 What is a rational number? › A number that can be written as a fraction (form A/B). Ex. a) 7 b) c) √9  Irrational number? › A number that can not be written as a fraction (form m/n, where n≠0). Ex. a) √2 b) ∏ c) 9

Ex1. -6 – 3 Ex2. (-2) + 5 Ex3. (+7) + (-4) = =

 Adding a negative  subtraction 3 + (-7)  › “The negative wins out”  Subtracting a negative  addition 5 - (-3)  *Skills assessment Wednesday

a) b) 3 + (-4) c) (-1) + (-1) d) (-2) + (-4) e) (+9) – (-8) f) (-5) – (-5) = 2 = 3 – 4 = -1 = -1 – 1 = -2 = -2 – 4 = -6 = = 17 = = 0

 Complete Lesson #1

 The top of Currie Mountain is 156m above the St. John River. Mr. Glenwright’s house in Devon is 14m below the St. John River. What is the difference in altitude between the top of Currie Mountain and Mr. Glenwright’s house. a) (-3) + (-7) b) (+6) – (-9) c) (-6) – (-5)+ (-7)

 The top of Currie Mountain is 156m above the St. John River. Mr. Glenwright’s house in Devon is 14m below the St. John River. What is the difference in altitude between the top of Currie Mountain and Mr. Glenwright’s house.

Ex. Does the order of the integers affect the answer? If so, how? a) (+14)- (-12) and (-12) – (+14) b) (-11)+(-9) and (-9)+(-11)

Ex2. Evaluate when x = -2, y = +4, and z = -7 a) x – y – z b) x + y + z c) y – z - x

 A positive multiplied by a positive equals a positive. Ex. 3 x 4 = 12  A positive multiplied by a negative equals a negative. Ex. 4 x (-3) = -12 › “The negative wins out”.  A negative multiplied by a negative equals a positive. Ex. (-4) x (-3) = 12 › “Two negatives make a positive”.

 A new notation: 4x3 can be written as (4)(3) 4x-3 can be written as (4)(-3)  Imagine a “x” symbol in between the brackets.

a) -6 x 8b) 3 (-4) c) (-1)(-1) d) (-2)(-4) e) (+9) (-8) f) (-5)(-5)(-3) = -48 = -12= 1 = 8= -72 = 25 (-3) = -75

 Same rules as multiplication. +/+  + +/-  - -/+  - -/-  +  Reminder – Every fraction is a division Ex. -12 ÷ 4 is the same as = -3

a) -15 ÷ 3b) -32 c) d) (-2)(-4) e) (+2) (-8) f) 4(-2)(-6) 2 (-4)(2) (-2)(3)(-2) = -5 = -4 = 8 2 =4 = = 2 = -8 (-6) -6(-2) = = 4

 Recall: BEDMAS BEDMASBEDMAS rackets : ex (2+3) Xponents : ex 3 2 Ivision ultiply dd ubtract

a) -15 ÷ 3+ 8 b) (-4 +6) x 3 c) -24 ÷ (8 – 20) d) (-2)(-4) e) (+2) (-8) f) 4(-2)(-6) 2 (-4)(2) (-2)(3)(-2) = = 3 = 2 x 3 = 6 = -24 ÷ -12 = 2 = 8 2 =4 = = 2 = -8 (-6) -6(-2) = = 4

a) -15 ÷ 3+ 8 b) (-4 +6) x 3 c) -24 ÷ (8 – 20) d) (3)(-2 + 4) e) ( x 3) x (1+ 2) 2 1-(-1)(2) = = 3 = 2 x 3 = 6 = -24 ÷ -12 = 2 = 3 (2) 1-(-2) = 6 3 = (16 – 2 x 3) x (3) 2 = (16 – 6) x 9 = 10 x 9 = 90 = 2

a) ÷ 3 b) 2(-4 +6) 2 c) -12 ÷ (2 3 ÷ 4) d) Write a math sentence for the following, then solve: Mr. Glenwright is sky-diving, descending at a steady rate of 10m per second for 3 minutes. How far did he descend? Hint – how many seconds in a minute? = = -11 = 2(2) 2 = 2(4) =8 = -12 ÷ (8 ÷ 4) = -12 ÷(2) = -6

d) Write a math sentence for the following, then solve: Mr. Glenwright is sky-diving, descending at a steady rate of 10m per second for 3 minutes. How far did he descend? Hint – how many seconds in a minute? 3 minutes = ?seconds 3 minutes x 60sec/min = 180 seconds 180 sec x 10m/sec = 1800m Mr. Glenwright descended 1800m

d) Write a math sentence for the following, then solve: Mr. Glenwright is sky-diving, descending at a steady rate of 10m per second. How many minutes would it take him to descend 2400m? Hint – how many seconds in a minute?

 Recall: what is a rational number?  A number that can be written as a fraction (form A/B).  Rational numbers may appear in different forms but all of them can be written as a fraction in the form a over b. Rational Number Form a/b Rational Number Form ¾ _ 2 3

Recall: Fractions consist of a… numerator and a denominator The numerator tells us how many fractional “pieces” there are. The denominator tells us what the fraction is “out of” On top On bottom

► NUMERATOR – Top digit of a fraction ► DENOMINATOR – Bottom digit of a fraction ► EQUIVALENT FRACTIONS - are fractions that have the same value. Ex. ► MIXED FRACTION - is a whole number plus a fraction. Ex. ► IMPROPER FRACTIONS - have the numerator part greater or equal to the denominator part. Ex =

You have a pizza with 8 slices and you eat 3 of them, what fraction do you have left? “There are 5 pieces of pizza out of a total of 9 left.”

If the denominator of two fractions are the same, the fraction with the largest numerator is the larger fraction. Ex. Which is greater? or >

You have a pizza with 8 slices and you eat 3 of them, what fraction do you have left? “There are 5 pieces of pizza out of a total of 9 left.”

Which