Math Quiz 2 chapter

-4x^-15x-10-6x+12+9x^

-4x^-15x-10-6x+12+9x^ -4x^+9x^-15x-6x-10+12 5x^-21x-2

Distributive property:

-A number times a group of numbers -x(y+2)=xy+2x -3(4+5)=3•4+3•5 -2•3.5=2.3+2.5

Associative Property of Addition and multiplication

-Changing the grouping of the values you are adding or multiplying does not change the sum or product

Commutative Properties (addition and subtraction)

-Changing the order of the value you are adding or multiplying does not change the sum or product -These properties only work exclusively with addition and multiplication not division or subtraction

The number of feet in I

1÷12

3(X+9)

3•x=3x 3•9=27 3x+27

Inverse properties multiplication:

For multiplication: Multiplying a number by its reciprocal gives it 1 Examples:3•1/3=1,(-3)•(-1/3)=1

2-5 Equations with Integers, Fractions, and Decimals

Goal: To solve one step equations using subtraction and to solve one step equations using addition solving real world problems

2-2: The Distributive Property:

Goal: To use the distributive property with Algebraic expressions

2-4: Variables and Equations

Goal:To classify types of equations and to check equations using substitutions

2-3: Simplifying Variable Expressions:

Goal:To idnetify parts of a variable expression and simplify and expression

14•14=196

Numerical

80÷8=10

Numerical

Vocab:

Terms of variable expression

Identify properties of addition and multiplication

The sum of any numbers and zero is the original number. The product of any number and I is the original number

Whats the point of DP

To simplify/multiply expressions that contain variables

Inverse operations:

When solving an equation you must get the variables alone by using inverse operations

How do we know when to use the DP

When you see an unknown (variable) inside a pair of parenthesis that is being added or subtracted and theres a number on the outside of the parenthesis

9 meters higher than altitude x

X+9

Your mother gave you 13.32 with which buy a present this covered 3/5 of the price. How much did the present cost?

X=Represents the cost of the present 3/5= of is multiplication 13.32= Represents 3/5 of the price 3/5x=13.32 5•3=13.32•5 3 5 3 answer=22.2

Using addition to solve equations

You an add the same number to each side of an equation

Example 2

[-8y]+{2x} (-Y)+[9x^]{-8x}-(21x^)

Coefficient:

a number that multiplies a variable ex (6a 6-8)

Term:

a term is a number of the product of a number and variables

Example 1:

when you see a variable by itself you must also see that there are many invisible ones around it

One Step Equations with Integers, Fractions, and Decimals (2-5, 2-6, 3-5, 3-6, 5-7, 5-8)

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Real world Problems:

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Number of pounds in z onces

16(z)

Distributive property of multiplication over addition or subtraction

A number times a group of numbers/variables in parenthesis can be distributed -(IE the number multiplied with each part separately)

Solution of an equation:

A value for a variable that makes an equation true you substitute a number for a variable to determine whether the number is a solution of the equation

Examples using distributive property with algebraic expressions

A) 4(3x-4) is the -4 minus 4 or negative 4•3=12 4•4=16 4x3x-16=12x-16

Product:

Answer to a multiplication problem

Ex

Arithmetic Algebra 10=2(b) if, A=B A and B are = 10-5=5 2(5)-5 A-c=b-c 5=5

Associative examples:

Arithmetic: Algebra: (2+7)+3=2+(7+3) (a+b)+c=A+(b+c) (9•4)5=9(4•5) (ab)c=a(bc)

Identify Property:

Arithmetic: Algebra: 12+=12;•1=10 a+0=a;1=a

Commutative Examples:

Arithmetic: Algebra: 6+4=4+6 a+b=b+a 9•5=5•9 a•b=b•a

Example:

Arithmetic: Algebra: b=2(4) If a=b 8+3=2(4)+3 then a+b=b+c

3-5, 3-6, 5-7, 5-8 One Step Equations with Integers, Fractions, and Decimals

-Solving Equations with fractions and decimals -Goal: To solve one step equations algebraic

2-6 One Step Equations with Integers, Fractions, and Decimals

-To solve one step equations using division and multiplication -Remember division and multiplication are inverse operations -To solve algebraic equation you must isolate the variale meaning getting variable by its quick check

Extra notes

-You must multiply reciprocals together you will always get 1 -When you have a fraction just multiply it by its reciprocal -Make sure you make the work vertical

1-1: Variables and Expressions

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2-1: Properties of Numbers:

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DP examples:

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Expressions:

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Inverse properties of addition or of multiplication

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Variables:

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Word Problem: Create an algebraic equation to solve the word problem

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You can write and solve equations describing real world situations to help check decide whether your solution is correct using the original problem

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Quick Check 2: 1) R/5-10

1) -5•R=10-5 1-5 1

Quick Check 1) 123-55=R

1) 123-55=R 123-55=R R=68

Quick Check 1: 1) 9-7=3 2) 8+x=2 3) 4•5=20

1) 9-7=3 False 9-6=3 2) 8+x=2 Open sentence because there is a variable 3) 4•5=20 True, 5•4=20 20=20

How to combined like terms

1. Identify the like term 2. add or subtract only the coefficient 3.The variables stay the same

Open step equations and word problems:

1. Identify what the variable is going to represent. (Usually what the last question in the word problem) 2. Identify the other important number/phrase that will help you make your equation 3. Create your algebraic equations using any of the information found in the equation.

9$ cheeper than 4 times price

4x-9

Ex 1: 5 1/3y=3 4/5

5 1/3y=3 4/5 -17=19 3y 6 3•17=19• 3=57 -17 3 6 17 85

5 times a number increased by 8

5x+8

8 times the um of a number and 5

8(2x+5)

Quick Check: A) 4x=84 B) 91=7y

A) 4x=84 B) 91=7y ÷4 ÷4 ÷7 ÷7 x=21 y=13

1) Classifying Equations:

A) 6+12=18, True, Because 18=18 B) 6=4+3, False because6≠7 C) 6y=3+5y, an open sentence because it has a variable

Quick check: A) X=-5 B) 5=d+1 C) C+-4=-5

A) X=-5 B) 5=D+1 C) C+-4=-5 8-3=-5 D=4 +4 +4 5-1=4 C=-1

Quick Check 3: A) Y-5=8 B) P-30=42

A) Y-5=8 B) P-30=42 +5 +5 +30 +30 Y=13 P=72

Open sentence:

An equation with one or more variables

Inverse properties addition:

For addition:Adding a number to its opposite gives 0 Example:2+(-2)=0

Real world problem solving: Weight of tent 61lb. Your backpack and the tent together weigh 33lb. Use the equation to find whether that back weighs 27lb.

Ex: Weight of ten lus weight of pack is 27lb 61lb 133 x 61lb+33lb=X (6+x=33)

Equation:

Is a mathematical sentence with an equal sign

1) m-1 1/2=5/4

M-1 1=-5 2 4 3=5 2 4 2/3•3/2=-5/4•2/3 m=1/4

Like terms:

Must have identical variables and exponents ex (4a 7a)

One step Equations with word problems: Lisa is cooking muffins the recipe calls for 7 cups of suger. She has already put in two cups. How many more cups does she need to put in?

N: Number of cups she needs 2x=7 -2 -2 n+2=7

2) Writing an equation

Nine times the opposite of five is forty-five 9 • -5 = 45 9•-5=45 The equation is false 9•(-5)=-45

Constants

doesn't change is a term that has no variable

D dozen eggs

dx12

The number of quarts in a gallon

g÷4