Multiplication and Division of Integers: Multiplication and Division of Integers Sir Gerald Banaag Math 7 Elizabeth Seton School
Essential Questions: Essential Questions Why are real numbers important? Is it possible to only have one number form? Why or why not? How does the study of real numbers promote understanding of real-life situations? How does the study of the properties of real numbers deepen one’s understanding of mathematical relationships? How does mathematics represent the world? How are mathematical operations related with each other? How do we formulate mathematical generalizations?
What you’ll learn…?: What you’ll learn…? Connect the concept of multiplication and division of signed numbers to real-life. Discover rules in multiplying and dividing signed numbers. Find the product of signed numbers. Find the quotient of signed numbers.
Exploration: Exploration Multiplication Table X 3 2 1 0 -1 -2 -3 3 9 6 3 0 -3 -6 -9 2 6 4 2 0 -2 -4 1 3 2 1 0 -1 0 -1 -2 -3
Exploration: Exploration Multiplication Table X 3 2 1 0 -1 -2 -3 3 9 6 3 0 -3 -6 -9 2 6 4 2 0 -2 -4 1 3 2 1 0 -1 0 0 -1 -3 -2 -6 -3 -9
Exploration: Exploration Multiplication Table X 3 2 1 0 -1 -2 -3 3 9 6 3 0 -3 -6 -9 2 6 4 2 0 -2 -4 1 3 2 1 0 -1 0 0 0 -1 -3 -2 -2 -6 -4 -3 -9 -6
Exploration: Exploration Multiplication Table X 3 2 1 0 -1 -2 -3 3 9 6 3 0 -3 -6 -9 2 6 4 2 0 -2 -4 1 3 2 1 0 -1 0 0 0 0 -1 -3 -2 -1 -2 -6 -4 -2 -3 -9 -6 -3
Exploration: Exploration Multiplication Table X 3 2 1 0 -1 -2 -3 3 9 6 3 0 -3 -6 -9 2 6 4 2 0 -2 -4 1 3 2 1 0 -1 0 0 0 0 0 -1 -3 -2 -1 0 -2 -6 -4 -2 0 -3 -9 -6 -3 0
Exploration: Exploration Multiplication Table X 3 2 1 0 -1 -2 -3 3 9 6 3 0 -3 -6 -9 2 6 4 2 0 -2 -4 1 3 2 1 0 -1 0 0 0 0 0 0 -1 -3 -2 -1 0 1 -2 -6 -4 -2 0 2 -3 -9 -6 -3 0 3
Exploration: Exploration Multiplication Table X 3 2 1 0 -1 -2 -3 3 9 6 3 0 -3 -6 -9 2 6 4 2 0 -2 -4 1 3 2 1 0 -1 -2 0 0 0 0 0 0 0 -1 -3 -2 -1 0 1 2 -2 -6 -4 -2 0 2 4 -3 -9 -6 -3 0 3 6
Exploration: Exploration Multiplication Table X 3 2 1 0 -1 -2 -3 3 9 6 3 0 -3 -6 -9 2 6 4 2 0 -2 -4 -6 1 3 2 1 0 -1 -2 -3 0 0 0 0 0 0 0 0 -1 -3 -2 -1 0 1 2 3 -2 -6 -4 -2 0 2 4 6 -3 -9 -6 -3 0 3 6 9
Guide Questions:: Guide Questions: How did you answer the remaining boxes? How did you know the correct signs to use in solving the items? Can you think of a real-life situation that corresponds to 5 x (-2)?
Connecting to Real Life: Connecting to Real Life The temperature in Moscow in a harsh winter steadily decreased by 2 C for five days daily. If on the first day, the temperature was 0 C, what was the temperature after 5 days?
Guide Questions:: Guide Questions: How do you think can the problem be solved? How do you represent the values in the given problem? Can you think of a real-life situation to represent the product of two negative integers?
Connecting to Real Life: Connecting to Real Life Jeffrey spends ₱ 50.00 each day for transportation from home to school. Thus, his budget for transportation in a month is ₱ 1000.00 (assuming ₱ 50.00 x 20 days = ₱ 1000.00). Due to a number of holidays and class suspensions, there were 6 fewer days on August than usual. What will be the impact of spending on transportation for 6 fewer days on his budget? M Tu W Th F √ √ √ √ X √ √ √ √ √ √ X X X X √ √ X √ √
Guide Questions:: Guide Questions: How do you represent the given information in the problem? What operation will you use to solve the problem? How can you justify the fact that the resulting value is positive and not negative?
Rules in Multiplying Integers: Rules in Multiplying Integers When you multiply two numbers with the same sign , the product is ________. (+)(+) = (+) (–)(–) = (+) When you multiply two numbers with different signs , the product is _________. (+)(–) = (–) (–)(+) = (–) positive negative
Try This. . . : Try This. . . Find the product of the following integers: (– 7)(– 5) = _______ (– 10)(9) = _______ 8 ● 12 = ______ ( – 50 )(4) = _______ (14)( – 1 ) = _______ ( – 6 )( – 4 )( – 2 )( – 1 ) = ______ (10)( – 5 )( – 4 )(8) = ______ (– 3)(2)(–11)(– 4)(5) = _______ 35 -90 96 -200 -14 48 -1320 1600
Integration to Science: Integration to Science Ions are atoms or group of atoms with positive and negative electrical charges. The charges of some ions are given below. Find the total charges of the following: 16 oxide and 6 magnesium 20 phosphate and 18 silver 14 aluminum, 10 chloride, 8 silver Magnesium +2 Aluminum +3 Chloride –1 Silver +1 Oxide –2 Phosphate –3 - 20 - 42 40
On the other hand. . . : On the other hand. . . How do you think the rules in multiplying integers related to the process of dividing integers?
Rules in Dividing Integers: Rules in Dividing Integers When two numbers with the same sign are divided, the quotient is _________ . When two numbers with different signs are divided, the product is _________. = (+) = (+) = (–) = (–) positive negative (+) (+) (–) (–) (+) (–) (–) (+)
Try This. . . : Try This. . . Find the quotient of the following integers: (– 63) 9 = _______ (– 88) (– 8) = _______ (– 50) (– 5) = ______ (125) (– 5) = _______ (– 150) (25) = _______ (– 56) (– 7) = ______ 0 (50) = ______ (– 21) 0 = ________ - 7 11 10 - 25 - 6 8 undefined 0
Formative Assessment: Formative Assessment Dyad Activity : Vocabulary and Concepts. Fill in the blanks to make a true statement. When you multiply numbers with the same sign, the answer is _______. When you multiply numbers with ________ sign, the answer is negative. When you multiply a number by zero, the answer is ________. When two numbers with the same sign are divided, the quotient is always ________. The quotient of two integers with different signs is _______ .
Life Lessons: Life Lessons 1. The Virtue of Sharing Gospel: The Multiplication of Loaves Matthew 14:13-21 Taking the five loaves and the two fish, and looking up to heaven, he said the blessing, broke the loaves, and gave them to the disciples, who in turn gave them to the crowds. They all ate and were satisfied. 2. Being Tact and Respectful “Be mindful of your own words, for it so strong, it can ruin a man’s life and destroy a community”
Summing up: Summing up Can you share to the class some new terms you learned today? Which definition struck you the most? If you can share a topic that you learned today to a friend, what would it be? Why?