* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Unit 3: Rational Numbers Rational Numbers
Survey
Document related concepts
Ethnomathematics wikipedia , lookup
Law of large numbers wikipedia , lookup
Infinitesimal wikipedia , lookup
Georg Cantor's first set theory article wikipedia , lookup
Foundations of mathematics wikipedia , lookup
Mathematics of radio engineering wikipedia , lookup
Location arithmetic wikipedia , lookup
Positional notation wikipedia , lookup
Bernoulli number wikipedia , lookup
Large numbers wikipedia , lookup
Surreal number wikipedia , lookup
System of polynomial equations wikipedia , lookup
Transcript
November 15, 2011 Unit 3: Rational Numbers How many numbers are there in between -35 and -40? Rational Numbers How many numbers can you write between 11 and 12? 11 12 In pairs or by yourself, create a number line from 11 to 12. Write expressions or numbers in the following __ ways and place them on your number line: - A decimal - A repeating number - A sum - A fraction - A product - A difference - A mixed fraction - A quotient November 15, 2011 Rational Numbers Can you do the same thing with negative numbers? -12 -11 - A decimal - A fraction - A mixed fraction - A repeating number - A product - A quotient - A sum - A difference 3.1 What is a Rational Number? Rational Number: - Any number that terminates (stops) or has a repeating pattern - Any number that can be written in the form: 1 ex. 7, 12.2215, -5.8, 0.2, 9 What are some examples of non-rational numbers? The label on a package of frozen cranberries says that it must be stored at a temperature between -18˚C and -22˚C. What are some possible temperatures that they could be stored at? m n where n≠0 November 15, 2011 3.1 What is a Rational Number? -18˚C -22˚C Determine each quotient (evaluate): 12 2 12 -2 -12 2 Based on your answers above, What do you know about -3 2 3 -2 - 3 2 ? Place the following rational decimal numbers on the number line below: 5 0 -5 -12 -2.09 1.2 7 -3.99 24 5 November 15, 2011 Place 3 more numbers on the following number lines: -0.25 -0.26 - 1 1 2 2 Order the following numbers on the number from least to greatest: 2 -2 5 1.13 -3 10 3 7 -3.4 -4 - 2.7 6 Practice P. 101-103 #5, 6a, 8ac, 12cfh, 13, 16ace, 18ac, 20, 25b November 15, 2011 3.2 Adding Rational Numbers Find the answer to the following: 3+7= -3 + 7 = -3 + (-7) = 3 + (-7) = 3.2 Adding Rational Numbers Find the answer to the following: 3 8 + 7 8 = 3 8 + 7 8 = 3 8 +( 7 ) 8 = 3 8 +( 7 ) 8 = November 15, 2011 3.2 Adding Rational Numbers Find the answer to the following: 7 + 2 1 8 = 3 8 7 2 + 1 8 = 3 8 7 ) = ( + 2 1 8 3 8 7 3 1 8 + ( 28) = 3.2 Adding Rational Numbers Strategies for adding rational numbers: - Use a number line: move to the right when adding positive numbers Ex. -4 + 5 move to the left when adding negative numbers Ex. -3 + (-2) November 15, 2011 3.2 Adding Rational Numbers Use common denominators or equivalent fractions when adding positive and negative fractions or: 1 4 + 7 8 = use compatible number lines: 3.2 Adding Rational Numbers 1 4 + ( 87 ) = 2 5 +( 4 10 ) = November 15, 2011 3.2 Adding Rational Numbers Red = Negative Black = Positive What is the largest sum that can be made with two random cards? What is the smallest sum that can be made with two random cards? 3.2 Adding Rational Numbers Homework: p.111 November 15, 2011 3.3 Subtracting Rational Numbers Using any two numbers between -10 and 10 What is the largest number you can make with an addition? What is the smallest number you can make with an addition? What is the largest number you can make with a subtraction? What is the smallest number you can make with a subtraction? 3.3 Subtracting Rational Numbers Red = Negative Black = Positive What is the largest difference possible between two random cards? What is the smallest difference possible? November 15, 2011 3.3 Subtracting Rational Numbers Find the answer to the following: 3-7= -3 - 7 = -3 - (-7) = 3 - (-7) = 3.2 Subtracting Rational Numbers Find the answer to the following: 3 8 - 7 8 = 3 8 - 7 8 = 3 8 -( 7 ) 8 = 3 8 -( 7 ) 8 = November 15, 2011 3.3 Subtracting Rational Numbers Find the answer to the following: 7 2 1 8 = 3 8 7 2 1 8 = 3 8 7 ) = ( 2 1 8 3 8 7 3 1 8 - ( 28) = 3.3 Subtracting Rational Numbers Strategies for subtracting rational numbers: - Use a number line: move to the left when subtracting positive numbers Ex. -1 - 3 move to the right when subtracting negative numbers Ex. -3 - (-2) November 15, 2011 3.3 Subtracting Rational Numbers 1 4 - ( 87 ) = 2 5 -( 4 10 ) = 3.3 Subtracting Rational Numbers Homework: 3cd, 5cd, 7def, 8, 9def, 10, 11, 13cd, 14cd, 15ace November 15, 2011 3.4 Multiplying Rational Numbers If a x b = c Solve the following: a x -b = -a x b = -a x -b = 3.4 Multiplying Rational Numbers Review: Ex: (+) Number x (+) Number = (+) Answer 7x8= (-) Number x (-) Number = (+) Answer -7 x -8 = (+) Number x (-) Number = (-) Answer 7 x -8 = (-) Number x (+) Number = (-) Answer -7 x 8 = November 15, 2011 3.4 Multiplying Rational Numbers Multiplying Fractions: 1. Multiply the numerators together 2. Multiply the denominators together * Tip = if there is a "negative", move it to the numerator () 3 6 X 5 7 11 1 12 3 For mixed fractions, convert them to improper fractions first, then multiply 2 35 X 6 9 1 7 9 1 85 3.4 Multiplying Rational Numbers Fractions should always be written in simplest terms: Common factors can be found at the end or at the beginning: 11 X 7 21 44 ( )( ) 8 3 7 4 November 15, 2011 3.4 Multiplying Rational Numbers Homework: p.127 #3cd, 4cd, 6-10, 11cd, 12cd, 13-15 3.5 Dividing Rational Numbers If a ÷ b = c Solve the following: a ÷ -b = -a ÷ b = -a ÷ -b = November 15, 2011 3.5 Dividing Rational Numbers Ex: Review: (+) Number ÷ (+) Number = (+) Answer 20 ÷ 5 = (-) Number ÷ (-) Number = (+) Answer -20 ÷ -5 = (+) Number ÷ (-) Number = (-) Answer 20 ÷ -5 = (-) Number ÷ (+) Number = (-) Answer -20 ÷ 5 = 3.5 Dividing Rational Numbers Dividing Fractions: 1. Find the reciprocal of the second fraction 2. Multiply * Tip = remember whole numbers can be turned into fractions by putting them over 1 3 6 ÷ 5 7 11 1 ÷ 12 3 For mixed fractions, convert them to improper fractions first 8÷ 3 5 November 15, 2011 3.5 Multiplying Rational Numbers Homework: p.134 #3cdef, 4ef, 6, 8, 9def, 10, 11, 12cdef, 13, 14, 15, 17cd, 18cd, 19 3.6 Order of Operations with Rational Numbers Evaluate: (-8) - 2(24 ÷ (-8))2 Try it with your calculator Try it without your calculator Did you get the same answer? November 15, 2011 3.6 Order of Operations with Rational Numbers Evaluate: ( )( ) ( ) ÷ [ ( )] 1 2 - 1 2 - - 2 3 1 3 + - 3.6 Order of Operations with Rational Numbers Remember our order of operations: B E D M A S 3 12 November 15, 2011 3.6 Order of Operations with Rational Numbers Using your calculator: Key in the expression -2.8 - 1.4 x 4.5 in your calculator Does your calculator follow order of operations from left to right? What is the answer? -9.1 or -18.9 3.6 Order of Operations with Rational Numbers Practice: a) (-3.2) - 0.9 ÷ [0.7 - (-1.2)]2 b) (- ) ÷[ + (- )] x ( ) 2 3 1 4 1 2 1 3 November 15, 2011 3.6 Order of Operations with Rational Numbers Treat 'fraction bars' the same as brackets Ex. -0.3 x 1 4 + (- 21 ) 4 3.6 Order of Operations with Rational Numbers In Wood Buffalo national park, the highest temperature for the month of January was -21.8oC and the lowest temperature was - 31.7oC. What was the mean temperature for that month? Show the order of operations that you will use. November 15, 2011 3.6 Order of Operations with Rational Numbers Homework: p. 140 #3cd, 4cd, 7cd, 8, 9, 10, 11, 12cd, 13 - 17 Challenge: p. 143 #19-21