Unit 1 Notes_Number Sense I PDF

Unit 1: Number Sense I Lesson #1 Adding and Subtracting Integers: Adding Integers: When adding…  Two positives – the numbers will always be positive!’ o Example: (+7) + (+4) = (+11) where both are positive, therefore the result is pos...

Unit 1: Number Sense I Lesson #1 Adding and Subtracting Integers: Adding Integers: When adding…  Two positives – the numbers will always be positive!’ o Example: (+7) + (+4) = (+11) where both are positive, therefore the result is positive!  Two negatives – the numbers will always be negative! o Example: (-7) + (-4) = (-11) where both are negative, therefore the result is negative!  A positive and a negative - The sign of the larger number will be the sign of the resulting answer. o Example: (+7) + (-4) = (+3) has more positives, therefore the result is positive! o Example: (+2) + (-5) = (-3) has more negatives, therefore the result is negative! In summary:  If the integers have the same sign, add the integers together and use the same sign to find the sum.  If the integers have a different sign, take the sign of the larger number and subtract the integers to find the sum. Subtracting Integers: When subtracting…  We will use the “Add to the Opposite Method” – Leave the first number, change then subtraction sign in the middle to an addition sign, AND then change the sign of the second numbers to the opposite sign. o Example where the second number is positive: (+5) – (+2) is the same as (+5) + (-2)  both equal +3! o Example where the second number is negative: (-7) – (-4) is the same as (-7) + (+4)  both equal -3! Examples: 1) (+4) + (-6) = 2) (-5) + (-2) = 3) (-9) + (+4) = 4) (+5) + (-9) = 1  5) (+9) - (+3) = 6) (+8) - (-2) = 7) (-3) - (+4) = 8) (-19) - (-3) = 9) (+1.3) – (-1.2) = 10) (-7) - (+4) = 11) (-8) - (-6) = 12) (+2.1) – (-1.2) = 13) (+7) – (-9) + (+6) = 14) (-17) + (+3) – (+1) = Word Problem: 1. a) The temperature in Edmonton on Christmas Day was -21°C. Due to a chinook, on Boxing Day it was 30° warmer. What was the temperature? b) The next day the chinook was gone and the temperature dropped 15°C. What is the new temperature? 2  Assignment 1) (+2) − (−6) = 2) (−4) + (−3) = 3) (−3) − (−6) = 4) (+2) + (−5) = 5) (−7) − (+4) = 6) (+9) − (−8) = 7) (−5) + (−3) = 8) (+1) − (−6) = 9) (+8) + (−2) = 10) (−6) − (−9) = 11) (+4) + (−6) = 12) (+3) − (−7) = 13) (−9) − (+4) = 14) (−8) + (+5) = 15) (−2) − (−1) = 16) (+7) + (−6) = 17) (0) − (−5) = 18) (+7) + (+3) = 19) (+2) − (−9) = 20) (−4) + (−5) = 21) (+9) + (−2) = 22) (−4) − (+9) = 23) (−8) + (+6) = 24) (−1) − (−6) = 25) (−4) − (−4) = 26) (−12) + (−6) = 27) (+9) − (−16) = 28) (+14) + (−6) = 29) (+22) + (−16) = 30) (+8) − (−16) = 31) (+5) + (−16) = 32) (+11) − (−6) = 33) (+43) − (−6) = 34) (+15) + (−17) = 35) (−31) + (−6) = 36) (−27) − (−8) = 37) (+25) + (−7) = 38) (+5) − (−16) = 39) (−20) + (−8) = 40) (+2) − (−18) = 41) It is -27˚C in Whitehorse and -5˚C in Edmonton. What is the difference in temperature? 42) How much debt will Jon be in if he spent $84 on a new video game if he only had $58 in his bank account? 3  Answers: 1) +8 2) -7 3) +3 4) -3 5) -11 6) +17 7) -8 8) +7 9) +6 10) +3 11) -2 12) +10 13) -13 14) -3 15) -1 16) +1 17) +5 18) +10 19) +11 20) -9 21) +7 22) -13 23) -2 24) +5 25) 0 26) -18 27) +25 28) +8 29) +6 30) +24 31) -11 32) +17 33) +49 34) -2 35) -37 36) -19 37) +18 38) +21 39) -28 40) +20 41) -22 ˚C 42) -26 Difference of 22 4 Lesson #2 - Multiplying and Dividing Integers Multiplying/Dividing Integers: When multiplying OR dividing… o A positive times/divided by a positive is a positive! o A positive times/divided a negative is a negative! o A negative times/divided a positive is a negative! o A negative times/divided a negative is a positive! *** Always remember the rules are the same for multiplication and division *** What about a more complex question such as: (−6) × (−2) × (−4) = (−8) × (−2) × (−9) × (−1) = Examples: 1) 4×5= 2) 4 × (−5) = 3) (−40) ÷ 8 = 4) 72 ÷ (−9) = 5) (−3) × 6 = 6) 3 × (−6) = 7) (−6) ÷ (−3) = 8) 6 ÷ (−3) = 9) (−42) ÷ (−6) = 10) (−3) × (−8) = 11) 200 ÷ (−5) = 12) (−136) ÷ (−2) = 13) (−128) ÷ (−4) ÷ 8 = 14) (−42) × (−6) ÷ 3 = 5  Assignment 1) (+3) × (−6) = 2) (−24) ÷ (−3) = 3) (−5) × (−6) = 4) (+25) ÷ (−5) = 5) (−28) ÷ (+4) = 6) (+9) × (−8) = 7) (−30) ÷ (−3) = 8) (+1) × (−6) = 9) (+9) × (−2) = 10) (−54) ÷ (−9) = 11) (+4) × (−2) = 12) (+49) ÷ (−7) = 13) (−42) ÷ (−6) = 14) (−7) × (+5) = 15) (−2) ÷ (−1) = 16) (+8) × (−6) = 17) (0) × (−5) = 18) (+18) ÷ (+3) = 19) (+2) × (−9) = 20) (−40) ÷ (+5) = 21) (+18) ÷ (−2) = 22) (−4) × (+9) = 23) (−12) ÷ (+6) = 24) (−1) × (−6) = 25) (−4) × (−4) = 26) (−12) ÷ (−6) = 27) (+9) × (−6) = 28) (+36) ÷ (−6) = 29) (+42) ÷ (−7) = 30) (+8) × (−7) = 31) (+15) ÷ (−3) = 32) (+11) × (−6) = 33) (+4) × (−6) = 34) (+15) ÷ (−1) = 35) (−3) × (−4) = 36) (−27) ÷ (−9) = 37) (+35) ÷ (−7) = 38) (+5) × (−2) = 39) (−24) ÷ (−8) = 40) (+2) × (−8) = 6  Answers: 1) -18 2) +8 3) +30 4) -5 5) -7 6) -72 7) +10 8) -6 9) -18 10) +6 11) -8 12) -7 13) +7 14) -35 15) +2 16) -48 17) 0 18) +6 19) -18 20) -8 21) -9 22) -36 23) -2 24) +6 25) +16 26) +2 27) -54 28) -6 29) -6 30) -56 31) -5 32) -66 33) -24 34) -15 35) +12 36) +3 37) -5 38) -10 39) +3 40) -16 7 Extra Practice: 1) (+72) ÷ (−18) = 2) (+6) + (−3) = 3) (−9) × (−9) = 4) (−2) − (−21) = 5) (−8) + (+22) = 6) (−3) × (+13) = 7) (+9) − (+11) = 8) (+168) ÷ (+24) = 9) (+11) × (−23) = 10) (−15) − (−13) = 11) (+44) ÷ (+4) = 12) (−3) ÷ (+3) = 13) (−5) − (−15) = 14) (+15) × (−5) = 15) (+13) − (−15) = 16) (+9) + (−20) = 17) (−1) + (−15) = 18) (+8) − (+14) = 19) (−21) + (+4) = 20) (+196) ÷ (−14) = 21) (+10) × (−2) = 22) (+15) × (+22) = 23) (−110) ÷ (−11) = 24) (+7) + (+14) = 25) (−8) × (+23) = 26) (−315) ÷ (+15) = 27) (+12) × (+8) = 28) (+2) + (−7) = 29) (+2) + (+5) = 30) (−13) × (+15) = 31) (−46) ÷ (−23) = 32) (−4) × (+15) = 33) (−17) × (−18) = 34) (−24) ÷ (+4) = 35) (−9) + (+25) = 36) (−25) − (−21) = 37) (−10) + (−15) = 38) (+13) − (−11) = 39) (+3) + (−11) = 40) (+12) × (−8) = Answers: 1) -4 2) +3 3) +81 4) +19 5) +14 6) -39 7) -2 8) +7 9) -253 10) -2 11) +11 12) -1 13) +10 14) -75 15) +28 16) -11 17) -16 18) -6 19) -17 20) -14 21) -20 22) +330 23) +10 24) +21 25) -184 26) -21 27) +96 28) -5 29) +7 30) -195 31) +2 32) -60 33) +306 34) -6 35) +16 36) -4 37) -25 38) +24 39) -8 40) -96 8 Lesson #3 - Rational Numbers 𝑎 When a number can be written in the form, , 𝑏 ≠ 0 it is said to be a rational number (AKA: a 𝑏 fraction). It is important to note that we refer to a as the numerator (top) and b as the denominator (bottom). Types of fractions: Proper Fraction Improper Fraction Mixed Fraction 3 7 1 − 3 4 4 2 Numerator: ___________ Numerator: ___________ Numerator: ___________ Denominator: ___________ Denominator: ___________ Denominator: ___________ Definition: Definition: Definition: Converting Fractions: Examples: 25 2 1. = 2. 4 = 3 3 ______________  ______________ ______________  ______________ Steps: Steps: - Divide the numerator by the - Multiply the denominator by the denominator. number in front of the fraction (if it is - The remainder will be the new negative, then ignore the negative). numerator. - Add that number with the numerator. - The quotient will be the number in - Your result will be your new numerator. front of the fraction. - The denominator stays the same. - The denominator stays the same. 9 *Cannot convert proper fractions to improper fractions and vice versa. Equivalent Fractions: Fractions are equivalent ( = ) when they reduce (divide the numerator and denominator by the same number) to the same form. It is best to reduce an answer to simplest form. Always try to reduce fractions before applying any operations (this will make your calculations easier). 50 5 1 Ex. = =  All representations of “a half.” 100 10 2 Examples: 1. Reduce the following fractions, if possible. 12 24 a) b) 52 28 16 50 c) d) 24 75 −42 8 e) f) 49 6 2. Determine whether the following are equivalent fractions. 5 1 16 64 a) = b) = 55 12 48 192 3. Convert the following from mixed to improper or vice versa. 17 −23 a) b) 5 7 1 2 c) 2 d) 5 8 3 1 −99 e) −4 f) 2 5 10  Adding & Subtracting Fractions:  Fractions must have the same denominator in order to add or subtract. It is EASIER to add or subtract with mixed fractions when they are written in improper format, so be sure to do the conversion, if necessary. Steps:  “Like fractions” are fractions with the same denominator. You can add and subtract like fractions easily - simply add or subtract the numerators and write the sum over the common denominator. Do not add or subtract the denominators.  Ensure your final answer is in simplest (reduced) terms.  OR  Before you can add or subtract fractions with different denominators, you must first find equivalent fractions with the same denominator, like this: - Find the smallest multiple (LCM) of both numbers in the denominator. - Rewrite the fractions as equivalent fractions with the LCM as the denominator (in each fraction, you will have to multiply the numerator and denominator by the same number, keeping in mind that the denominator has to equal the LCM).  Once the fractions are “like fractions” - simply add or subtract the numerators and write the sum over the common denominator. Do not add or subtract the denominators.  Ensure your final answer is in simplest (reduced) terms. Examples: 5 3 2 1 2 1 1. + 2. − 3. + 6 6 5 2 5 6 5 7 5 1 1 1 4. + 5. + 6. − 9 10 8 2 8 7 11  1 2 3 2 24 2 7. 1 +2 8. −2 − 1 9. +1 4 5 7 5 7 3 Assignment Simplify the following fractions to simplest terms: 10 6 18 1) = 2) = 3) = 12 18 36 30 12 63 4) = 5) = 6) = 45 21 77 42 21 128 7) = 8) = 9) = 77 56 256 Convert the following from Improper Fractions to Mixed Fractions: 7 37 25 10) = 11) = 12) = 5 6 9 53 −40 59 13) = 14) = 15) = 7 9 6 83 53 16 16) − = 17) = 18) = 12 12 5 12  Convert the following from Mixed Fractions to Improper Fractions: 2 4 5 19) 3 = 20) 4 = 21) 7 = 5 5 8 4 8 2 22) −7 = 23) 3 = 24) 8 = 15 9 5 2 4 3 25) 7 = 26) −3 = 27) 9 = 7 15 7 Solve the following. Simplify to lowest terms: 5 7 4 2 1 1 28) − = 29) + = 30) − = 10 10 7 7 5 7 3 1 24 1 3 5 31) − = 32) +1 = 33) − + (− ) = 8 2 5 6 7 6 1 2 3 1 3 1 34) 1 +3 = 35) −2 − −2 = 36) 1 − 2 = 2 5 8 2 4 7 13  5 5 3 3 1 5 37) + = 38) −2 − 4 = 39) − − = 8 6 5 7 3 7 1 1 2 5 7 4 40) −2 + 3 = 41) − = 42) − (− ) = 4 6 5 9 8 5 2 7 2 2 1 3 1 1 43) + = 44) 3 +2 −1 = 45) −4 + 2 − (−3 ) = 3 6 5 3 2 5 3 2 Answers: 5 1 1 2 4 9 6 3 1 2 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 1 6 3 2 3 7 11 11 8 2 5 1 7 4 4 5 11 5 1 17 24 11) 6 12) 2 13) 7 14) −4 15) 9 16) −6 17) 4 18) 3 19) 20) 6 9 7 9 6 12 12 5 5 5 61 −109 35 42 51 −49 66 −1 6 2 21) 22) 23) 24) 25) 26) 27) 28) 29) 30) 8 15 9 5 7 15 7 5 7 35 −1 29 11 9 1 −11 11 1 1 2 31) 32) 5 33) −1 34) 4 35) 36) 37) 1 38) −7 39) −1 40) 1 8 30 42 10 8 28 24 35 21 3 7 27 5 17 7 41) − 42) 1 43) 1 44) 4 45) 1 45 40 6 30 30 14  Lesson #4 - Multiplication and Division of Rational Numbers * You do NOT have to have the same denominator in order to multiply or divide fractions. * Remember that the best way to multiply or divide is to change the fraction into improper format. Multiplication of Fractions: Steps:  When multiplying fractions, only multiply the numerators with the numerators and the denominators with the denominators.  Ensure your final answer is in lowest (reduced) terms. Consider the following: Method 1: Simply at the end Method 2: Cross-Simplification 5 36 5 36 × × 6 55 6 55 5 × 36 *5 and 55 can be divided by 5! 6 × 55 *6 and 36 can be divided by 6! 180 1 6 330 × 1 11 180 ÷ 30 1×6 330 ÷ 30 1 × 11 6 6 11 11 *Cross-simplification can ONLY be used for multiplication problems! 1. Evaluate the following. Ensure your final answer is in lowest terms! 2 1 3 3 12 1 a) × = b) − ×1 = c) ×1 = 7 6 5 12 20 4 15 Division of Fractions: Think about this: We know that 6 divided by 2 is 3, because there are 2 groups of three in six. So, what is 6 divided by ½? Steps:  Change the division sign to multiplication and take the reciprocal (flip the fraction) of ONLY the last fraction.  Repeat the steps for multiplying fractions.  Ensure your final answer is in lowest (reduced) terms. 2. Evaluate the following. Ensure your final answer is in lowest terms! 1 5 3 7 2 3 a) ÷ = b) ÷ = c) 1 ÷ −2 = 9 6 8 8 3 4 2 7 3 7 d) ÷ = e) ÷ = 5 6 4 8 Fraction Word Problems (All Operations) 3 1 1. Nancy created a mixture using of a cup of sugar and cup of cinnamon to add to 4 2 1 some hot apple cider. If Nancy uses of a cup per serving of hot apples cider, how 16 many people can she serve? 16  3 7 2. The fuel tank of Andy’s car holds 8 gallons of gas. If Andy’s car uses of a gallon 4 8 of gas to get to work in the morning, how many round trips to work and home can he make using the gas he has remaining Assignment 1) Use either ˃ or ˂ to write a true statement. 3 7 2 3 a) ___ b) ___ 5 5 9 7 5 3 1 1 c) ___ d) 2 ___ 2 4 2 4 5 2) Simplify the following fractions. 4 12 48 54 a) = b) = c) = d) = 18 27 56 81 3) Change from mixed fractions to an improper fraction. 4 3 a) 5 = b) −2 = 7 4 4) Change from improper fractions to mixed fractions. 11 27 a) = b) = 4 2 17 5) Solve. 9 1 3 1 a) × = b) × = 10 3 11 2 5 4 2 5 c) × = d) − × (− ) = 6 3 7 6 1 1 1 2 e) 2 × 2 = f) ×2 = 2 4 4 9 1 3 2 2 g) 1 ×3 = h) × (− )= 10 4 3 11 3 9 5 3 i) −4 × 1 = j) −2 × 1 = 5 11 7 5 2 2 1 3 2 1 k) × × = l) −2 × 2 × (−3 ) = 5 3 2 5 3 2 6) Solve. 5 10 4 10 a) ÷ = b) ÷ = 8 7 3 3 1 5 1 1 c) ÷ = d) −1 ÷ = 6 9 3 2 18  1 2 13 5 e) 1 ÷ = f) ÷ = 4 9 7 7 Answers: 1a. ˂ b. ˂ c. ˂ d. ˃ 2 4 6 2 2a. b. c. d. 9 9 7 3 39 −11 3 1 3a. b. 4a. 2 b. 13 7 4 4 2 3 3 1 5 5 5 5a. b. c. 1 d. e. 5 f. 10 22 9 21 8 9 1 −4 4 12 2 4 g. 4 h. i. −8 j. −4 k. l. 24 8 33 11 35 15 15 7 2 3 2 5 3 6a. b. c. d. −2 e. 5 f. 2 16 5 10 3 8 5 19 Fractions Mixed Assignment: 1) Solve and simplify: 1 5 2 1 a) + = b) − = 6 9 3 2 27 2 15 5 c) × = d) ÷ = 28 9 7 14 8 21 15 5 e) − × = f) (− )÷ = 9 16 16 2 3 15 1 2 g) ÷ = h) 4 + 3 = 4 8 6 5 5 11 1 7 i) + = j) (−3 ) − = 8 12 4 9 1 5 12 20 k) 3 − (− ) = l) 15 × 9 = 6 3 2 1 1 5 m) −3 × 5 = n) 2 + = 5 3 9 7 1 7 1 2 o) 5 ÷ = p) −1 = 4 9 6 9 20  4 5 16 15 q) + = r) × = 11 2 25 12 7 2 7 5 s) − (− ) = t) 6 ÷ = 2 6 5 27 49 1 2 u) × = v) 3 + = 7 18 5 9 5 25 8 3 w) ÷ = x) × (− )= 6 9 9 14 2 5 1 2 y) 5 + 3 = z) − − (− ) = 3 6 8 9 2) Solve each word problem: 7 1 a) Sabrina has 3 yards of fabric. She needs 1 yards to make costumes for the school play. How 8 4 many costumes can she make? 21  5 8 b) Out of 18 basketball shots, Carol made a basket of the time and Dana made a basket of the 6 9 time. Who had more points? How many more compared to the other player? 2 c) Eric watched a YouTube video that featured a Filipino chicken recipe. He bought 5 pounds of 3 1 chicken from the local store. If the recipe called for 2 pounds of chicken, how many pounds of 4 chicken remain unused? d) Amy took an online practice test and attempted two-thirds of the total number of questions. If one-sixth of the questions attempted were incorrect, what fraction of questions did she get right? 22 Answers: 1. 13 1 1 3 2 17 17 6 3 13 a) b) c) d) e) −1 f) − g) h) 7 i) 1 j) 2 18 6 14 6 8 5 30 24 36 5 7 2 52 3 1 19 4 17 7 k) 4 l) 1 m) −18 n) 2 o) 6 p) −1 q) 2 r) s) 1 t) 6 9 15 63 4 18 22 5 30 15 1 19 3 4 1 7 u) 10 v) 3 w) x) − y) 9 z) 2 45 10 21 2 72 2. a) 3 costumes. 5 b) 15 & 16: Dana had one more shot than Carol. c) 3 of chicken. 12 1 d) of the questions. 2 23 Lesson #5 – Introduction to Exponents Exponents are an abbreviated form of multiplication. 43 For example: 43 = 4 × 4 × 4 = 64 Important Vocabulary Power: _____________________________________________________________________ Base: _____________________________________________________________________ Exponent: __________________________________________________________________ Examples: Expand and evaluate each of the following: a) 42 = b) −42 = c) (−4)2 = d) 61 = e) 25 = f) 53 = g) 23 + 102 = h) 103 − 34 = i) −24 + 33 = j) 5.22 = k) 3.162 = l) −53 = 3 2 m) ( ) = 2 3 n) ( ) = o) 0.54 = 4 3 p) 70 = q) −25 = r) (−0.7)2 = 24  Assignment Evaluate: 1) (4) × (−2) × (−3) = 2) (−3) × (−2) × (−5) = 3) (6) × (2) × (−3) = 4) 32 = 5) −32 = 6) (−3)2 7) 62 = 8) −62 = 9) (−6)2 = 10) 53 = 11) −53 = 12) (−5)3 = 13) 40 = 14) 23 + 1 = 15) 8 − 32 = 16) 5 + 23 = 17) 23 − (−1) = 18) 42 − 7 = Answers: 1) 24 2) -30 3) -36 4) 9 5) -9 6) 9 7) 36 8) -36 9) 36 10) 125 11) -125 12) -125 13) 1 14) 9 15) -1 16) 13 17) 9 18) 9 25 Lesson #6 - Order of Operations When solving multi-step problems it is important to follow the rules of BEDMAS. Brackets – Not always obvious! For instance, the numerator/denominator of a complex fraction. Exponents - Watch the signs. Division These two steps are interchangeable - work left to right Multiplication - Addition Subtraction Examples: Evaluate 1) 2(7 − 4) + 6 2) 3 + 2 × 42 − 7 3) 32 ÷ 3(2 + 1) 4) (5 − 2)2 − (3 × 27 ÷ 9)2 4+32 4×0+7+2 5) 6) +1 3×5+(−2) 15÷5 7) 18 ÷ 3 + 72 ÷ 12 + (4 + 2)2 8) (32 + 60 ) ÷ 51 26  Assignment 1) 7 + 2 × 5 2) 32 − 2 × 5 3) 7 − (2 × 4)2 4) 18 − 12 ÷ 4 − 2 5) 54 ÷ 6 ÷ 3 × 2 6) (−5 − 3) − 2 7) (35 ÷ 32 )(31 × 32 ) 8) (5+3)(6) 9) 5 + 3(24 − 12)2 (6+2)(3) 10) 9 − 2 + 8 ÷ 4 11) 5 × 10 − (7 + 3) ÷ 5 12) −7 × 2 − 5 + 8 13) 24 ÷ 22 × 25 ÷ 23 2 14) ((−6) − 4) ÷ (−4) 15) ((−9) + 8) × 52 16) 17) 18) (−2)2 − 6 + (−9) × (−3) (−2)3 ÷ 4 + (−6) − (−7) (−7) × ((−8) − (−6) + 8 ÷ 23 ) 27  Answers: 1) 17 2) -1 3) -57 4) 13 5) 6 6) -10 7) 729 8) 2 9) 53 10) 9 11) 48 12) -11 13) 16 14) -25 15) -25 16) 25 17) -1 18) 7 28 Lesson #7 - Substitute & Evaluate Often in math and the sciences, you will need to substitute values into an equation to determine an answer. This is called substitution (where we substitute a number for a variable) and evaluate (determine an answer to an expression or equation). ***ALWAYS use brackets when substituting*** When might this be important? Example: Determine the value of y if x = 3, given the function below. 𝑦 = 𝑥 2 + 2𝑥 + 5 What about when 𝑥 = −3? Examples: Substitute and evaluate 1. 𝑥 = −3, 𝑦 = 4, 𝑧 = −9 a. 𝑥 + 𝑦 + 𝑧 b. 𝑥 − 𝑦 − 𝑧 2 2. 𝑎 = −2, 𝑏 = 4, 𝑐 = −4 a. 𝑎𝑏𝑐 b. −4𝑎𝑏 3. 𝑚 = −2, 𝑛 = −1 a. – 𝑚𝑛 b. −𝑚2 𝑛3 29 4. Complete the table of values: 1 a) 𝑦 = 𝑥 − 1 b) 𝑦 = 2𝑥 + 5 2 x y x y -2 -2 -1 -1 0 0 1 1 2 2 30  Assignment Evaluate 1) 𝑎 = 2, 𝑏 = −2, 𝑐 = 7 a) 𝑎 + 𝑏 − 𝑐 b) 𝑐 − 𝑏 − 𝑎2 2) 𝑟 = −2, 𝑠 = −4, 𝑡 = 6 a) 𝑟 + 𝑠𝑡 b) −5𝑟𝑡 − 𝑠 3) 𝑚 = 3, 𝑛 = −4 a) – 𝑚𝑛 b) −𝑚 2 𝑛3 4. Complete the table of values: a) 𝑦 = −3𝑥 b) 𝑦 = 5𝑥 − 3 x y x y -2 -2 -1 -1 0 0 1 1 2 2 31 c) 𝑦 = 2𝑥 2 + 5 d) 𝑦 = −2𝑥 + 7 x y x y -10 -10 -5 -5 0 0 5 5 10 10 2 1 5 e) 𝑦 = 𝑥 + 1 f) 𝑦 = 𝑥 + 3 3 6 x y x y -2 -2 -1 -1 0 0 1 1 2 2 g) 𝑦 = 2𝑥 2 + 3𝑥 − 5 x y -2 -1 0 1 2 32  Answers: 1) a) -7 b) 5 2) a) -26 b) 64 3) a) 12 b) 576 4) a) 6, 3, 0, -3, -6 b) -13, -8, -3, 2, 7 c) 205, 55, 5, 55, 205 d) 27, 17, 7, -3, -13 1 1 5 7 1 1 5 7 3 e) − , , 1, , f) , , , , 3 3 3 3 6 2 6 6 2 g) -3, -6, -5, 0. 9 33 Extra Practice – Order of Operations and Substitution Assignment 1) 7+2×5 2) 32 − 2 × 5 3) 7 − (2 × 4)2 4) 18 − 12 ÷ 4 − 2 5) 54 ÷ 6 ÷ 3 × 2 6) (−5 − 3) − 2 7) (35 ÷ 32 )(31 × 32 ) (5+3)(6) 9) 5 + 3(24 − 12)2 8) (6+2)(3) 10) 9 − 2 + 8 ÷ 4 11) 5 × 10 − (7 + 3) ÷ 5 12) −7 × 2 − 5 + 8 13) 24 ÷ 22 × 25 ÷ 23 2 14) ((−6) − 4) ÷ (−4) 15) ((−9) + 8) × 52 16) (−2)2 − 6 + (−9) × (−3) 17) (−2)3 ÷ 4 + (−6) − (−7) 18) (−7) × ((−8) − (−6) + 8 ÷ 23 ) 34 Answers: 1. 17 2. -1 3. -57 4. 13 5. 66 6. -10 7. 729 8. 2 9. 53 10. 9 11. 48 12. -11 13. 16 14. -25 15. -25 16. 25 17. -1 18. 7 35