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Transcript of algebra
December 31, 3102 Chapter 1 Lesson vocabulary Quantity- is anything that can be measured or counted.
Variable-is a symbol, usually a letter, that represents the values of a variable quantity.
Algebraic expression is a mathematical phrase that includes one or more variables.
numerical expression-is a mathematical phrase involving numbers and operation symbols, but no variables. writing expressions with subtraction writing expressions with multiplication and division 9*n or 9n 9 times a number n The quotient of a number y and 6
y/6 writing expression with two operations 3 more than twice a number x 3+2x Using words for an expression three times number x 3*x lesson vocabulary Power-has two parts, a base and an exponent.
Exponent-tells you how many times to use base as a factor.
Simplify-To replace an expression with it's simplest name or form.
Evaluate- an algebraic expression by replacing each variable with given number Simplifying powers 10 =10*10*10*10*10*10*10 7 = 10,000,00 Lesson vocabulary A number a is a square root of a number b if a 2 = b . Radicand- The expression under the radical symbol.
Radical-Together the radical symbol and radicand form this.
Perfect square-The square of an integer.
Set-is a well-defined collection of objects each object is called element of the set.
Subset-consist of elements from the given sets.
Inequality- is a mathematical sentence that compares the value of two expressions using an inequality symbol. lesson vocabulary Equivalent expressions-are algebraic that have the same value for all values of the variables.
Deductive reasoning-is the process of reasoning logically from given facts to a conclusion.Counter Example - An example to prove that a statement is false. Commutative Property of Addition
a + b = b + a 2 + 3 = 3 + 2
Commutative Property of Multiplication
a • b = b • a 2 • ( 3 ) = 3 • ( 2 )
3. Associative Property of Addition
a + ( b + c ) = ( a + b ) + c 2 + ( 3 + 4 ) = ( 2 + 3 ) + 4
4. Associative Property of Multiplication
a • ( b • c ) = ( a • b ) • c 2 • ( 3 • 4 ) = ( 2 • 3 ) • 4
5. Distributive Property
a • ( b + c ) = a • b + a • c 2 • ( 3 + 4 ) = 2 • 3 + 2 • 4
6. Additive Identity Property
a + 0 = a 3 + 0 = 3
7. Multiplicative Identity Property
a • 1 = a 3 • 1 = 3
8. Additive Inverse Property
a + ( -a ) = 0 3 + (-3) = 0
9. Multiplicative Inverse Property
Note: a cannot = 0
10. Zero Property
a • 0 = 0 5 • 0 = 0 5(3n)=(5*3)n = 15n 1-5 Adding and Subtracting Real Numbers You can add or subtract any real numbers using a number line model. You can also add or subtract real numbers using rules involving absolute value. Essential understanding Lesson vocabulary Absolute value- Is its distance from 0 on a number line. absolute value is always nonnegative since distance is always nonnegative. ex. Opposite- Two numbers that are the same distance from 0 on a number line but lie in opposite directions. Additive inverse- A number and its opposite Inverse property of addition-is when you want to find the sum of a number and its opposite. 0-25+16-47+29
=-27 Write an expression
Use rule for subtracting real numbers.
commutative property of addition
Group addends with the same sign
add inside grouping of addition
identity property of addititon
use rule for adding numbers with different signs. A reef explorer dives 25ft to photograph brain coral an then rises 16ft to travel over a ridge before diving 47ft to survey the base of the reef. then the diver rises 29ft to see an underwater cavern. what is the location of the cavern in relation to sea level. The cavern is at -27ft in relation to sea level. 1-6 Multiplying and Dividing Real Numbers essential understanding
The rules for multiplying real numbers are related to the properties of real numbers and the definition of operations. Lesson vocabulary
Multiplicative inverse- Every fraction with a nonzero numerator.
reciprocal- 1-7 Distributive Property Distributed property Lesson vocabulary Term- is a number, a variable or the product of a number and one or more variables. constant- is a term that has no variable.
Coefficient- is a numerical factor of a term.
Like terms- have the same variables factors. Obj: To use the distributive property to simplify expressions Obj: To classify, graph, and compares real numbers to find and estimate square roots. obj: To identify and use properties
of real numbers Obj: To find sums and differences of real numbers Obj: To find products and quotients of real numbers 3(x+8)
= 3x+24 simplify Distributive Property simplifying expressions 1-8 An Introduction to Equations Obj: To solve equations using tables and mental math lesson vocabulary
Equation- is a mathematical sentence that uses an equal sign (=).
Open sentence- It contains one or more variables and may be true or false depending on the values of its variables. classifying equations
A. 24+18 =20+22 true, because both expressions equal 42
B. 7* 8=54 false, because 7*8=56 and 56 = 54
C. 2x-14=54 open, because there is a variable / Solution of an equation- containing a variable is a value of the variable that makes the equation true. Identifying solutions of an equation Is x=6 a solution of the equation 32=2x+12
32= 2x +12
32=2(6)+12 substitute 6 for x
32= 24 simplify
no, x = 6 is not a solution of the equation 32= 2x+12 1-9 Patterns, Equation, and Graph Obj: To use tables, equation, and graphs to describe relationship Lesson vocabulary
Solution of an equation-with two variables x and y is any ordered pair (x,y) that makes the equation true.
Inductive reasoning-is the process of reaching a conclusion based on an observed pattern.