MULTIPLYING AND DIVIDING INTEGERS Guided Notes

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1 Notes Name: Date: Period: MULTIPLYING AND DIVIDING INTEGERS Guided Notes Target Objective 1: Multiply, and divide integers Target Objective 2: Describe situations involving arithmetic operations with integers Target Objective 3: Describe and solve situations represented by integers and absolute value I. Review of Multiplication Symbols There are 4 symbols that are generally used to represent multiplication: traditional Ex) 2 x 2 = 4 dot Ex) 3 2 = 6 parentheses Ex) 4(2) = 8 or (4)2 = 8 or (4)(2) = 8 asterisk Ex) 5 * 2 = 10 II. Rules for Multiplying and Dividing Integers -When multiplying/dividing two integers with the same sign (two positives or two negatives), the answer is always positive. Examples: 3 x 6 = 18-5 x (-4) = 20 6(2) = 12 Examples - When multiplying/dividing two integers with different signs (positive and negative), the answer is always negative. Examples: -4 * 6 = x (-8) = -80-3(9) = -27 Ex) 2 x (-12) Ex) 2 (-3) Ex) 3(-5) Ex) (4)(-8) Ex) -4 x (-4) Ex) -3 (-2) Ex) 4 x 5 Ex) 1 8 Ex) 16 (-4) Ex) 72 (-9) Ex) 14 2 Ex) -24 (-8) Ex) -81 (-9) Ex) 36 4 Ex) Ex) 1

2 C. Division Involving Zero When you have zero divided by some number, then it is equal to zero. 0 0 Ex) 0 10 = 0 Ex) 0 (-9) = 0 Ex) = 0 Ex) When you divide a number by zero, then it is equal to not possible. 2 6 Ex) 10 0 = n.p. Ex) -5 0 = Ex) = n.p. Ex) 0 0 *Example: Let s say you have 10 apples. Mrs. Watkins tells you to divide the group of apples up into 0 groups. Is this task possible or impossible? II. Real-Life Applications of Integers Integers are used to describe some of the following real-life situations: Depth (below sea level) / Elevation (above sea level) Football Money (or Stock Market) Temperature Time Weight Winning/ Losing For each situation, look for certain key words that will signal whether you are talking about positive integers or negative integers: Situation Depth/ Elevation or Altitude Positive Integer above ascend Example (Positive Integer) 10 meters above sea level = +10 ascend 10 meters = +10 Negative Integer below descend Example (Negative Integer) 10 meters below sea level = -10 descend 10 meters = -10 Football gain 10 yard gain = +10 loss 10 yard loss = -10 Money profit earn deposit stock went up profit of $10 = +10 earn $10 = +10 deposit $10 = +10 stock went up $10 = +10 debt owe withdraw stock went debt of $10 = -10 owe $10 = -10 withdraw $10 = -10 stock went down $10 = -10 down Temperature above zero 10 F above zero = +10 below zero 10 F below zero = -10 Time after 10 seconds after take off = +10 before 10 seconds before take off = -10 Weight gain gain 10 pounds = +10 lose lose 10 pounds = -10 Winning/ Losing win win by 10 points = +10 lose lose by 10 points = -10

3 *NOTES: You may find some of these key words in different tenses (past or present). If they are in a different tense, they will still have the same meaning. These are most of the key words you will see on the Unit 1 test but not necessarily all of them. You can often use a number line to help you visualize some of these situations. Let s define some new words: - Altitude means how far up / above sea level - Ascend means to rise up - Descend means go down - Profit means make money - Debt or Debit means owe or remove money - Deposit means put money in - Withdraw or Withdrawal means take out money Checks for Understanding 1) Depth is a measure of: 2) Elevation or altitude is a measure of: A) how far down (or how low) you are A) how far down (or how low) you are B) how far up (or how high) you are B) how far up (or how high) you are 3) Below sea level means you are working with: 4) Above sea level means you are working with: 5) To ascend means to: 6) To descend means to: A) go up A) go up B) go down B) go down 7) When you are ascending, you are working with: 8) When you are descending, you are working with: 9) A 10 yard gain in football can be described using: 10) A 10 yard loss in football can be described using:

4 11) Profit means that you: 12) Debt or debit means that you: A) earned or gained more money A) earned or gained more money B) owe (or lost) money B) owe (or lost) money 13) Profit can be described using: 14) Debt or debit can be described using: 15) Deposit means that you: 16) Withdraw means that you: A) you put more money into your bank account. A) you put more money into your bank account B) you took money out of your bank account. B) you took money out of your bank account 17) Deposits can be described using: 18) Withdrawals can be described using: 19) If your stock goes down in the stock market, then you: 20) If your stock goes up in the stock market, then you: A) have earned or made more money. A) have earned or made money B) have lost money. B) have lost money 21) If the temperature is above zero, then you can: 22) If the temperature is below zero, then you can: A) describe it using positive integers A) describe it using positive integers B) describe it using negative integers B) describe it using negative integers 23) If it is 7 seconds after takeoff, you can describe the: 24) If it is 7 seconds before takeoff, you can: A) describe the situation using positive integers A) describe the situation using positive integers B) describe the situation using negative integers B) describe the situation using negative integers

5 Examples Directions: Use a positive or negative integer to describe the following situations. Ex) 15 meters below sea level Ex) lose 10 pounds Ex) 25 degrees above zero Ex) profit of $30 Ex) 22 seconds after take off Ex) 2 seconds before takeoff Ex) deposit $15 into your bank account Ex) withdrawal of $100 from your bank account