Chapter 4

 integer  negative sign  opposites  absolute value

 4.1 Integers & the Number Line  4.2 Adding Integers on the Number Line  4.3 Adding Integers Using Addition Rules  4.4 Subtracting Integers  4.5 Multiplying Integers  4.6 Dividing Integers  4.7 Integers & Order of Operations  4.8 Comparing Positive & Negative Numbers

4.1

Integers = made up of two categories Positive numbers (or integers) Negative numbers (or integers) Negative numbers Positive numbers

-4 and

-2, 4, 0, 3,

You are starting a part-time car washing business. Your profits for six months are shown below. Use a number line to order these profits from least to greatest. Which profit is least? MonthAprilMayJuneJulyAugustSeptember Profit(s)

 Four and negative four are the same distance from one. True or False?  Complete the statement: On a horizontal number line, greater numbers are to the ___ of lesser numbers

Order the integers from least to greatest  -3, -8, 3, -9, 0  -3, 9, -8, 12, 5,

4.2

Find the sum 2 + (-5) Method: start at 0 then move 2 units to the right. Then move 5 units to the left Solution: Your final position is -3. Therefore 2 + (-5) =

Find the sum Method: start at 0 then move 6 units to the left. Then move 8 units to the right Solution: Your final position is 2. Therefore =

Find the opposite of the number 11  The opposite of 1 is -1. Both are 1 unit from zero.  -7  The opposite of -7 is 7. Both are 7 units from zero. 00  The opposite of 0 is

Find the sum of Start at 0. Move 3 units to the left. Then move 3 units to the right. Your final position is 0. Therefore =

 7 + (-3)   

 -9 + (-5)  -4 + (-11)  

4.3

Absolute value = the distance of the number from zero l a l = a Find the absolute value of

To add two integers with the same sign, add their absolute values and write the common sign. To add two integers with different signs, subtract the lesser absolute value from the greater absolute value and write the sign of the integer with the greater absolute value. The sum of zero and any integer is the integer.

Positive + Positive = Positive Negative + Negative = Negative Sum of a negative and a positive number: subtract and use the sign of the larger number.

(-7) (-9) (-3) (-3) 5 + 4

(-7) + (-2) (-2) (-24) (-10) 13 + (-2)

4.4

3-6? To find the difference 3 – 6, begin at 0. Move 3 units to the right. Then move 6 units to the left. Your final position is

6 – (-4)? To find the difference 6 – (-4), begin at 0. Move 6 units to the right. Then move 4 units to the left. Your final position is

To subtract an integer (b) from an integer (a), add the opposite of b to a. a – b = a + (-b) Example: = 6 + (-8) = -2

Negative - Positive = Negative Positive - Negative = Positive + Positive = Positive Negative – Negative = Negative + Positive = Use the sign of the larger number and subtract (change double negatives to a positive)

(-5) – 5 = 5 – (-3) = (-7) – (-3) = (-3) – (-5) = (-5) = = (-7) + 3 = (-3) + 5 =

-4 – (-12) 0 – (-9) -100 – (-50) 150 –

Evaluate the expression when x = 6 and when x = -1 x – 5 0 – x 12 – x -4 – x x

Suppose you start at 2600 feet above sea level. Then you descend into Death Valley until you reach an elevation of 200 feet below sea level. Describe the change in your elevation.

Find the difference of -200 and final elevation – initial elevation = change in elevation

If Embarcadero Station has an elevation of -20 feet, by how much do you change your elevation to reach the deepest point in the tunnel at -135 feet?

4.5

The product of two positive integers is positive The product of two negative integers is positive. The product of two integers with different signs is negative The product of an integer and 0 is 0

Positive x Positive = Positive Negative x Negative = Positive Positive x Negative = Negative Negative x Positive = Negative

3 x 2 (-2)(-8) (-3)4 3(-5) (3)(3)

(-10)(-5)(8) 6(5)(-1)(2) (-30)(-5) 2(-4)(-9) 17(-3)

4.6

The quotient of two positive integers is positive. The quotient of two negative integers is positive. The quotient of two integers with different signs is negative. The quotient of 0 and a nonzero integer is 0. The quotient of a nonzero integer and 0 is undefined.

12/4 (-12)/(-2) (-12)/3 76/(-4) -45/(-9)

Find the average: -10, -6, 7, -13, 5, 10, , 1, 0, -1, -2, 1 -2, -4, 2, -1, -2, -3, 2, 0, , -17, -6, 4, 10, 18

4.7

 Evaluate expressions inside grouping symbols  Parentheses  Evaluate powers  Exponents  Multiply and divide from left to right  x and ÷ always →  Add and subtract from left to right  + and - always →

a(b – c) = ab – ac Example: 3(2-6) = 3(2) – 3(6) -a(b + c) = -ab – ac Example: -6(5+2) = -6(5) – 6(2)

48 ÷ (-6) + 3 Twice the difference of -7 and 16 54/(-6) /((-3)(4)) (-8 + 2)/(-3 + 2)

Evaluate the expression when x = -4 & y = 2 x 2 – (-6) 8/xy (x-y)/2

x 3 – (-5) + 12 x (-6) ÷ (-3) 9 + (-8) – (-8) x (-4) – (-18) ÷ ÷ 3

4.8

Compare: ½ / /

Put in order least to greatest: 0, ½, -3, -3.2, - 16 / , -7, - 7 / 2, -1 3 / 4, , 26 / 9, -2 1 / 11, -0.1, - 1 / 8