Unit 1. Day 7.

Quick Review Integer Division

2 3 4 −7 −7 ∙ −7 −8 −8 ∙ −8 ∙ −8 −9 −9 ∙ −9 −9 ∙ ∙ −9 = = = 𝑊ℎ𝑎𝑡 𝑑𝑜𝑒𝑠 𝑡ℎ𝑖𝑠 𝑚𝑒𝑎𝑛 …? 2 −7 −7 ∙ −7 = 3 −8 −8 ∙ −8 ∙ −8 = 4 −9 −9 = ∙ −9 −9 ∙ ∙ −9

− 3 ∙ − 3 − − − ∙ ∙ − ∙

−4 2 −4 −4 ∙ − − 4 2 4 4 ∙

−6 3 −6 −6 −6 ∙ ∙ − − 6 3 6 6 6 ∙ ∙

−4 2 = −4∙4 = − 16 −4 2 = −4∙−4 = + 16 −5 3 = −5∙5∙5 = − 125 −5 3 = Example A: −4 2 = −4∙−4 = + 16 Example B: −5 3 = −5∙5∙5 = − 125 Example C: −5 3 = −5∙−5∙−5 = − 125 Example D:

Example E: − − −1 6 = −1∙−1∙−1∙−1∙−1∙−1 = − 1 = −1

Quick Review Integer Division

+ 8 −5 8−5 Remember … subtraction addition ++++++++ −−−−− We can think of subtraction as addition. + 8−5 8 −5 ++++++++ −−−−− subtraction addition

Division is REALLY a form of multiplication. 20÷4 = 5 1 1 20 1 ∙ 1 4 20 4 2∙2∙5 2∙2 5 1 = = = = 5

Division is REALLY a form of multiplication. 24÷8 = 3 1 1 24 1 ∙ 1 8 24 8 2∙2∙2∙3 2∙2∙2 3 1 = = = = 3

IF *Division is REALLY a form of multiplication. *And these are the rules of integer multiplication + ∙ + =+ − ∙ − =+ + ∙ − =− − ∙ + =− THEN *These rules apply to integer division too! + ÷ + =+ − ÷ − =+ + ÷ − =− − ÷ + =−

− 9 + 6 − 2 + ÷ + =+ − ÷ − =+ + ÷ − =− − ÷ + =− + 1 + 3 − 2 + 8 − 6 Example F: −54÷6 = − 9 𝐼𝑛𝑡𝑒𝑔𝑒𝑟 𝐷𝑖𝑣𝑖𝑠𝑖𝑜𝑛 Example G: 36÷6= + 6 Same signs:+ Different signs:− Example H: 8÷−4 = − 2 + ÷ + =+ − ÷ − =+ + ÷ − =− − ÷ + =− Example I: −5÷−5= + 1 Example J: 12÷4= + 3 Example K: 16÷ −8 = − 2 Example L: −72÷−9= + 8 Example M: −18÷3= − 6

÷

Division 16 ÷ −2

+ ÷ + =+ − ÷ − =+ + ÷ − =− − ÷ + =− Example N: 48 −6 = − 8 𝐼𝑛𝑡𝑒𝑔𝑒𝑟 𝐷𝑖𝑣𝑖𝑠𝑖𝑜𝑛 Example O: 42 6 = Same signs:+ Different signs:− + 7 + ÷ + =+ − ÷ − =+ + ÷ − =− − ÷ + =− Example P: 20 −4 = − 5 Example Q: −25 −5 = + 5 Example R: 32÷4= + 8 Example S: 27 −3 = − 9

+ ÷ + =+ − ÷ − =+ + ÷ − =− − ÷ + =− Example T: −66 −11 = + 6 𝐼𝑛𝑡𝑒𝑔𝑒𝑟 𝐷𝑖𝑣𝑖𝑠𝑖𝑜𝑛 Example T: −66 −11 = + 6 Same signs:+ Different signs:− + ÷ + =+ − ÷ − =+ + ÷ − =− − ÷ + =− Example U: − −18 −6 = − 3

Are the answers the same or different? Why/Why not? −14÷7 14÷ −7 − 14÷7

dividend quotient 16 ÷ −2 =−8 16÷−2=−8 divisor