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INTRO PACKET

Algebra 1

Name _________________________________________________

Date Received: _________________ Date Due: ______________

Math Teacher: ___________________________________________

August 2012

Integer Addition, Subtraction,

Multiplication, Division

BASIC DEFINITIONS:

INTEGERS – Positive and Negative numbers (and zero) whose decimal digits are zeros.

ABSOLUTE VALUE – Distance from zero on a number line.

OPPOSITES – Two numbers the same distance from zero on a number line but on different sides of zero.

INTEGER ADDITION:

- Do the integers have the same sign?

YES NO

-ADD their absolute values -SUBTRACT their absolute values

-Keep the common sign -Keep the sign of the integer with the larger

absolute value.

INTEGER SUBTRACTION:

- Add the opposite. How?

Step 1: Keep the first integer the same

Step 2: Change the subtraction symbol to addition

Step 3: Change the sign (to its opposite) of the sign that follows the subtraction symbol

Step 4: Follow the rules of addition above.

INTEGER MULTIPLICATION and DIVISION:

- Do the integers have the same sign?

YES NO

-MULTIPLY or DIVIDE their absolute values -MULTIPLY or DIVIDE their absolute values

-Your answer will always be positive -Your answer will always be negative

Name _____________________________________Integer Operations: Add/ Subtract Alg. 1 Intro Packet

Simplify by performing the operation. Do not use a calculator:

1) [pic] 2) [pic] 3) [pic]

4) [pic] 5) [pic] 6) [pic]

7) [pic] 8) [pic] 9) [pic]

10) [pic] 11) [pic] 12) [pic]

13) [pic] 14) [pic] 15) [pic]

Simplify by performing the operation. Do not use a calculator:

1) [pic] 2) [pic] 3) [pic]

4) [pic] 5) [pic] 6) [pic]

7) [pic] 8) [pic] 9) [pic]

10) [pic] 11) [pic] 12) [pic]

13) [pic] 14) [pic] 15) [pic]

Name ______________________________________Integer Operations: Mult. & Divide Alg. 1 Intro Packet

Simplify by performing the operation. Do not use a calculator:

1) [pic] 2) [pic] 3) [pic]

4) [pic] 5) [pic] 6) [pic]

7) [pic] 8) [pic] 9) [pic]

10) [pic] 11) [pic] 12) [pic]

13) [pic] 14) [pic] 15) [pic]

16) [pic] 17) [pic] 18) [pic]

19) [pic] 20) [pic] 21) [pic]

22) [pic] 23) [pic] 24) [pic]

Name ______________________________________________________Alg. 1 Intro Packet

MIXED INTEGER REVIEW

Add, subtract, multiply or divide the following integers. Do not use a calculator:

1) [pic] 2) [pic]

3) [pic] 4) [pic]

5) [pic] 6) [pic]

7) [pic] 8) [pic]

9) [pic] 10) [pic]

11) [pic] 12) [pic]

13) [pic] 14) [pic]

15) [pic] 16) [pic]

17) [pic] 18) [pic]

19) [pic] 20) [pic]

ALGEBRAIC PROPERTIES

These basic algebraic properties, which do not affect an expression’s outcome, are categorized by:

-Movement of terms

-Grouping of terms

-Special results from performing certain operations.

MOVEMENT OF TERMS:

COMMUTATIVE PROPERTY

(To ‘commute’ means ‘to move’)

of Addition: of Multiplication:

[pic] [pic]

[pic] [pic]

[pic] [pic]

[pic] [pic]

GROUPING OF TERMS:

ASSOCIATIVE PROPERTY

(To ‘associate’ implies who is grouped together)

of Addition: of Multiplication:

[pic] [pic]

[pic] [pic]

[pic] [pic]

[pic] [pic]

SPECIAL RESULTS FROM PERFORMING CERTAIN OPERATIONS:

DISTRIBUTIVE IDENTITY

PROPERTY PROPERTY

[pic] of Addition: of Multiplication:

[pic] [pic]

[pic]

[pic] [pic] [pic]

[pic] [pic] [pic]

[pic] [pic]

*Distributive Property in reverse, [pic] , can still be called the Distributive Property, but is more commonly known in algebra as ‘FACTORING’ (through GCF).

Name _________________________________________Algebraic Properties Alg. 1 Intro Packet

Match the expression change with the algebraic property that justifies it:

1) [pic]

2) [pic] [A] Commutative Property of Addition

3) [pic]

4) [pic] [B] Commutative Property of Multiplication

5) [pic]

6) [pic] [C] Associative Property of Addition

7) [pic]

8) [pic] [D] Associative Property of Multiplication

9) [pic]

10) [pic] [E] Distributive Property

11) [pic]

12) [pic] [F] Additive Identity (‘Identity Property of Addition’)

*13) [pic]

[G] Multiplicative Identity (‘Identity Property of Multiplication’)

Replace the question mark with the missing information:

14) Associative Property of Addition: [pic]

15) Associative Property of Multiplication: [pic]

16) Distributive Property: [pic]

17) Additive Identity (Identity Property of Addition): [pic]

18) Commutative Property of Addition: [pic]

Name _________________________________________Distributive Property Alg. 1 Intro Packet

Use the Distributive Property to simplify the following expressions:

1) [pic] 2) [pic]

3) [pic] 4) [pic]

5) [pic] 6) [pic]

7) [pic] 8) [pic]

Simplify Like Terms:

9) [pic] 10) [pic]

11) [pic] 12) [pic]

13) [pic] 14) [pic]

15) [pic] 16) [pic]

EXPRESSIONS and EQUATIONS

EXPRESSION – Collection of numbers, operations, and variables.

Examples: [pic] [pic] [pic] [pic] [pic] [pic] [pic]

EQUATION – Two expressions separated by an equals sign.

Examples: [pic] [pic] [pic]

EVALUATING EXPRESSIONS:

To evaluate an expression, substitute/replace the variable with the number and simplify:

Examples: [pic] if [pic] [pic] if [pic] [pic] if [pic]

[pic] [pic] [pic]

[pic] [pic] [pic]

SOLVING EQUATIONS:

OPEN SENTENCE – Equation with at least one variable to be solved.

Equations can be True, False, or Open.

[pic] [pic] [pic]

REPLACEMENT SET – Collection of numbers that are substituted in for the variable(s).

Example: Solve for [pic] using replacement set [pic]

Solutions: [pic] [pic] [pic] [pic]

[pic] [pic] [pic] [pic]

NO NO NO YES

Solution Set: {3}

To solve an equation without a replacement set provided, performing the inverse operation of the one(s) in the original equation helps to isolate the variable.

Examples: [pic] [pic] [pic] [pic]

WRITING EQUATIONS:

Addition Words Subtraction Words Multiplication Words Division Words

Sum Difference Product of Quotient

Add Subtracted from Multiplied by Divided by

More than Less than Times

Increased by Fewer than Double

Decreased by Triple

“Is” means ‘equal to’.

“Of” often means multiplication.

To write an equation, use your key words to translate the phrases into algebraic expressions/equations.

Examples: Five more than g is 34 72 is one-sixth of y

Solutions: [pic] (or also [pic]) [pic] (or also [pic]) [pic] [pic]

[pic] [pic]

Name ___________________________________ One-Step Equations: Addition/Subtraction Alg. 1 Intro Packet

Solve each equation by isolating the variable. Show all work:

1) [pic] 2) [pic] 3) [pic]

4) [pic] 5) [pic] 6) [pic]

7) [pic] 8) [pic] 9) [pic]

Solve each equation by isolating the variable. Show all work:

10) [pic] 11) [pic] 12) [pic]

13) [pic] 14) [pic] 15) [pic]

16) [pic] 17) [pic] 18) [pic]

Name _______________________________________ One-Step Equations: Mult./ Division Alg. 1 Intro Packet

Solve each equation by isolating the variable. Show all work:

1) [pic] 2) [pic] 3) [pic]

4) [pic] 5) [pic] 6) [pic]

7) [pic] 8) [pic] 9) [pic]

Solve each equation by isolating the variable. Show all work:

10) [pic] 11) [pic] 12) [pic]

13) [pic] 14) [pic] 15) [pic]

16) [pic] 17) [pic] 18) [pic]

Name _______________________________________ One-Step Equations: Mixed Review 1 Alg. 1 Intro Packet

Solve each equation by isolating the variable. Show all work:

1) [pic] 2) [pic] 3) [pic]

4) [pic] 5) [pic] 6) [pic]

7) [pic] 8) [pic] 9) [pic]

10) [pic] 11) [pic] 12) [pic]

13) [pic] 14) [pic] 15) The sum of a number

and 8 is negative 3.

Name _______________________________________ One-Step Equations: Mixed Review 2 Alg. 1 Intro Packet

Solve each equation by isolating the variable. Show all work:

16) [pic] 17) [pic] 18) [pic]

19) [pic] 20) [pic] 21) [pic]

22) [pic] 23) [pic] 24) [pic]

25) [pic] 26) [pic] 27) [pic]

28) [pic] 29) [pic] 30) The difference of

a number and 1 is 3.

Name _______________________________________ Writing & Solving Equations Alg. 1 Intro Packet

A) Write and equation and B) Solve for the missing variable. Show all work:

1) Nine more than a number is four. 2) Ten less than a number is eight.

3) The product of negative five and a number . 4) One-fifth of a number is negative three.

is two-hundred fifteen.

5) A number decreased by sixteen is negative 6) Four less than a number is eight.

twenty six.

7) Four copies of a book cost $44. Find the price 8) Jen added $150 to her savings account. Her

of one book. balance is now $525. How much was it before?

9) Terri is 60 inches tall. This is 24 inches more 10) The perimeter of a square is 60 inches. Find

than Kevin’s height. How tall is Kevin? the length of each side.

EXPONENTS

Exponents show repeated multiplication in shorthand form. An exponent tells us how many times to multiply the base by itself.

EXAMPLES:

[pic] In this problem, 5 is called the base and 3 is its exponent.

[pic] Note in this problem that 3 is the exponent of base a , not the 4.

[pic] However in this example the 4 is included in the repeated multiplication. Both 4 and a are bases to exponent 3.

-Writing an expression as just a base with its exponent is called writing it in exponential notation, such as [pic] becoming [pic] ‘in exponential notation’.

ORDER OF OPERATIONS

An order has been agreed upon to which operations are performed before others. Several shortcut ways to remember this ranking system have been developed, with most popular being PEMDAS, or “Please Excuse My Dear Aunt Sally”. However, note that although there are six operations, two ranks of order have two operations in them.

Step #1: Parentheses – Compute within any grouping symbol first, if available.

Step #2: Exponents – Compute powers next, if available.

Step #3: Multiply or Divide – Compute in order from left to right.

Step #4: Add or Subtract – Compute in order from left to right.

- If more than one grouping symbol exists within a problem, such as (parentheses), [brackets], or {braces}, work from the inside out.

EXAMPLES: Evaluate the following by using the Order of Operations:

[pic] [pic] [pic]

[pic] [pic] [pic]

[pic] [pic] [pic]

[pic] [pic] [pic]

[pic]

[pic] [pic] [pic] [pic]

Name _________________________________________ Order of Operations, page 1 Alg. 1 Intro Packet

Find the answer by applying the Order of Operations. SHOW EACH STEP! Use example 1 as a guide:

1) [pic] 2) [pic] 3) [pic]

[pic]

[pic]

[pic]

4) [pic] 5) [pic] 6) [pic]

7) [pic] 8) [pic] 9) [pic]

10) [pic] 11) [pic] 12) [pic]

13) [pic] 14) [pic] 15) [pic]

Name _________________________________________ Order of Operations, page 2 Alg. 1 Intro Packet

Find the answer by applying the Order of Operations. SHOW EACH STEP!

16) [pic] 17) [pic] 18) [pic]

19) [pic] 20) [pic]

Substitute and simplify each expression

21) [pic] when [pic] 22) [pic] when [pic] 23) [pic] when [pic]

24) [pic] when [pic] 25) [pic] when [pic] 26) [pic] when [pic]

& [pic]

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