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Self-Directed Course: Transitional Math Pre-Algebra Lesson #1: Review of Integers and BEDMAS Before we move into Algebra, we need to review several important terms. 1) Integers: any number that is not a fraction 2) BEDMAS: an acronym that will help remind you that order of operation Brackets, Exponents, Divide or Multiply (whichever comes first), Add or Subtract (whichever comes first) The following exercises that we will work on do not have letters attached to them. To get comfortable working with the concept of BEDMAS, we will just use integers with no variables. Let’s look at following examples. Adding with Positive Integers 14 + 8 = 22 3 + 11 = 14 5 + 7 = 12 –8 + 5 = (–24) + (–12) = Adding with Negative Integers 12 + (–4) = Before we can answer these questions, we have to understand how they work. We have two different types of numbers. One is positive and the other is a negative number. The easiest way to remember if your answer is going to be a positive or negative, is to see which has more charges. Opposite charge will cancel each other out. For example: –4 + 7 In this example, we have 4 negative charges and 7 positive charges. – – – – and + + + + + + + One negative charge will cancel a positive charge, leaving you with 3 positive charges – – – – and + + + + + + + = 3 or +3 (they mean the same thing) 12 + (–4) = There are 12 positive charges and 4 negative charges. Cancel them out, and you will get your answer. 12 + (–4) = 8 –8 + 5 = There are 8 negative charges and 5 positive charges. Cancel them out, and you will get your answer. –8 + 5 = –3 Property of: Portage la Prairie School Division Self-Directed Course: Transitional Math Pre-Algebra (–24) + (–12) = There are 24 negative charges and 12 negative charges. When they are both negative, you add them together and keep the negative sign. (–24) + (–12) = –36 Subtracting with Positive Integers 21 – 4 = 17 8 – 12 = –4 10 – 17 = –7 Notice that with the last two examples we get negative numbers. 10 – 17 = If we break the 17 into 10 and 7 and rewrite the question, we will see: 10 – 10 – 7 = 10 – 10 = 0 0 – 7 = –7 Subtracting with Negative Integers 21 – (–4) = 8 – (–14) = 8 – 17 = The brackets are just used to separate the negative signs. Many students get confused when subtracting negative integers because they are not as comfortable when subtracting and find it easier to add integers. So to make it easier for yourself, rewrite the question so you are adding instead of subtracting. In order to do this, you have to change the last two signs to its opposite. In the end, you will be adding the opposite and get the same answer. 21 – (–4) = 21 + 4 = 25 8 – (–14) = 8 + 14 = 22 Property of: Portage la Prairie School Division 8 – 17 = 8 + (–17) = –9 Self-Directed Course: Transitional Math Pre-Algebra Multiplying Integers When multiplying integers, remember the following chart: + + – – x x x x + – + – = = = = + – – + 2x4=8 8 x (–2) = –16 (–5) x 4 = –20 (–6) x (–3) = 18 Dividing Integers When dividing integers, remember the following chart: + + – – ÷ ÷ ÷ ÷ + – + – 12 ÷ 4 = 3 = = = = + – – + 15 ÷ (–3) = –5 Property of: Portage la Prairie School Division (–6) ÷ 2 = –3 (–28) ÷ (–7) = 4 Self-Directed Course: Transitional Math Pre-Algebra Order of Operation The last part that we will look at is order of Operation. Here we will apply the rule of BEDMAS: Brackets, Exponents, Divide or Multiply (whichever comes first), Add or Subtract (whichever comes first). Always remember to read the question from left to right. Brackets: divide before add Finish brackets Divide (5 + 14 ÷ 2) ÷ 2 (5 + 7) ÷ 2 12 ÷ 2 6 Multiply first Divide (7 x 6 ÷ 2) 42 ÷ 2 21 Brackets: multiply before add Finish brackets Divide (8 x 5 + 8) ÷ 2 (40 + 8) ÷ 2 48 ÷ 2 24 Brackets: multiply before subtract Finish brackets Multiply before adding together Add (24 – 8 x 2) + 8 x 6 (24 – 16) + 8 x 6 8 + 42 50 Property of: Portage la Prairie School Division Self-Directed Course: Transitional Math Pre-Algebra Assignment #1: Review of Integers and BEDMASS Solve the following. 1) 20 – (–7) __________ 18) 17 – 11 __________ 2) 5 + 12 __________ 19) 28 – 6 __________ 3) –8 + (–3) __________ 20) 35 – (–7) __________ 4) 9 + 14 __________ 21) 4 – 20 __________ 5) –7 + (–6) __________ 22) 6 x 11 __________ 6) 3 + 20 __________ 23) 3 x 10 __________ 7) 17 – 6 __________ 24) 7 – (–9) __________ 8) 14 x 15 __________ 25) –6 x (–4) __________ 9) 7 x 17 __________ 26) 5 – 16 __________ 10) 7 x 20 __________ 27) 21 x 4 __________ 11) –8 – 10 __________ 28) –4 + 11 __________ 12) 14 + 14 __________ 29) 17 – 3 __________ 13) –4 – (–5) __________ 30) 8 x (–8) __________ 14) –8 + 13 __________ 31) –3 + (–12) __________ 15) 9 ÷ (–3) __________ 32) 11 – 6 __________ 16) 8 – 10 __________ 33) 3 + (–5) __________ 17) 11 + 6 __________ 34) 5 x 11 __________ Property of: Portage la Prairie School Division Self-Directed Course: Transitional Math Pre-Algebra 1) (9 – 1 + 5) __________ 19) (12 + 5) – 2 __________ 2) (7 + 8 ÷ 8) ÷ 4 __________ 20) (5 ÷ 25) + 7 __________ 3) (6 x 4 ÷ 2) __________ 21) 4 x (2 x 23) ÷ 4 __________ 4) (4 x 4) ÷ 2 __________ 22) (43 + 5 – 2) __________ 5) (24 ÷ 3 ÷ 2) + 9 x 6 __________ 23) (6 x 3) x 2 + 9 __________ 6) 8 – (11 – 2) + 5 x 6 __________ 24) (42 – 23 – 4) __________ 7) (4 x 5) x 6 __________ 25) (53 + 6) x 2 __________ 8) (7 + 8 – 3) __________ 26) 14 – (8 + 22 ÷ 2) __________ 9) (9 x 3 ÷ 3) + 9 + 9 __________ 27) 16 – (3 + 82 x 13) + 6 __________ 10) (6 + 7 – 4) __________ 28) (2 ÷ 6 x 5) __________ 11) (15 – 18) + 9 __________ 29) 18 – (4 + 43) x 6 __________ 12) (13 + 11) x 2 __________ 30) 3 x (23 – 6) x 7 __________ 13) (22 – 3) – 7 __________ 31) (8 x 9 + 6) __________ 14) (6 + 5) x 6 __________ 32) (11 + 14 – 5) __________ 15) (21 x 2 – 7 x 3) __________ 33) 6 x (4 ÷ 12 + 7) __________ 16) (9 + 7 – 5) __________ 34) (4 – 72 + 6 – 3) __________ 17) 12 + (18 – 4 – 7) __________ 35) 22 ÷ (6 ÷ 12) – 5 __________ 18) (6 + 12 x 3) __________ 36) (5 + 12 + 6) __________ Property of: Portage la Prairie School Division