(-,+) (+,+) Plotting Points

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Hannah Robertson
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1 Algebra Basics

2 +y (-,+) (+,+) -x +x (-,-) (+,-) Plotting Points -y

3 Commutative Property of Addition/Multiplication * You can commute or move the terms * This only applies to addition and multiplication Distributive Property of Addition/Multiplication Inverse Property of Addition/Multiplication Associative Property of Addition/Multiplication *You can change what terms are associated (or grouped) together * This only applies to addition and multiplication Algebra Properties

4 Multiply/Divide **You do NOT need a common denominator Adding/Subtracting **You MUST have a common denominator Example: Example: You need to reduce your fraction by dividing the numerator and denominator by 3 Example: The common denominator is 15 so multiply the first fraction by and the second fraction by Example: When dividing fractions you copy, change, flip *Copy the first fraction, change the division to multiplication and flip (take the reciprocal) of the second fraction **You may leave your answer improper unless your answer needs to include units. For example, it doesn t make sense **Always reduce fractions if you can to say that you ran miles, instead you would say that you ran miles. Fractions

5 Degree of a polynomial: The greatest degree of the terms of a polynomial How to find the degree of a term Look at the exponents on the variables only x has an exponent of 2 y has an exponent of 1 Add these 2 values together When simplifying expressions, put your answer in order from highest degree to lowest degree Example: Simplify Addition is commutative so rewrite the expression with the like-terms next to each other Now combine your like terms *Note: Constants have a degree of zero **Note: *Notice how the expression is written from the highest degree, of 2, down to the lowest degree, of 0. Exponent Basics

6 Vocabulary * Coefficient: The number being multiplied by the variable * Constant: A term that has no variable part * Terms: The parts of an expression that are being added or subtracted Example: Simplify the expression Distribute the ½ Combine like-terms Example: Simplify the expression Distribute the 4 and -3 Combine like-terms Example: Simplify the expression Distribute the -3 Combine like-terms Combining Like-Terms

7 Integer: A set consisting of negative integers, zero, and positive integers Adding Integers When dealing with integers, change all subtraction to addition Multiplying/Dividing Integers Follow these rules: * When the signs are the same, the answer is positive Conversions between addition/subtraction Follow these rules: * When the signs are the same, add the numbers together and then take the sign of the numbers * When the signs are different, the answer is negative * When the signs are different, subtract the numbers. The answer has the same sign as the larger value Integer Operations

8 rouping symbols xponents Example: Simplify the expression Exponents Grouping Symbol dd ivide ultiubtract Multiply Example: Simplify the expression Grouping Symbols *Note: Start with the innermost grouping symbols first and work your way outward Exponents Grouping Symbols Multiply Order of Operations

9 Operations Words Examples 5 more than a number, n Add Plus, add, sum, total, more than The sum of n and 5 Subtract Less than, subtract, difference, minus, take away The difference of n and 5 5 less than a number, n Multiply Divide Times, product, of Quotient, ratio, divided by, ratio 10 percent of 20 The quotient of x and 5 Equals is Translating Expressions

10 **When solving equation, always simplify each side of the equation first Example: Solve the following equations for the given variable *Each side of the equation is already simplified *There are 4 different ways to start this problem so choose one. *For this example, we are going to add 8x to both sides *Simplify each side of the equation by distributing the 2 and ½ *Again, there are 4 different ways to start this problem *For this example, subtract 6g from both sides Subtract 17 from both sides *Our variable cancelled out but we are left with a true statement. The answer for this problem is: infinite solutions or all real numbers Divide both sides by 12 *Note: If you have a problem where all of the variables cancel out and you are left with a false statement like 11=17, you have no solution. Solving Equations

Rational number operations can often be simplified by converting mixed numbers to improper fractions Add EXAMPLE:

$Rational number operations can often be simplified by converting mixed numbers to improper fractions Add EXAMPLE:$ Rational number operations can often be simplified by converting mixed numbers to improper fractions Add ( 2) EXAMPLE: 2 Multiply 1 Negative fractions can be written with the negative number in the numerator