Confidential 1 This is Mrs. Bisanz. I will be your teacher today! OUR LESSON: Multiplying and Dividing Integers Hello William ! Confidential 2 WARM-UP: 1.)(-26) - 9 = (-35) 2.)17 - (-37) = (54) 3.)(-16) - 38 = (-54) 4.) = (-24) Confidential 3 Let's review what we learned in the last lesson. 6/1/4 Multiplying Integers Confidential 4 5 6 We are very familiar with Addition and it is easy for us to add = 12 We can also think of this as three groups of 4 OR 3 x 4 = 12 Let's Get Started! Confidential On a number line, this might look like x 4 = 12 Confidential 8 So, let's look at (-4) + (-4) + (-4) = -12 We know from our Addition Rules that when we add NEGATIVE numbers together, our sum is NEGATIVE. We can also look at this as three groups of (-4) OR 3 x (-4) = -12 Confidential 9 On a number line, this might look like x (-4) = (-12) Confidential 10 But what happens when we multiply a NEGATIVE number by a NEGATIVE number?????? Multiplying by a NEGATIVE number is the opposite of multiplying by a POSITIVE number so our products have opposite signs. If 3 x (-4) = -12 Then (-3) x (-4) = +12 Remember that a "product" is the answer to a multiplication problem. Confidential 11 Rules for Multiplying Integers The product of two integers with the SAME sign is always POSITIVE. The product of two integers with DIFFERENT signs is always NEGATIVE. 6 x 7 = +42 (-5) x (-4) = x (-4) = -32 (-9) x 3 = -27 Confidential 12 Let's try a few! Remember: SAME SIGNS Positive DIFFERENT SIGNS Negative 1.)-6 x 4 = (-24) 2.)10 x -5 = (-50) 3.)(-8) x (-9) = 72 4.)7 x 6 = 42 5.)-11 x 8 = -88 Confidential 13 When we multiply 3 or more numbers together, (-4) x 5 x (-2) =...we begin by multiplying 2 at a time and inserting the appropriate sign. (-20)x (-2) +40 (-4) x 5 x (-2) = +40 Confidential 14 You try some. 6x (-10) x (-2) = 120 (-5) x 7 x 2 = -70 Confidential 15 There is a relationship between DIVISION and MULTIPLICATION 12 6 = 2 2 x 6 = 12 Confidential 16 Let's look at that relationship with POSITIVE and NEGATIVE numbers! DIVISION MULTIPLICATION (-3) X 5 = -15 Remember that a Negative times a Positive number equals a Negative number. (-15) 5 = (-3) And, in division, a Negative divided by a Positive number ALSO equals a Negative number. Confidential 17 Let's look at another relationship! DIVISION MULTIPLICATION (-4) x (-5) = +20 Remember that a Negative times a Negative number equals a Positive number. (-25) (-5) = +5 And, in division, a Negative divided by a Negative number ALSO equals a Positive number. Confidential 18 RULES FOR DIVIDING INTEGERS The quotient of two integers with the same sign is always POSITIVE. The quotient of two integers with different signs is always NEGATIVE. 244 = 6 (-12)(-3) = 4 32(-8) = -4 (-27)3 = -9 Remember that the QUOTIENT is the answer to a division problem Confidential 19 This is very similar to our MULTIPLICATION rule. Signs are the same result is POSITIVE Signs are different result is NEGATIVE Confidential 20 Remember: SAME SIGNS Positive DIFFERENT SIGNS Negative 1.) 18 (-3) = -6 2.) 24 6 = 4 3.) (-35) 7 = -5 4.) (-50)(-5) = 10 5.) 45 (-9) = -5 Let's try a few! Confidential 21 Confidential 22 GAME Click here to play a Game Confidential 23 1) Which expression can be used to find out how many 0.3 meter lengths of rope can be cut from an 8.5 meter length of rope? a.) b.)8.5 0.3 c.)8.5 0.3 d.)8.5 x 0.3 Option b is correct Confidential 24 2)Mr. Morgan bought 2 dozen cans of soda priced at 6 cans for $1.80 and 18 bottles of water priced at 6 bottles for $2.25. What is the total amount she spent, not including tax, on soda and bottled water? Mr. Morgan spent $13.95 Confidential 25 3)A bowler scored between 145 and 160points per game. Which is the best estimate of the total points she scored in 8 games? a)From 950 to 1,150 b)From 1,150 to 1,350 c)From 1,350 to 1,550 d) From 1,550 to 1,750 Option b is correct Confidential 26 1.)(-8) x 12 = )(-6) x (-20) = )2 x (-5) x 4 = )(-7) x (-3) x (-1) = )3 x (-3) x 2 x (-2) = 36 6.)32 x (-4) = 128 Your turnYour turn Confidential 27 7.) 24 (-8) = -3 8.) (-36) (-4) = 9 9.) 200 10 = ) (-120) 12 = ) 45 (-9) = ) (-90) (-6) = 15 Confidential 28 Confidential 29 Confidential 30 Confidential 31 Great Job Today! Practice what you have learned!