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Chapter 1 Project
Transcript of Chapter 1 Project
X and Y are the variables because they could be replaced by another value. In this lesson you will learn about real numbers and number lines. Here you will learn about properties of real numbers.
In order for two algebric expressions to be equivalent expressions they have the same values of the variables. In this leson you will learn about Adding and Subtracting Real Numbers.
When you add numbers with the same sign, add their absolute value. The sum has the same signs as th addends. Here you will learn about Multiplying and Dividing Real Numbers. The rules for multiplying real numbers are related to the properties of real numbers and the definitions of operations. Now don't worry I'll show you how. All I need is your undivided attention. Stressed Out!! An algebric expression is a mathamatical phrase that includes one or more variables.
4 less than the number 20
In an numeric expression ( which is a phrase in numbers) it would look like this. 20-4
Another example is
56 less than a number n
The answer would be
56-n Don't be like this Guy! Here are some practice problems
20 less than a numer n.
92 plus the sum of a numer and 2
sometimes this problems may be used
the quotient of 207 and a number n The answer would be
Or in multiplication
the product of 9 and a number t
the answer 9t In this lesson you will learn how to Evaluate Expressions and Order of Operations.
This lesson won't bust your brain. It's simple. A power has two parts a base and an exponent. Here are some practice problems
Find the simplest form:
(0.2)^5 =0.00032 Remember Order of Operations
1. Perform any operation inside parenthesis
2. Simplify powers
3. Multiply and Divide from left to right
4. Add and subtract from left to right. Here practice:
32 This lesson also contains rational number
that you can write in a form where a and b are intergers and b is not equal to zero. Also could be in a decimal form such as 5.45 or repeating like 0.416666..... Also this lesson contains natural and whole numbers, integers and irrational numbers. Irrational numbers cannot be represented as a quotient
of two integers and cannot repeat.
rational: 2 or 5
irrational: 1.73205080 or 3.16227766 Inequality Symbols:
< Less than
>greater than less than or equal to greater than or equal to Ordering Real Numbers Practice order
from least to greatest
-2/3, 0.4, -0.9, 1/5
-0.9, -2/3, 1/5, 0.4 Commutative Properties of Addition and Multiplication
Changing the order of the addends does not change the sum. Changing the order of the factors does not change the product.
Multiplication: 92*56=56*92 Associative Properties of Addition and Multiplication
Changing the grouping of the grouping of the addends does not change the sum. Changing the grouping of the factors does not change the product.
Multiplication: (27*5)*4=27*(5*4) Identity Properties Of Addition and Multiplication
The sum of any real number and 0 is the original number. The product of any real number and 1 is the original number.
Multiplication: 67*1=67 Zero Property of Multiplication
The product of a and 0 is 0 Multiplication Property of -1
The product of -1 and a is -a Deductive reasoning is the process of reasoning logically from given facts to a conclusion.
Counterexample is an example showing that a statment is false. Practice
What properties are this:
5*6=6*5 Absolute value is a numbers distance from zero on the numberl line. To add two numbers with different signs subtract their absolute values. The sum has the same sign as the addend with the greater absolute value. Examples: A number and its opposite are called additive inverses. To find the sum of a number and its opposite use the Inverse Property of Addition. For every real number a, there is an additive inverse -a such that a+(-a)= -a+a=0 Multiplying real Numbers:
The product of two real numbers with different signs is negative.
The product of two real numbers with the same sign is positive.
2(3)=6 or -2(-3)=6 Dividing Real Numbers The quotient of two real numbers with different signs is negative.
-20/5=4 or 20/-5=-4
The quotient of two real numbers with the same sign is positive.
20/5=4 or -20/-5=4 Division Involving 0
The quotient of 0 and any nonzero real number is 0. The quotient of any real number and 0 is undefined.
0/8=0 or 8/0=undefined Inverse Property of Multiplication
For every nonzero real number a, there is a multiplicative inverse 1/a such that a(1/a)=1
Section 7 Here you will learn about The Distributed Property. This property helps you to simplify expressions. A term is a number, a variable, or the product of a number and one or more variables. A constant has no variables. A coefficient is a numerical factor or term. Section 8 In this lesson you will learn about equations. An equation is a mathematical sentence that uses an equal sign. An equation is true if the expressions on either side of the equal sign.
1+1=2, x+x=2x An equation is false if the expressions on wither side of the equal sign are not equal.
1+1=3, x+x=3x An equation is open it it contains one or more variables and may be true or false depending on the values of its variables.
2x-14=54 (has a variable) A solution of an equation containing a variable
is a value of the variable that makes the equation
true. Section 9 In this lesson you will learn about Patterns, Equations, and Graphs. A solution of an equation with two variables x and y is called an ordered pair (x,y). An ordered pair makes an equation true. Is (3,10) a solution: