Unit 1. Day 3.

What is an integer? Real Irrational π, e, 2 Rational -3.24, 2/3, 6.71, -5/2, … Integers -1, -2, -3, -4, … Irrational π, e, 2 Whole Natural 1, 2, 3, 4, …

Subtracting Integers “The difference” Add/Subtract Large Integers

= 7 − + + + + + + + + − − − − − − − − − − − − − − − Example A: Find 8−15 + + + + + + + + − − − − − − − − − − − − − − − − 1 2 3 4 5 6 7 8 9 10 11 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 -11

Understand subtraction of rational numbers as adding the additive inverse, p - q = p + (-q). 8−5 8 −5 ++++++++ −−−−− subtraction addition

Example B*: Find 7−10 Example C*: Find −8−15

= 3 − + + + + + + + − − − − − − − − − − Example B: Find 7−10 1 2 3 4 5 1 2 3 4 5 6 7 8 9 10 11 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 -11

= 23 − − − − − − − − − − − − − − − − − − − − − − − − Example C: Find −8−15 − − − − − − − − − − − − − − − − − − − − − − − − 1 2 3 4 5 6 7 8 9 10 11 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 -11

4−7 ++++ −−−−−−− 4− 7 ++++ −−−−−−− 4− 7 + ++++ −−−−−−−

= 14 − − − − − − − − − − − − − − − Example D: Find −8− +6 1 2 3 4 5 6 1 2 3 4 5 6 7 8 9 10 11 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 -11

= 10 Example E*: Find −8− +2 − − − − − − − − − − −

Please get out the assignment from last class. Please get out your notes from yesterday. Please complete the quiz, and write your answers in the answer box

I will not, not punch you He is not, not my boyfriend We will not, not go to the movies Dr. Woodfork will not, not say the pledge Michael is not, not my best friend

+ 3 − − 1 2 3 4 5 6 7 8 9 10 11 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 -11

+ 8 − − 1 2 3 4 5 6 7 8 9 10 11 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 -11

+ 9 − − 1 2 3 4 5 6 7 8 9 10 11 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 -11

+ = 3 − − − − − − − − + + + + Example F: Find −7− −4 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 10 11 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 -11

Example G*: Find 2− −8 Example H*: Find −4− +5

+ = 10 + + + + + + + + + + + Example G: Find 2− −8 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 10 11 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 -11

= 9 − − − − − − − − − − Example H: Find −4− +5 1 2 3 4 5 6 7 8 9 10 11 1 2 3 4 5 6 7 8 9 10 11 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 -11

Please get out the assignment from last class. Please get out your notes from yesterday. Please complete the quiz, and write your answers in the answer box

Subtracting Integers “The difference” Add/Subtract Large Integers

What is the difference between Spiderman’s and Batman’s money? Spiderman has $52 Batman has $39 What is the difference between Spiderman’s and Batman’s money? − 52 39 = 13 Example -:

What is the difference between Spiderman’s and Batman’s money? Spiderman has $63 Batman has -$41 What is the difference between Spiderman’s and Batman’s money? − + 63 −41 = 104 Example I:

What is the difference in sales growth between Android and Apple? Android phones saw a 24% increase in sales. Apple iPhones saw a 13% increase in sales What is the difference in sales growth between Android and Apple? − 24 13 = 11 Example -:

What is the difference in sales growth between Android and Apple? Android phones saw a 24% increase in sales. Apple iPhones saw a 8% decrease in sales What is the difference in sales growth between Android and Apple? − + 24 −8 −8 −8 = 32 Example J*:

Please get out the assignment from last class. Please get out your notes from yesterday. Please complete the quiz, and write your answers in the answer box

Subtracting Integers “The difference” Add/Subtract Large Integers

21 5−9 87 ++++++++++++++++++++ ++++++++++ ++++++++++ ++++++++++ ++++++++++ ++++++++++ ++++++++++ ++++++++++ ++++++++++ ++++++++++ ++++++++++ ++++++++++ ++++++++++ ++++++++++ ++++++++++ ++++++++++ ++++++++++ ++++++++++ ++++++++++ +++++++++++++++ −−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−− +++++ −−−−−−−−−

= 5 − = − −27+22 2 7 − 2 2 5 5 Example K: Find −27+22 −−−−−−−−−−−−−−−−−−−−−−−−−−− ++++++++++++++++++++++ −27+22 = − 2 7 − 2 2 5 5

= 24 − = − 4−28 2 8 − 4 2 4 2 4 Example L: Find 4−28 + + + + − − − − −

= 35 − = − −12−23 1 2 + 2 3 3 5 3 5 Example M: Find −12−23 − − − − − −

= 45 + = + 18+27 1 8 + 2 7 4 5 4 5 Example N: Find 18+27 + + + + + + +

= 2 + = + −36+38 3 8 − 3 6 2 2 Example O: Find −36+38 − − − − − − − −

= 6 + = + 34−28 3 4 − 2 8 6 6 Example P: Find 34−28 + + + + + + + + +

− − − − − − − − − − − − − − − − − + + + + + + + + + + + + Example K: −17+12= − 5 − − − − − − − − − − − − − − − − − + + + + + + + + + + + + Example L: 4−28= − 24 + + + + − − − − − − − − − − − − − − − − − − − − − − − − − − − − Example M: −12−23= − 35 − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − Example N: 18+27= + 45 + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + Example O: −36+38= + 2 − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + Example P: 34−28= + 6 + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + − − − − − − − − − − − − − − − − − − − − − − − − − − − −

+ + + − − − − + − + − + Rules 84+36= −56−27= −42+19= 64−48= 1 𝑆𝑎𝑚𝑒 𝑠𝑖𝑔𝑛𝑠:𝐴𝑑𝑑 𝑎𝑛𝑑 𝑘𝑒𝑒𝑝 𝑡ℎ𝑒 𝑠𝑖𝑔𝑛 8 4 + + 3 6 + + 84+36= 120 1 2 1 5 6 − − − −56−27= + 2 7 8 83 3 𝐷𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑡 𝑠𝑖𝑔𝑛𝑠:𝑆𝑢𝑏𝑡𝑟𝑎𝑐𝑡 𝑎𝑛𝑑 𝑘𝑒𝑒𝑝 𝑡ℎ𝑒 "larger" 𝑠𝑖𝑔𝑛 3 1 4 2 − + − −42+19= − 1 9 2 23 3 5 1 6 4 + − + 64−48= − 4 8 16 1 6