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 equationsOut 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 withdifferent 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)=

- -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?