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
