## Presentation on theme: "1.1 Operations with Integers BobsMathClass.Com Copyright © 2010 All Rights Reserved. 1 The Negative Integers are negative numbers only: {…, -3, -2, -1}."— Presentation transcript:

1.1 Operations with Integers BobsMathClass.Com Copyright © 2010 All Rights Reserved. 1 The Negative Integers are negative numbers only: {…, -3, -2, -1}. The Positive Integers are the whole numbers greater than zero: {1, 2, 3, …}. Zero is neither positive nor negative. In, algebra, it is necessary for us to be familiar with the various terms that are used to classify different types of Real Numbers: The Natural Numbers is the set of numbers we can use to count things: {1, 2, 3, 4, …}. It does not include zero or negative numbers. The three dots indicates that the list continues forever (there is no last element). The Whole Numbers are the nonnegative numbers, including zero: {0, 1, 2, 4, 5, …} Integers The Integers are negative integers, zero, and positive integers: {…, -3, -2, -1, 0, 1, 2, 3, …} which is shown below on the number line. 01254376-4-3-2-5 Next Slide

1.1 Operations with Integers BobsMathClass.Com Copyright © 2010 All Rights Reserved. 2 Inequalities Greater than: If a number is to the right of another number then it is greater than (>) the other number. Less than: If a number is to the left of another number, then it is less than (<) the other number. Note: The inequality symbol must always point toward the smaller number. Example 1a: i.) 6 > 4 6 is greater than 4 ii.) 8 < 12 8 is less than 12 iii.) –9 > –16 –9 is greater than –16. (–9 is to the right of –16.) We could also say that the inequality symbol opens up to the larger number. In part iii.) above, -9 is the larger number. Would you rather owe \$9 or owe \$16? You would probably rather owe the \$9. Next Slide

1.1 Operations with Integers BobsMathClass.Com Copyright © 2010 All Rights Reserved. 4 Answers: a. > b. < c. > d.13 e. 7 f. -8 g. 45 Your Turn Problem #1 Place the correct inequality symbol between the two numbers. a. 32 12 b.-18 -15 c. 0 -7 Evaluate each of the following: d.-(-13) e. |-7| f. -|-8| g. |45|

1.1 Operations with Integers BobsMathClass.Com Copyright © 2010 All Rights Reserved. 8 Example 5. Perform the following: b) –13 – 12 – (–10)a) 11 – 20 – 18 Answers: When subtraction occurs several times in a problem, rewrite each subtraction as addition of the opposite. Then perform the addition. –27 11 + (–20) + (–18) –9 + (–18) –15 –13 + (–12) + (+10) –25 + (+10) Your Turn Problem #5 Perform the following: b) 15 – (–5) – (–7) a) –18 – 13 – (–10) Answers: b) 27 a) –21

1.1 Operations with Integers BobsMathClass.Com Copyright © 2010 All Rights Reserved. 9 Example 6.Mt. Korabi in Albania has an elevation of 3100 meters and Death Valley in the United States has an elevation of  86 meters. Find the difference in elevation between Mt. Korabi and Death Valley. Solution: Mt. Korabi = 3100 meters Death Valley =  86 meters We want the difference in elevation. Difference means to subtract. Remember to keep the sign of the 86. Let D = the difference in elevation. D = 3100  (  86) = 3100 + 86 Mrs. Lazzara has a checking account with Bank of America. The statement she received in May showed an account balance of \$4875. In June, the account balance was  \$5 (overdrawn). Find the difference in statements. Your Turn Problem #6 Answer: \$4880

1.1 Operations with Integers BobsMathClass.Com Copyright © 2010 All Rights Reserved. 10 Procedure: To multiply two numbers: 1. Determine sign of answer:(+) (+) = + (+) (  ) =  (  ) (+) =  (  ) (  ) = + 2. Multiply numbers and write sign from step 1 in front of the product. Multiplying Integers Example 7. Multiply the following: b) (–7)(–8)a) (–7)(8)c) (7)(–8) Answers: –5656 –56 Answers:c) –60b) –36a) 120 Your Turn Problem #7 Multiply the following: b) (–18)(2)a) (–12)(–10)c) (15)(–4)

1.1 Operations with Integers BobsMathClass.Com Copyright © 2010 All Rights Reserved. 11 Multiplying by more than two factors follows same procedure as addition. Method 1: Find the product of the first two factors using procedures above; then multiply it by the third factor; then multiply its product by the fourth factor, etc. Method 2: Find the sum of the number of negative factors in the problem. If that sum is even, then the product to the problem will be + ; if that sum is odd, then the product to the problem will be . Multiply the factors without regard to the signs. Attach the sign determined from counting the number of negatives to the product. Example 8. Multiply the following: b) (–4)(–1)(–2)(–2)(3)a) (–2)(3)(–2)(–8) Answers: b) –48a) 30 –96 (three negatives= –) 48 (four negatives= +) Your Turn Problem #8 Multiply the following: b) (–2)(3)(–2)(4)(–1)a) (–1)(–5)(–3)(–2)

1.1 Operations with Integers BobsMathClass.Com Copyright © 2010 All Rights Reserved. 13 Procedure: To calculate an average. 1.Find the sum of all of the numbers 2.Divide the sum by the amount of numbers given. Averages Example 10. During a period of 5 days Anchorage, Alaska the temperature was as follows:  7  C, 2  C,  1  C,  4 , and  5  C. Find the average temperature in Anchorage, Alaska for the 5 days. Solution: Step 1:  7 + 2 + (  1) + (  4) + (  5) =  14 Step 2:  15  5 =  3 Answer: The average temperature for the 5 days was  3  C. Answer: 191 mph Your Turn Problem #10 The speed of the first five cars in the preliminaries in the Dayton 500 were as follows: 210mph, 180mph, 200mph, 195mph and 170mph. Calculate the average speed of the first five cars. The End B.R. 4-23-07

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