Lesson 1-2 Guided Notes
Variable - a ________________, usually a letter, used to represent a number.
Algebraic expression - contains at least a ___________, a number, and one operation symbol.
Numerical expression - when we replace the n with a number, the expression is ______________.
Evaluate - to find the numerical _________________________ of an expression. Get the answer!!!
ORDER OF OPERATIONS (Plyease Draw in the Symbol yourself.
Order
Opposite: Used to solve equations
Out of parenthesis
Exponents
Divide
Divide
Add
Add
Solve:
1.
2.
3.
Powers - _____________ such as 72 and 23 are called powers and represent repeated multiplication
7
7
or 2
2
2
Where is the exponent?
Evaluate
1.
2.
Evaluate
1.
2.
Equation- A ____________________ sentence that contains an equal sign (=) is called
an equation.
Open Sentence- An equation that contains a _____________________
The Properties
Distributive:
Lesson 1-3 guided Notes
Negative Number- a ____________________ less than zero.
Integers- a set of ______________ that can be represented on a number line.
Ex: 1, 2. -4,-5, 0
Not Example: ½, .25, -3.9
Write an integer for each situation.
a.
b.
c.
Inequality- A sentence that _____________ two different numbers or quantities. Examples are below.
Replace each ___ with <, >, or = to make a true sentence
-3 ___ 3
-2 ___ -1
-3 ___ 2
Absolute Value- is the distance a number is from _______________ on the number line
Lesson 1-4 Guided Notes _______________________________ Name___________________
To ___________ integers with the same sign, ___________ their absolute
values. Give the result the same sign as the integers.
-8 + (-4) =
-21 + (-5) =
15 + 22 =
-43 + -11 =
To _____________ integers with different signs, _______________ their
absolute values. Give the result the same sign as the integer with the
greater absolute value.
a.
b.
c.
Opposites- two numbers that have the same absolute value but ________________
signs.
Additive Inverse- An integer and its _________________________.
Additive Inverse Property- The sum of any number and its additive inverse is
______________
7 + (-7) = 0
2 + (-5) + (-2) =
-4 + (-12) +5 =
-17 + 6 + 17 + 20 =
Lesson 1-5 Guided Notes_____________________________Name___________________
To subtract an integer, add its opposite or _________________ inverse
Find 2 – 6.
Find -7 – 5.
Find 11 – (-8).
Find -6 – (-9).
Evaluate each expression if p = 6, q = -3, and r = -7.
12 – r=
q - p=
Lesson 1-6 Guided Notes Name_________________Title______________________________
The _____________ of two integers with different signs is __________________.
2(-5) = -10
-5(2) = -10
1. 8(-4)=
2.
-5(7)=
The product of two integers with the same sign is ________________________.
2(5) = 10
-2(-5) = 10
3.
-12(-12)
4.
6(-2)(-4)
The ___________________ of two integers with different signs is _____________.
The quotient of two integers with the ____________ sign is ______
__________.
Lesson1-7 Name______________________ Title___________________________
Defining a Variable- when you choose a variable and an unknown quantity
for the variable to represent
Write each verbal phrase as an algebraic expression.
Double the price of a loaf of bread.
Stalks of celery are divided into 4 portions.
Write “the price of the book plus $5 shipping is $29” as an algebraic
equation
Lesson 1-8Guided Notes Name______________ Title__________________
Solve- to find the values of the variables that makes the equation
true.
Solution- the value to a variable that makes an equation true.
Subtraction Property of Equality- if you subtract the same number from each
side of an equation, the two sides remain equal
Solve and check your solution.
15 + c = 7
y + 3 = -8
5=n+4
Inverse operations- __________________ that “undo” each other.
(addition and subtraction).
Addition Property of Equality- if you _____________ the same number from
each side of an equation, the two sides remain _________________.
z – 16 = -5
b – 4 = -10
7 = p - 12
Lesson 1-9 Guided Notes Name____________________Title_______________
Division Property of Equality: If you __________ each side of an equation
by the same nonzero number, the two sides remain the _______.
Multiplication Property of Equality: If you ____________ each side of an
equation by the same number, the two sides remain the ________.
Solve
7z = -49
8x = 72
-12 = -6k
4.
5.
6.
English mathematician Edmund Gunter lived around 1600. He invented the
chain, which was used to measure land for maps and deeds. One
chain equals 66 feet. If the south side of a property measures
330 feet, how many chains long is it?