Bellringer 7 = 10 = -100 = 5 - 8 = (7^2 – 3^2 + 10^2) / 7 =

Bellringer 7 = 7 10 = 10 -100 = 100 5 - 8 = -3= 3 (7^2 – 3^2 + 10^2) / 7 = 20

Did not have to show work Go Over Homework Textbook page 33 #12-46 even 12-38 just answers Did not have to show work Due Monday 18pts. Do not need to show work

Ch. 1-7 Adding & Subtracting Integers

Ch. 1-7 Adding and Subtracting Integers Steps Big Rocks 1.) Rewrite if needed - Whenever you see two negatives side by side rewrite as one positive. Ex: 7 – (- 8) = 7 + 8 - (-8) = +8 - (-7) = + 7

Ch. 1-7 Adding and Subtracting Integers Steps Big Rocks 1.) Rewrite if needed - Whenever you see two negatives side by side rewrite as one positive. Ex: 7 – (- 8) = 7 + 8 - (-8) means -1(-8) which simplifies to +8 2.) Same Signs – If signs are the same ADD. Add the numbers and keep the sign of whatever they are. 2 + 3 = 5 -2 + -3 = -5 -2 - 3 = -5

Adding Integers - Same Sign We can show this same idea using a number line. 9 -5 5 10 -10 What is 5 + 4? Move five (5) units to the right from zero. Now move four more units to the right. The final point is at 9 on the number line. Therefore, 5 + 4 = 9.

Adding Integers - Same Sign -9 -5 5 10 -10 What is -5 + (-4) = or -5 – 4 = Move five (5) units to the left from zero. Now move four more units to the left. The final point is at -9 on the number line. Therefore, -5 + (-4) = -9.

Ch. 1-7 Adding and Subtracting Integers Steps Big Rocks 1.) Rewrite if needed - Whenever you see two negatives side by side rewrite as one positive. Ex: 7 – (- 8) = 7 + 8 - (-8) means -1(-8) which simplifies to +8 2.) Same Signs – If signs are the same ADD. Add the numbers and keep the sign of whatever they are. Example: 2 + 3 = 5 -2 + -3 = -5 3.) Different Signs – If signs are different subtract. Subtract the numbers and keep the sign of the number with the greatest absolute number. Example: 2 + (-3) = -1 -2 + 3 = 1

Ch. 1-7 Adding and Subtracting Integers Steps Big Rocks 1.) Rewrite if needed - Whenever you see two negatives side by side rewrite as one positive. Ex: 7 – (- 8) = 7 + 8 - (-8) means -1(-8) which simplifies to +8 2.) Same Signs – If signs are the same ADD. Add the numbers and keep the sign of whatever they are. Example: 2 + 3 = 5 -2 + -3 = -5 3.) Different Signs – If signs are different subtract. Subtract the numbers and keep the sign of the greater number. Example: 2 + (-3) = -1 -2 + 3 = 1 3 – 2 = 1 3 – 2 = 1 |3| = 3 |-2| = 2 |-3| = 3 |2| = 2 Positive Negative 2 + (-3) = 1 2 + (-3) = -1

Adding Integers - Different Signs Add the following integers: (-4) + 7. -5 5 10 -10 Start at zero and move four units to the left. Now move seven units to the right. Are the signs the same? The final position is at 3. Therefore, (-4) + 7 = 3. Subtract or add? If Subtract – answer has the sign of the number that has the largest absolute value

Adding Integers - Different Signs -5 5 10 -10 Start at zero and move nine places to the left. Now move three places to the right. The final position is at negative six, (-6). Therefore, (-9) + 3 = -6.

Additive Inverses Two numbers whose sum is zero. -9 + 9 = 0 8 – 8 = 0 rewrite as 8 + (-8) = 0 C + (-C) = 0

Additive Inverse What is (-7) + 7? -5 5 10 -10 10 -10 To show this, we can begin at zero and move seven units to the left. Now, move seven units to the right. Notice, we are back at zero (0). For every positive integer on the number line, there is a corresponding negative integer. These integer pairs are opposites or additive inverses. Additive Inverse Property – For every number a, a + (-a) = 0

Example 1: Add the following integers. a.) 5 + (-2) b.) -19 + -3 c.) -12 + 8 Different Subtract Same Different 3 -22 -4 AV = + Add Subtract AV = - (neg) Example 2: Subtract the following integers. a.) 12 – (-15) b.) -8 – 4 c.) 10 – 12 Same Rewrite - - = + Different Add Same 10 + -12 = -2 12 + 15 = 27 Subtract -8 + -4 = -12 Add AV = - (neg) Example 3: Write an expression for the scenario below and evaluate the answer. a.) An airplane descended 120 ft. and rose 140 ft. Different Subtract -120 + 140 = AV = + 20 ft.

Example 4: Evaluate each expression below by substituting numbers in for the variables. x = 5 y = -6 a.) x – y b.) x + y c.) 2x - y 5 – (-6) = 5 + (-6) 2(5) – (-6) = Rewrite - - = + Different Rewrite - - = + Subtract 10 + 6 5 + 6 = Same Same AV = - (neg.) Add Add = -1 = 11 = 16

Which is equivalent to -12 – (-3)? 12 + 3 -12 + 3 -12 - 3 12 - 3 Answer Now

7 – (-2) = ? -9 -5 5 9 Answer Now

|7| – |-2| = ? -9 -5 5 9 Answer Now

|-4 – (-3)| = ? -1 1 7 Purple Answer Now

Textbook page 41, problem 14-30 even Same Different Different Homework Time Textbook page 41, problem 14-30 even 14-24 write out steps Same Different Different Add Subtract Subtract Positive Negative