponents
Product of Powers Property:
To multiply powers with the same base, add their
exponents
Lake Powell, the reservoir behind the Glen
Canyon Dam in Arizona, can hold about 10^12
cubic feet of water when full. There are about 10^
Section 5.1
Rational number: a number that can be written as a
quotient of two integers.
Show that the number is rational by writing it a a
quotient of two integers.
7=
-10=
=
Terminating decimal: When you divide you have a
remainder of 0
Repeating decima
Section 5.4 Multiplying Fractions
What is the sum
Write
?
as a product
The product of two or more fractions is equal to the
product of the numerators over the denominators
Multiplying whole numbers and fractions
You ask 150 people to tell whether or not t
Section 5.6 Using Multiplicative Inverses to Solve
Equations
To solve an equation that has a fractional coefficient,
you can multiply each side of the equation by a
fractions multiplicative inverse.
Multiplicative inverse:
The product of a number and its
Section 5.5 Dividing Fractions
Two nonzero numbers whose product is 1, such
as
are reciprocals
Every number except 0 has a reciprocal.
Write the number as a fraction, then switch the
numerator and the denominator.
To divide by any nonzero number, multiply
Section 5.7 Equations and Inequalities with
Rational Numbers
Another way to solve an equation with fractions is to
clear fractions by multiplying each side of the
equation by the LCD of the fractions.
Solving equations with a decimal
2.3 = 5.14 + 0.8m
Bec
Section 6.1 Ratios and Rates
Guy to Girl ratio
A ratio uses division to compare two quantities.
How to write ratios of two numbers
a to b, a:b, a/b
Read as the ratio of a to b
Write our guy to girl ratio in three ways
Winter sport to not playing a sport r
Section 6.2 Writing and Solving Proportions
A proportion is an equation that states two ratios are
equivalent
Solve proportions. Compare denominators.
Solve Using Algebra
Yesterday you rode your bike 18 miles in 2.5 hours.
Today you plan to ride for 3.5 h
Section 6.3 Solving Proportions using Cross Multiplying
A cross product of two ratios is the product of the
numerator of one ratio and the denominator of the other
ratio.
Tell whether the ratios form a proportion.
Human hair grows about .7 cm in 2 weeks.
Section 7.1 Percents and Fractions
The word percent means per hundred. A percent is
a ratio whose denominator is 100.
Symbol for %
Write 29 % and 45 % as fractions in simples form
Write
Write the percent as a fraction in simplest form or
write the fractio
Section 7.6 Percent Applications
A street vendor buys bracelets from a manufacturer
for $7 each. The vendor marks up the price by
150%. What is the retail price
Method 1: Add the markup to the whole sale price
7 + 150% *7
Method 2: Multiply the whole sale
Section 8.2 Linear Equations in Two Variables
Equations in two variables 2x y =5.
A solution to this equation is an ordered pair(x,y)
Tell whether the ordered pair is a solution of
2x y =5
(1,-3)
(4,7)
Tell whether the ordered pair is a solution 3x +2y=-8
Section 8.4 The Slope of a line
How many people going skiing?
Difficulty is determined by the slope or the steepness
Slope =
A ramp has a rise of 6 feet and a run of 10 feet. Find
its slope
Slope of a line more formally
Formula m =
m=
Positive slope climb
Section 9.1 Square Roots
Box drawing activity
Notes to copy:
A square root is writing with the symbol
Any positive number has two square roots, a
positive root and a negative
Zero has one square root
We can write our roots with this symbol
Find the s
Section 1.1 Variables in Algebra
Variables: Letter used to represent numbers
Variable expression: A collection of numbers variables, and operations.
Evaluating expressions: Plugging in numbers for variables in an expression
Evaluate when y =2
a) 8y
c) y +
Section 1.2 Powers and Exponents
A power is the result of the
repeated multiplication of
factors. A power has a base and
a number called an exponent.
4 = 4* 4* 4
3
Example:
Writing products as exponents:
Base used a certain amount of times
13*13*13*13 =
Section 1.3 Order of Operations
PEMDAS
Evaluate when x = 4
Working left to right when things have the same priority
24 8 -6
15 * 2
16 + 4
Use a fraction bar as a grouping symbol
In NJ we are taxed 7% on all non clothing purchases. If I buy a shirt for $28
Section 1.4 Equations and Inequalities
Equations include an equal sign between two expressions.
An open sentence contains one or more variables
A number that makes a true statement is a to the equation
Check whether 2 and 3 are solutions to 3x + 1 = 7
Che
Section 2.1 The Real Number Line
Real numbers:
Origin:
Negative numbers:
Positive numbers
Graph the numbers and -2.3 on a number line
Graph the numbers
Graph -4 and -5, then write an inequality comparing the two.
Write two inequalities that compare -1/2 a
Section 2.2 -2.3 Addition and Subtraction of Real Numbers
7 + -3
-8 + 2
1.4 + (-2.6) +3.1
-1/2 + 3 +
-0.7 + 1.9 + 0.7
-3 + 2/3 + 1/3
On a standardized tests, students receive a score of +1 for each correct
answer and -1 for each incorrect answer. Those q
Section 3.1 Solving Equations Using Addition and Subtraction
Inverse Operations
X 5 = -13
y+5=8
-8 = n (-4)
11 = r -4
t- (-4) = 5
|-6| + y =11
Linear Equations: Do not occur in the denominator, all in a
square root symbol, or inside absolute value symbols