Number Sense and Numeration Integers Multiplying and Dividing PRESENTED BY MATHMANIAC Mathematics, Grade 8 Integers Multiplying and Dividing Introduction Welcome to today s topic Parts of Presentation, questions, Q&A Housekeeping Your questions Satisfaction meter Downloading slides 1
Integers Multiplying and Dividing What you will learn After viewing this presentation, you will be able to multiply and divide integers using one of two methods: the table method or the like/unlike method. Integers Multiplying and Dividing Agenda Real-life applications Definition and terms Methods to multiply and divide integers Table method Like/unlike method Extensions 2
Integers Multiplying and Dividing Agenda Real-life applications Definition and terms Methods to multiply and divide integers Table method Like/unlike method Extensions Integers Multiplying and Dividing Real-life applications You can apply knowledge of integers to real-life situations, such as temperature, sea level, money, and time. 3
Integers Multiplying and Dividing Agenda Real-life applications Definition and terms Methods to multiply and divide integers Table method Like/unlike method Extensions Integers Multiplying and Dividing Definition and Terms Integer The set of all positive and negative whole numbers and zero. For example, 75, 112, 0, 3, 24 are considered integers, but 1½ and 112.76 are NOT considered integers. 4
Integers Multiplying and Dividing Definitions and Terms Number Lines The whole numbers you use every day that are greater than zero are positive integers. The number line you may be familiar with begins at zero and moves to the right. Integers Multiplying and Dividing Definitions and Terms Integer Number Line The integer number line includes the negative numbers (numbers that are less than zero). 5
Integers Multiplying and Dividing Agenda Real-life applications Definition and terms Methods to multiply and divide integers Table method Like/unlike method Extensions Integers Multiplying and Dividing Agenda Real-life applications Definition and terms Methods to multiply and divide integers Table method Like/unlike method Extensions 6
Integers Multiplying and Dividing Solve: 7 x (3) Operation Symbol for 1 st integer Symbol for 2 nd integer x Result Integers Multiplying and Dividing Solve: 7 x (3) Step 1: Look at your first symbol. It is positive. Look at your second symbol. It is positive. Therefore, you are multiplying a positive by a positive. x 7
Integers Multiplying and Dividing Solve: 7 x (3) Step 1: Look at your first symbol. It is positive. Look at your second symbol. It is positive. Therefore, you are multiplying a positive by a positive. x Integers Multiplying and Dividing Solve: 7 x (3) Step 1: Look at your first symbol. It is positive. Look at your second symbol. It is positive. Therefore, you are multiplying a positive by a positive. The answer is positive. x 8
Integers Multiplying and Dividing Solve: 7 x (3) Step 2: Multiply the numbers as you normally would. 7 x 3 = 21 x Integers Multiplying and Dividing Solve: 7 x (3) Step 1: Look at your first symbol. It is negative. Look at your second symbol. It is positive. Therefore, you are multiplying a negative by a positive. x 9
Integers Multiplying and Dividing Solve: 7 x (3) Step 1: Look at your first symbol. It is negative. Look at your second symbol. It is positive. Therefore, you are multiplying a negative by a positive. x Integers Multiplying and Dividing Solve: 7 x (3) Step 1: Look at your first symbol. It is negative. Look at your second symbol. It is positive. Therefore, you are multiplying a negative by a positive. The answer is negative. x 10
Integers Multiplying and Dividing Solve: 7 x (3) Step 2: Multiply the numbers as you normally would. 7 x 3 = 21 x Integers Multiplying and Dividing Solve: 7 x (3) Step 3: You know your answer is negative and the product is 21. Put these together to get an answer of 21. x 11
Integers Multiplying and Dividing Let s try another question. Solve: 12 x (5) x Integers Multiplying and Dividing Solve: 12 x (5) Step 1: Look at your first symbol. It is negative. Look at your second symbol. It is also negative. Therefore, you are multiplying a negative by a negative. The answer is positive. x 12
Integers Multiplying and Dividing Solve: 12 x (5) Step 2: Multiply the numbers as you normally would. 12 x 5 = 60 x Integers Multiplying and Dividing Solve: 12 x (5) Step 3: You know your answer is positive and the product is 60. Put these together to get an answer of 60. x 13
Integers Multiplying and Dividing Solve: 9/(3) = 3 Now solve for integer division. Integers Multiplying and Dividing Did you notice a pattern? / / / / 14
Integers Multiplying and Dividing Agenda Real-life applications Definition and terms Methods to multiply and divide integers Table method Like/unlike method Extensions Integers Multiplying and Dividing Integers: Like/Unlike Method Solve 28/(7) Step 1: Look at the symbols of the numbers that you are dividing (or multiplying). 15
Integers Multiplying and Dividing Integers: Like/Unlike Method Solve 28/(7) Step 1: Look at the symbols of the numbers that you are dividing (or multiplying). Step 2: Are the symbols the same or are they different? Integers Multiplying and Dividing Integers: Like/Unlike Method Solve 28/(7) Step 1: Look at the symbols of the numbers that you are dividing (or multiplying). Step 2: Are the symbols the same or are they different? If the symbols are the same the answer will be POSITIVE (). If the symbols are different the answer will be NEGATIVE (). 16
Integers Multiplying and Dividing Integers: Like/Unlike Method Solve 28/(7) Step 1: Look at the symbols of the numbers that you are dividing (or multiplying). Step 2: Are the symbols the same or are they different? If the symbols are the same the answer will be POSITIVE (). If the symbols are different the answer will be NEGATIVE (). Step 3: Divide (or multiply) as you normally would and use the sign from step 2. Integers Multiplying and Dividing Integers: Like/Unlike Method Solve 28/(7) Step 1: Look at the symbols of the numbers that you are dividing (or multiplying). 17
Integers Multiplying and Dividing Integers: Like/Unlike Method Solve 28/(7) Step 1: Look at the symbols of the numbers that you are dividing (or multiplying). Step 2: Are the symbols the same or are they different? They are different. Integers Multiplying and Dividing Integers: Like/Unlike Method Solve 28/(7) Step 1: Look at the symbols of the numbers that you are dividing (or multiplying). Step 2: Are the symbols the same or are they different? If the symbols are the same the answer will be POSITIVE (). If the symbols are different the answer will be NEGATIVE (). The answer will be NEGATIVE (). 18
Integers Multiplying and Dividing Integers: Like/Unlike Method Solve 28/(7) Step 1: Look at the symbols of the numbers that you are dividing (or multiplying). Step 2: Are the symbols the same or are they different? If the symbols are the same the answer will be POSITIVE (). If the symbols are different the answer will be NEGATIVE (). Step 3: Divide (or multiply) as you normally would and use the sign from step 2. 28/(7) = 4 Integers Multiplying and Dividing Methods to Solve Equations Let s apply what you ve learned. You read the weather report for today and it says that it will be 16 degrees Celsius in the morning. The report predicts that the high for the day will be double the morning temperature. What is the predicted high? 19
Integers Multiplying and Dividing Methods to Solve Equations You read the weather report for today and it says that it will be 16 degrees Celsius in the morning. The report predicts that the high for the day will be double the morning temperature. What is the predicted high? Step 1: Write out the question. 16 x (2) Integers Multiplying and Dividing Methods to Solve Equations You read the weather report for today and it says that it will be 16 degrees Celsius in the morning. The report predicts that the high for the day will be double the morning temperature. What is the predicted high? Step 2: Look at the symbols. Are they the same or different? 16 x (2) Both symbols are positive, therefore they are the same. 20
Integers Multiplying and Dividing Methods to Solve Equations You read the weather report for today and it says that it will be 16 degrees Celsius in the morning. The report predicts that the high for the day will be double the morning temperature. What is the predicted high? Step 3: Multiply the numbers as you normally would and take the symbol from step 2 (). 16 x (2) = 32 Integers Multiplying and Dividing Agenda Real-life applications Definition and terms Methods to multiply and divide integers Table method Like/unlike method Extensions 21
Integers Multiplying and Dividing Extensions Integer problems involving: Order of operations Square roots and exponents Addition and subtraction Multiplication and division Solving equations Integers Multiplying and Dividing Questions When multiplying integers, if the symbols are the same, will the answer be positive or negative? a) positive b) negative 22
Integers Multiplying and Dividing Questions When multiplying integers, if the symbols are the same, will the answer be positive or negative? a) positive b) negative Integers Multiplying and Dividing Questions When multiplying integers, if the symbols are the same, will the answer be positive or negative? a) positive b) negative The answer is positive whenever both symbols are positive or both are negative. This rule only applies when we are multiplying or dividing two numbers. 23
Integers Multiplying and Dividing Questions When dividing integers, if the symbols are different, will the answer be positive or negative? a) positive b) negative Integers Multiplying and Dividing Questions When dividing integers, if the symbols are different, will the answer be positive or negative? a) positive b) negative 24
Integers Multiplying and Dividing Questions When dividing integers, if the symbols are different, will the answer be positive or negative? a) positive b) negative Whenever the symbols are different, the answer is negative. This rule only applies when we are multiplying or dividing two numbers. Integers Multiplying and Dividing Questions When solving the expression 5y x (10) will the answer will be positive or negative? a) positive b) negative 25
Integers Multiplying and Dividing Questions When solving the expression 5y x (10) will the answer will be positive or negative? a) positive b) negative The answer is positive because both symbols are the same. This rule only applies when we are multiplying or dividing two numbers. Integers Multiplying and Dividing Resources Math League: Integer Help http://www.mathleague.com/help/ integers/integers.htm Math: Integer Lessons http://www.math.com/school/subject1/less ons/s1u1l12gl.html NLVM: Integer Multiplication http://nlvm.usu.edu/en/nav/frames_asid_ 322_g_2_t_1.html?from=grade_g_2.html 26