Transcript Algebra - SazeraMath

Algebra
Of Math Survival Guide
Basic Algebra Vocabulary
A letter that represents a
number; something that
changes
A collection of variables,
numbers and symbols
( +, -, *, ÷)
Translating Verbal Phrases
Words to numbers and
numbers to words
Writing Expressions
The following common words and phrases indicate,
addition, subtraction, multiplication, and division.
Addition
Plus
The sum of
Increased by
Total
More than
Added to
Subtraction
Minus
The difference of
Decreased by
Fewer than
Less than
Subtracted From
Multiplication
Division
Times
Divided by
The product of The quotient of
Multiplied by
Per
Of
Each
Translating Verbal Models
What is a verbal model?
1st answer this question…
What does the word verbal mean?
2nd …
What is a model of something?
Let’s look at a verbal models in math…
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The sum of 5 and 4
The difference of 10 and 8
The product of -3 and 9
The quotient of -25 and -5
Your turn!
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•
•
The sum of 8 and a number
The difference of 24 and a number
The product of 5 and a number
The quotient of 5 and a number
2/3 of a number
Check your work!
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•
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The sum of 8 and a number 8 + n
The difference of 24 and a number 24 - n
The product of 5 and a number 5n
The quotient of 5 and a number 5/n
2/3 of a number 2/3n
• Substituting a variable with the number it
represents (Plug it in, plug it in)
Evaluating Expressions
Evaluate the expression when x=6 and y=3.
1. 4x + 7y = _____________
4( )+7( )
4(6) + 7 (3)
24 + 21
45
Adding and Subtracting Linear
Expressions
Simplifying Expressions –
Combining Like Terms
Like Terms
• Like terms are terms that are exactly
alike
– You can add or subtract terms with the exact
same variables
– You can add and subtract constants
– EX:
3x + 2xy + 4x – 5xy
• Associative – you “associate” with your
group of friends
– Think of parentheses as groups of numbers
– This property relates to how numbers are
grouped
EX: (3+2) + 4 = 3 + (2 + 4)
• Distributive – a teacher distributes a
test to the class
– He/she hands out the test to each student
– You must pass the number outside the
parentheses to the numbers on the inside
– You MULITIPLY the numbers when they are
distributed
EX: -5(3x + 2)
• Commutative – we commute back and
forth to school
– This property is related to the order in which
numbers are placed
– Think of the word COP – Commutative
(Order) Property
EX: 4 + 2 + 12 = 12 + 4 +2
One-Step Equations
• You only need to complete ONE STEP to
solve the equation!
Wait a minute!
Yesterday you
said x equals 2!
X+2=5
X=3
One-Step Equation Check-list
1. Always start on the side with the VARIABLE
2. Identify the Inverse Operation
1.
2.
3.
4.
Inverse of adding =
Inverse of subtraction =
Inverse of multiplying =
Inverse of dividing =
3. Balance the equation
4. Solve
5. Check your answer!
Two-Step Equations
1.
2.
3.
4.
5.
6.
7.
8.
Always start on the side with the VARIABLE
Identify the Inverse Operation of the number
without a variable next to it (# farthest away from
the variable)
Balance the equation (Do the SAME thing to both
sides)
Solve
Identify the Inverse Operation of the number near
the variable
Balance the equation (do the SAME thing to both
sides)
Solve
Check your answer!
You are the variable and
you want to be ALONE!
Examples
1. 2x - 5 = 13
2. (x/2) + 3 = 5
3.
Get RID of your
friends and then
your family!
5 x
 1
6
• Determine what is being asked
• Define your variables
• Develop the equation you are going to use
to solve the problem
• Solve and interpret your answer
• Make sure you are able to explain how
you came to your answer
Example 1 –
Using a Variable Expression
You are taking a bike trip. After
riding 8 miles, you change your
speed to 12 miles per hour. What
is the total distance you travel if
you stay at this speed for 2
hours? For 3 hours?
Solution to Example 1
Let the variable t represent the time that
your ride the bike at 12 miles per hour.
So, the total distance your travel is
Solution to Example 1
Step 1: Write the hours traveled, t.
Step 2: Substitute for t in the expression 8 + 12t
Step 3: Evaluate to find the total distance.
=
=
Now it’s your turn…
use the formula 8+12(t)
1. If you travel for 4 hours, what is the total
distance?
2. If you travel for 1.5 hours, what is the
total distance?
Try this!
The cost at a store for a package of pens is
$3 and for a three-ring binder is $4.
a. Write a variable expression for the cost
of buying p packages of pens and b
binders.
b. How much would 3 packages of pens
and 8 binders cost?
Try this!
1. A triathlon event consists of 2.4 miles of
swimming, 112 miles of biking, and 26.2
miles of running.
a. Write a variable expression to find the
number of miles a person travels in n
triathlons
b. How far does a person travel in
completing 4 triathlons?
•
Plot points on a coordinate plane (x, y)
1.
2.
3.
4.
If x is positive, move to the right
If x is negative, move to the left
If y is positive, move up
If x is negative, move down
• Understand graphs, tables, and formulas
– How to use a table of values and then
graph the x and y’s
x
1
2
3
y
3
6
9
EQUATION:
_________________
• How does a change in one variable affect
the other
• EXAMPLE:
– In the Bike Tour, the more customers we had,
the more $$ we made
– The more hours you study, the better grades
you will make
• Direct and inverse relationships (graphs)
– Direct ( y = kx) → Multiplication
– Indirect (y = k/x) → Division
n
m