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Agenda 10/13/11 1. Correct/Discuss Ratio Proportion Quiz If you are still having trouble, visit www.khanacademy.org 2. Introduction to Algebra (Integers) 3. Adding and Subtracting Integers
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Working with Signed Numbers The Number Line Algebra uses NEGATIVE and POSITIVE numbers. Algebra also uses variables, or letters to represent the unknown values. 0 1 2 3 4 5 -1 -2 -3 -4 -5 The numbers in red are the numbers we have worked with so far. Algebra uses all of the numbers on the number line, both positive and negative.
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The Number Line 0 1 2 3 4 5 -1 -2 -3 -4 -5 6 7 8 9 10 -6 -7 -8 -9 -10
The arrows at both ends of the number line mean that the positive and negative numbers go on forever.
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A number on the number line is greater than any number to its left.
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A number on the number line is less than any number to its right.
Using the Number Line Positive numbers do not have to be written with a plus sign. Positive 8 is simply written as 8. Negative numbers MUST be written with a negative sign in front of them (-8)
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Absolute Value Absolute Value is the distance from a number to zero on the number line. Absolute Value is neither positive or negative. The absolute value of -5 is 5 .
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Using the Number Line A B C D E F G H I J 0 1 2 3 4 5 6 7 8 9 -9 -8 -7 -6 -5 -4 -3 -2 -1 C J 9. -3.5 10. -0.2 F +6 -3 -8 5. 6. 7. 8. 2.75 D E G B I A H
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Know the Rules: Same Sign Adding Two SAME-Signed Numbers: Add and give the total of the signed numbers. (-5) + (-5) = -10
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Know the Rules: Different Signs Adding when the signs are different: Subtract and keep the sign of the bigger number. 8 + (-15) Subtract : 15-8 =7 The sign of the larger number is negative So, the answer is -7
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Know the Rules: Subtracting Change the sign of the number being subtracted and drop the subtraction sign. -11 (-8) - (3)= Different Signs -5 (-8) - (-3)= Same Signs
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Adding a Series of Signed Numbers Simplify (-9) + (10) + (-8) + (4) = Step 1:Add the positive numbers. Step 2: Add the negative numbers. Step 3: Add sums together.
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Subtracting Signed Numbers This is where it gets weird. To subtract signed numbers: Step 1: Change the sign of the number being subtracted. Step 2: Follow the signs for adding signed numbers. -11
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Subtracting Signed Numbers This is where it gets weird. To subtract signed numbers: Step 1: Change the sign of the number being subtracted. Step 2: Follow the signs for adding signed numbers. -8
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Subtracting in a Series of Signed Numbers This is where it gets weird. Step 1: To solve a series of signed numbers, start by changing the signs of numbers being subtracted. Step 2: Find the sum of the positive numbers. Step 3: Find the sum of the negative numbers. Step 4: Find the difference. Follow the rules of addition. 6 + 4 = 10 -2+ (-5) = -7 10- 7 = 3
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Practice Take some time to practice the rules.
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Multiplying Signed Numbers If you gain 2 pounds a week for 5 weeks, you will weigh 10 pounds more than you weigh now. If you lose 2 pounds a week for 5 weeks, you will weigh 10 pounds less than you weigh now. (+2)(+5) = +10
Step 1: Multiply.
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Step 2: If same signs, make the product positive.
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Step 3: If different signs, make the product negative.
(-2)(+5) = -10
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If you have been gaining 2 pounds a week for 5 weeks, you weighed 10 pounds less five weeks ago. If you have been losing 2 pounds a week for 5 weeks, you weighed 10 pounds more 5 weeks ago. Multiplying Signed Numbers (+2)(-5) = -10
Step 1: Multiply.
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Step 2: If same signs, make the product positive.
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Step 3: If different signs, make the product negative.
(-2)(-5) = +10
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Multiplying 3 or more signed numbers Example 4: What is (-6)(+2)(-4)? Rule: Step 1: Multiply. Step 2: If there are even negative signs, the final product is POSITIVE. Step 2: If there are an odd number of negative signs, the final product is NEGATIVE. 48
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Rule Step 1: Multiply. Step 2: If same signs, make the product positive. Step 3: If different signs, make the product negative.
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Dividing Signed Numbers Rule: Step 1: Divide or reduce. Step 2: If like signs, quotient will be positive. Step 3: If different signs, quotient will be negative. + 30/-6
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Mixed Signed Numbers Problems Order of Operations Always go from LEFT to RIGHT. PEMDAS (Please Excuse My Dear Aunt Sally) Parentheses Exponents (powers and roots) Multiplication and Division Addition and Subtraction
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