Math 8



Review of IntegersWhat is an integer? Circle the numbers below that you feel are integers.035-6.518,000-16201217 78.06Define the term integer: Discuss with a partner then list as many examples that you can think of where integers are important!By the time you complete this review of integers you will know how to do all operations with integers including multiplying, dividing, adding and subtracting. Lesson 1: Multiplying and Dividing IntegersIf it is 0°C now and the temperature is dropping 2°C per hour, what was the temperature 4 hours earlier? What will the temperature be in five hours?A rock fell off a 42-metre cliff and landed on the ground after 6 seconds. What distance does the rock travel per second? How far does the rock fall after 5 seconds? Rule 1: To multiply or divide ONLY TWO integers: apply the operation – ignore the signs!-If signs are the same then the answer is positive, e.g. -If signs are different then the answer is negative, e.g.Examples:(a) 10 × - 7 = (b) -5 × -6 = (c) 8 ÷2 = d) 9 ÷ -3 = Rule 2: To multiply or divide any number of integers Multiply and/or divide the numbers (ignore signs) and get your answer. Then count the number of negative signs in the question. Be sure to follow order of operations!-If the number of negative signs is even, the answer is positive. i.e. 2, 4, 6 negative signs -If the number of negative signs is odd, the answer is negative. i.e. 1, 3, 5 negative signsMultiply to find the product: (a) -1 × 2 × -1 = (b) -3 × -4 × -1 = (c) 2 × -3 × 1 × 5 =(d) 10 ×( -2) × 3 × (-1) × 2 =Divide to find the quotient:(a) -45 ÷ (-5) =(b) -800 ÷ 20 = (c) = (d) =(e) =Bonus: --48-12 =-18 ÷9 ×-3 ÷-1= Replace with an integer to make the equation true.(+25) ÷= +5(b) ÷ (-9) = -10÷ (+5) = -12(d) (-63) ÷= +7If 24 times an integer is -312, what is the integer?______________Complete Practice on next page!Multiplication and Division Integer PracticeWithout a calculator, find the product or quotient.(+6) × 8 =(?5) × (+2) =(?7) × (?2) =9 × (?4) =(+2) · (+10) =(?6)(?9) =(?4) · 0 =(+3)(?1) =(?5) × 4 =?27 ÷ 3 =(+60) ÷ 5 =(?48) ÷ (?5) =0 ÷ (?11) =(?99) ÷ (?9) =(+12) ÷ (?2) =(?93) ÷ 3 =0 ÷ 4 =(?3) ÷ 0 = - Multiply7 × 4 · (?1) =(?4) × 0 × (?6) =(?3)(?3)(?3) =5 · (?5) · (?5) =(?3) × (?5) × (+2) × (?1) =(?2) × (?3) × (?3) × (?5) =Find the missing value.(?4) × ____ = 203 × ____ = ?12(?5) × ____ = +30____ × (?7) = 35?4 × ____ = ?32____ × (+5) = ?60(+25) ÷ ___ = +5___ ÷ (?9) = +10(?63) ÷ ___ = ?7___ ÷ (?3) = +7___ ÷ (+5) = ?12___ ÷ (?7) = ?7Lesson 2: Adding and Subtracting Integers66262411952100ADDING INTEGERS line Modelling Activity- using a number line to understand addition of integers.If (-) Go leftIf (+) go righti.e. - 6+ -3= 2+4= -8+12= 9+-7= SAME SIGNRule: If adding two integers with the same sign (both positive or both negative), add the numbers and keep the sign!Examples: (a) 8 + 7 = (b) 33 + 24 = (c) -8 + -7 = (d) -23 + -10 = UNLIKE SIGNSRule: Subtract the two numbers (ignore the signs) and then keep the sign of the larger integer.Examples: (a) -5 + 7 = (b) 8 + -9 = (c) -11 + 4 =(d) 15 + -3 =(e) -13 + 20 = (d) -12 + 12 =SUBTRACTING INTEGERSNumber line Modelling Activity- using a number line to understand subtraction of integers.If (-) Go leftIf (+) go right6 – 10 = -7 – 3 = -1 – (+7) = -3 – 3 = 7 – 4 = 4 – (- 6) =-9 – (-7) = An easy way to think of subtraction is to use temperature:If the outside temperature is -2 ○C and the temperature drops by 10○C the new temperature is ______. Rules to Subtract integersMethod 1: Add the opposite i.e. 2 – 5 = 2 + -5, and 2 – (-5) = 2 +(+5). Then use the rules given for adding integers. Same sign add/diff sign subtract. Keep the sign of the larger!!Method 2: If there is more than one sign between the two numbers being combined. Then the following is true, -2 -(-5) = -2 + 5 and -2 + (-6) = -2 - 6 First make the two signs one. Then compare the sign on each number, same sign add/different sign subtract. Keep the sign of the larger.So -2 +5 = 3, as signs differ (-2 vs +5) so subtract and keep sign of 5 as larger And -2 – 6 = -8, as signs the same (-2, -6 ) so add and keep the signExamples: (two methods)(a) +9 - +4 =(b) +9 – (-4) =(c) -9 - +4 = (d) -9 – (-4) =(e) -8 - 3 =(f) +17 – (-9) = (g) -12 - 15 = (h) -19 – (-23) =Practice: Complete addition and subtraction practice sheetsAdding and Subtracting PracticeArrange in order from least to greatest.15, 0, ?8, +6, ?29, ?1, 0, ?14, 3?9, ?5, 11, ?8, +4+3, ?4, 2, 5, ?1?6, +2, ?10, ?9, 13 5, ?3, +10, ?2, 7Which is greater. Circle your solution.?18 or ?25?9 or +30 or ?7Use the symbols < (less than), > (greater than), or = (equal to) to compare the integers?5 ___ 57 ___ 013 ___ +13?8 ___ ?1861 ___ ?70?25 ___ ?10?14 ___ ?7+8 ___ ?15 ?19 ___ +14?35 ___ ?120 ___ ?18 +21 ___ 21Use the integer line to answer the questions below. Model and write solution!?8 – (?5) = INCLUDEPICTURE "" \* MERGEFORMATINET INCLUDEPICTURE "" \* MERGEFORMATINET ?4 – (?5) = INCLUDEPICTURE "" \* MERGEFORMATINET INCLUDEPICTURE "" \* MERGEFORMATINET ?6 + 2 = INCLUDEPICTURE "" \* MERGEFORMATINET INCLUDEPICTURE "" \* MERGEFORMATINET ?7 – 2 = INCLUDEPICTURE "" \* MERGEFORMATINET INCLUDEPICTURE "" \* MERGEFORMATINET 8 – 12 = INCLUDEPICTURE "" \* MERGEFORMATINET INCLUDEPICTURE "" \* MERGEFORMATINET 3 – (?7) = INCLUDEPICTURE "" \* MERGEFORMATINET INCLUDEPICTURE "" \* MERGEFORMATINET ?8 + (?1) = INCLUDEPICTURE "" \* MERGEFORMATINET INCLUDEPICTURE "" \* MERGEFORMATINET ?4 – (?5) = INCLUDEPICTURE "" \* MERGEFORMATINET INCLUDEPICTURE "" \* MERGEFORMATINET 5 + (?10)= INCLUDEPICTURE "" \* MERGEFORMATINET INCLUDEPICTURE "" \* MERGEFORMATINET Use the positive and negative rules to rewrite and answer the questions below.2 ? (?4) =(+6) + (?3) =(?18) – (?7) =(?10) + (?4) =(+5) + 6 = 11 – (?3) =19 – (+20) =(?15) – (?6) =(?7) – (?7) =(+22) + (?5) =?1 – (?9) =(+6) + 4 =?10 – 10 =16 – (?8) =12 + 7 =14 – (+6) =(+60) + (?10) =(?12) – (?8) =45 – (?3) =(+56) – (?21) =Write an integer for each statement.A gain of $15$200 deposit29°C below10 minutes earlier20 kg heavier Loss of 10 kg$67 in debt40 mm removed Rise of 15°C $40 withdrawal$10 profit $5 reduction25 m longer5 point penalty2 floors downWarm-up – Apply Addition and Subtraction of Integers to Balancing a Bank Account037401500Lesson 3: Applying Order of Operations to Integers (BEDMAS)How many different ways can you evaluate this expression?9 – 2 × 3To ensure everyone gets the same value, we use order of operations:brackets firstapply exponents if any! i.e 32 = 3 x 3 = 9 so 2 x 32 = 2 x 9 =18× / ÷, in order of left to right+ / - , in order of left to rightPart A: Evaluate by applying order of operations(a) [(-6) + (-2)] ÷ (-4) + (-5)(b) (-15) ÷ (-3) – (+4) × (-2)(c) (-6) – (-9) + (-14) ÷ (+2)(d) -8 + (-2) × [4 + (-1)](e) - (4) 2÷ [(+5) – (+6) + (-7)](f) -2 × [5 + (-3)] + (-15)(g) 2 + 4 × -23-6(h) Part B: Solve the problem and apply order of operations!One week in Manitoba, the daily high temperatures were -2°C, -6°C, +1°C, +2°C, -5°C, -8°C, and +4°C. What was the mean daily high temperature for that week?Kim has $175 in her savings account at the beginning of summer. She wants to save money for school. If she puts $100 each week into her account for nine weeks.How much will she have saved by the end of summer? At school she then withdraws $60/week for expenses. How many weeks will it take her to spend all her savings?Complete: Order of Operations with Integers PracticeFill in the blank.If you are solving a problem with integers, you need to decide which ____________ to perform.Some expressions involve more than one operation, then the problem involves __________ of _______________.Number the statements in order according the order of operations.__________ multiply and divide, from left to right.__________ add and subtract, from left to right.__________ brackets.__________ exponentsEvaluate without a calculator.(+7)(+4) – (+5) =-10-2÷-2= 4?5-10-21-2+5=(?6) + (+4) × (?2) =7-34-5= -1 32-6-2-2=12 ÷ (2 × 3) – 2 =12 ÷ 2 × (3 – 2) =8-3?2-33÷11= =-8(2-5)÷(-4)=(–2)(–5) ÷ (–2) + (–7) = 34-7--6=(–7) + (–5) × (+6) ÷(–10) =(-2)3--5=Evaluate without a calculator.==== -32?5-72--9÷-3=5?3--33=Warm-up: Complete the table by applying the appropriate Integer Operationa, ba×ba+ba÷ba-b-8, -2-8×-2=-8-(-2)=12, -612×-6=12-(-6)=-20, 4-20×4=-20-4=-2, 1-2×1=-2-1=2, -12×-1=2-(-1)=Complete Integer Review Assignment (for marks) ................
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