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1 Lesson The Order of Operations

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2 Lesson The Order of Operations California Standard: Algebra and Functions 1.2 What it means for you: Key Words: Use the correct order of operations to evaluate algebraic expressions such as 3(2 x + 5) 2. You’ll learn about the special order to follow when you’re deciding which part of an expression to evaluate first. Parentheses Exponents PEMDAS

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3 Lesson The Order of Operations When you have a calculation with more than one operation in it, you need to know what order to do the operations in. There’s a set of rules to follow to make sure that everyone gets the same answer. It’s called the order of operations — and you’ve seen it before in grade 6. E.g. if you evaluate the expression by doing… So the order you use really matters = 20“add 7 to 3 and multiply the sum by 2.” = 13 “multiply 2 by 3 and add 7,” …you’ll get a different answer from someone who does…

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4 Finally follow any addition and subtraction instructions from left to right. First do any operations inside parentheses. Multiplication or Division Addition or Subtraction Parentheses ()[]{} x2 y7x2 y7 ×÷×÷ +–+– The Order of Operations is a Set of Rules Lesson The Order of Operations An expression can contain lots of operations. When you evaluate it you need a set of rules to tell you what order to deal with the different bits in. Order of operations — the PEMDAS Rule ExponentsThen evaluate any exponents. Next follow any multiplication and division instructions from left to right.

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5 Divide first, then multiply.9 ÷ 4 3 Lesson The Order of Operations When an expression contains multiplication and division, or addition and subtraction, do first whichever comes first as you read from left to right. Following these rules means that there’s only one correct answer. Use the rules each time you do a calculation to make sure you get the right answer. Multiply first, then divide – 3 9 – ÷ 3 Add first, then subtract. Subtract first, then add.

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6 Finally follow any addition and subtraction instructions from left to right. First evaluate anything grouped by parentheses, fraction bars or brackets Multiplication or Division Addition or Subtraction Grouping ()[]{} x2 y7x2 y7 ×÷×÷ +–+– You Can Also Use GEMA For the Order of Operations Lesson The Order of Operations GEMA is a nother way to remember the order of operations : ExponentsThen evaluate any exponents. Next follow any multiplication and division instructions from left to right. You can use either PEDMAS or GEMA — whichever one you feel happier with.

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7 Example 1 Lesson The Order of Operations What is 8 ÷ ? Solution 8 ÷ Finally do the addition to get the answer Then the multiplication Do the division first There are no parentheses or exponents = 11 = = You do the division first as it comes before the multiplication, reading from left to right. Solution follows…

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8 Guided Practice Lesson The Order of Operations Solution follows… Evaluate the expressions in Exercises 1– – – – – 10 ÷ ÷ ÷

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9 Always Deal with Parentheses First Lesson The Order of Operations When a calculation contains parentheses, you should deal with any operations inside them first. You still need to follow the order of operations when you’re dealing with the parts inside the parentheses. 2(4 5 2 ) + 1 2(4 25) + 1 2(100) + 1

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10 Example 2 Lesson The Order of Operations What is 10 ÷ 2 (10 + 2)? Solution The order of operations says that you should deal with the operations in the parentheses first — that’s the P in PEMDAS. = 60 = 5 12 Finally do the multiplication Do the addition in parentheses= 10 ÷ 2 12 Then do the division You do the division first here because it comes first reading from left to right. 10 ÷ 2 (10 + 2) Solution follows… First write out the expression

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11 Guided Practice Lesson The Order of Operations Solution follows… Evaluate the expressions in Exercises 7– – (4 + 3) ÷ (7 – 5) (2 + 4) – (8 ÷ 4) (18 ÷ 3) + ( ) – (4 + 2 – 3) 12. (5 – 7) (55 ÷ 11) (16 ÷ 2) –10 48

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12 PEMDAS Applies to Algebra Problems Too Lesson The Order of Operations The order of operations still applies when you have calculations in algebra that contain a mixture of numbers and variables. Do the addition in parentheses, then the multiplication 3 (2 + 4) a (2 + 4) 3 ( b + 4) Do the addition in parentheses, then the multiplication

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13 Example 3 Lesson The Order of Operations Simplify the calculation k (5 + 4) + 16 as far as possible. Solution = 9 k + 16 Do the addition in parentheses= k Then the multiplication k (5 + 4) + 16First write out the expression Solution follows…

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14 Guided Practice Lesson The Order of Operations Solution follows… Simplify the expressions in Exercises 15–20 as far as possible x ( y – 2) (4 2) t a 4 – ÷ (3 + 2) – r 20. p + 5 (–2 + m ) x 3 y – 6 8 t a – r p – m

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15 Independent Practice Lesson The Order of Operations Solution follows… 1. Alice and Emilio are evaluating the expression Their work is shown below. Explain who has the right answer. Alice = 11 4 = 44 Emilio = = 29 Emilio has the right answer because he has used the correct order of operations: he has done the multiplication before the addition.

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16 Independent Practice Lesson The Order of Operations Solution follows… The local muffler replacement shop charges $75 for parts and $25 per hour for labor. 2. Write an expression with parentheses to describe the cost, in dollars, of a replacement if the job takes 4 hours. 3. Use your expression to calculate what the cost of the job would be if it did take 4 hours (4 25) $175

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17 Independent Practice Lesson The Order of Operations Solution follows… 8. Paul buys 5 books priced at $10 and 3 priced at $15. He also has a coupon for $7 off his purchase. Write an expression with parentheses to show the total cost, after using the coupon, and then simplify it to show how much he spent. Evaluate the expressions in Exercises 4– ÷ 8 – (10 – 6 ÷ 3) (5 – 3) + (27 ÷ 3) – (5 10) + (3 15) – 7. He spent $88.

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18 Independent Practice Lesson The Order of Operations Solution follows… Simplify the expressions in Exercises 10–12 as far as possible. 10. x – y + x (4 + 3) – y (60 – x 3) 9. Insert parentheses into the expression – 6 4 to make it equal to 48. ( – 6) 4 x – 14 7x7x 66 – 3 x

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19 Round Up Lesson The Order of Operations This will feature in almost all the math you do from now on, so you need to know it. Don’t worry though — just use the word PEMDAS or GEMA to help you remember it. If you evaluate an expression in a different order from everyone else, you won’t get the right answer. That’s why it’s so important to follow the order of operations.

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