Algebra 1 SBHS 2016-2017Unit 1 Pre-Algebra Review Notes Packetmrs. Shafi

Algebra 1 SBHS 2016-2017Unit 1 Pre-Algebra Review Notes PacketMrs. Shafi

Name ______

Date ______Block ______

Notes Packet #1

Topics Covered / Homework
Day 1
8/29(A)
8/30( B) / Order of Operations and Integer Operations / Pre-Algebra Review Homework 1
Day 2
8/31(A)
9/1(B) / Translating Expressions and Equations, Combining Like Terms, and the Distributive Property / Pre-Algebra Review Homework 2
Day 3
9/2 (A)
9/6(B) / Evaluating Expressions and Properties / Pre-Algebra Review Homework 3

Integer Operations

Vocabulary! Integer –positive or negative whole numbers (..-2,-1, 0, 1, 2…)

Addition
Do the numbers have the same sign?
YES! ______(Just find the sum!)
(-3) + (-6) =
4 + 5 =
No! ______Find the difference and keep the sign of the LARGER number
5 + (-7) =
(-4) + 6 = / Subtraction
Try to change a – to + and follow the rules of addition
-3 – 2 =
5 – (-2) =
-6 + 2 – (-7) =
Multiplication
(+)(+) = (+) Even
(-)(-) = (+) Even
(+)(-) = (-) Odd
(-)(+) = (-) Odd
(3)(4) = (4)(- 5) =
(- 2)(- 3) = (- 8)(7) = / Division
(+)÷(+) = (+) Even
(-)÷(-) = (+) Even
(+)÷(-) = (-) Odd
(-)÷(+) = (-) Odd
6 ÷ 2 = -8/-4 =
-16 ÷ 4 =

Vocabulary!

Even- An integer that ends in 0, 2, 4, 6, 8

Odd- An integer that ends in 1, 3, 5, 7, 9

Order of Operations

Examples:

1)20 – 2 •22) 16 ÷ 4 + 10(3)3) 8[20 – (9-5)2]

Additional PEMDAS Problems

3(4 + 1) + 32(9 – 22)  5 = (3  3 + 32) – 6 =

(2 + 3)2 – (12  2) =(10-6)  22 =(2 + 3) · (3-1)2 2

Translating Expressions and Equations

Addition
The sum of 6 and a #
A # increased by 1
8 plus a #
8 more than a number / Subtraction
The difference of 3 and a #
4 less than a #
7 minus a #
A # decreased by 9
Multiplication
The product of 4 and a #
6 times a #
A # multiplied by 2
/ Division
The quotient of a # and 10
7 divided by a #

Equality

The product of 4 and a # is equal to7.

6 times anumber is5.

Vocabulary! Expression – A math phrase. Combination of numbers, variables and symbols

Examples of verbal expressions:Math expressions:

1)The product of eight andseven.______

2) The difference of nine anda number.______

3) The sum of seven, four, andeighteen.______

4) The quotient of eighty-one andthree.______

5) The sum of three times a number b and 33 ______

6) The difference of 32 and the quotient of a number m and 7______

Vocabulary!

Equation – A math sentence. Sets one expression equal to another.

Examples of verbal equations:Math equations:

7) Five less than twice a number is 7. ______

8) The cost decreased by tendollars is equal to 5. ______

9) The sum of a x and 7 is equal to the product of a x and 3. ______

10) Joan’s temperature increased by twodegrees is equal to 100. ______

COMBINING LIKE TERMS

Problem: -x + 2x + 8 -2x2

Vocabulary!

Terms (separated by a – or a + sign):

Coefficients (number in front of variable):

Like Terms:

Constant (a plain number):

Simplified (write the expression with the exponents in decreasing order):

For the following problems, combine like terms or simplify the expression.

Algebra 1 SBHS 2016-2017Unit 1 Pre-Algebra Review Notes PacketMrs. Shafi

The Distributive Property

The Distributive Property: The process of distributing the number on the outside of the parentheses to each term on the inside.

and

Simplify the following expressions.

Algebra 1 SBHS 2016-2017Unit 1 Pre-Algebra Review Notes PacketMrs. Shafi

The Commutative Property

The order in which two numbers are added or multiplied does not change their sum or product.

Commutative Property of Addition

Commutative Property of Multiplication

Complete the following equations to justify the Commutative Property.

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Algebra 1 SBHS 2016-2017Unit 1 Pre-Algebra Review Notes PacketMrs. Shafi

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Algebra 1 SBHS 2016-2017Unit 1 Pre-Algebra Review Notes PacketMrs. Shafi

The Associative Property

The way in which numbers are grouped when they are added or multiplied does not change their sum or product.

Associative Property of Addition

Associative Property of Multiplication

Complete the following equations to justify the Associative Property.

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Algebra 1 SBHS 2016-2017Unit 1 Pre-Algebra Review Notes PacketMrs. Shafi

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Algebra 1 SBHS 2016-2017Unit 1 Pre-Algebra Review Notes PacketMrs. Shafi

The Identity Property

A number when added or multiplied to by the identity, does not change the original number.

IdentityPropertyofAddition

IdentityPropertyofMultiplication

Complete the following equations to justify the Identity Property.

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Algebra 1 SBHS 2016-2017Unit 1 Pre-Algebra Review Notes PacketMrs. Shafi

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Algebra 1 SBHS 2016-2017Unit 1 Pre-Algebra Review Notes PacketMrs. Shafi

The Multiplicative Property of Zero

When any number is multiplied by zero, the product is zero.

Complete the following equations to justify the Multiplicative Property of Zero.

Algebra 1 SBHS 2016-2017Unit 1 Pre-Algebra Review Notes PacketMrs. Shafi

The Inverse Property

The sum of a number and its opposite (additive inverse) is zero.

Inverse Property of Addition

The product of a number and its reciprocal (multiplicative inverse) is one.

Inverse Property of Multiplication

Use the Inverse Property to complete the following expressions.

Algebra 1 SBHS 2016-2017Unit 1 Pre-Algebra Review Notes PacketMrs. Shafi

What is the multiplicative inverse of 4?

What is the additive inverse of 5?

Algebra 1 SBHS 2016-2017Unit 1 Pre-Algebra Review Notes PacketMrs. Shafi

Practice:Name the property shown in each of the following statements.

______

______

______

______

______

______

Evaluating Expressions

To EVALUATE an algebraic expression, ______the given values for the particular variables and SIMPLIFY the expression. (PEMDAS)

Calculator Hints:

Put all ______numbers and ______in parentheses when typing the problem.
If the problem starts as a fraction, substitute the values into the numerator and denominator separately. Then divide the 2 numbers you found.
To change a DECIMAL answer to a FRACTION, hit MATH – ENTER – ENTER.

Examples:

Algebra 1 SBHS 2016-2017Unit 1 Pre-Algebra Review Notes PacketMrs. Shafi

1)Evaluate 2x + 4y when x = 6 and y = 2.

2)Evaluate w + 3(4w - 8) when w = 11.

Algebra 1 SBHS 2016-2017Unit 1 Pre-Algebra Review Notes PacketMrs. Shafi

3)Evaluate the following expression if x = 4, y = -2, and c = 2.

4)Find the value of the expression to the nearest tenth if c = 2, d = 7, f = 10, and g= 8.

5)The formula for the circumference of a circle is C = . Find the circumference of the circle if the radius is 10 meters. Use = 3.14.

A. 15.14 m

B. 16.28 m

C. 47.28 m

D. 62.8 m