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Order of Operations

Mathematics, Grade 6

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Study Guide Order of Operations Mathematics, Grade 6

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What Is Evaluating Numerical Expressions Using Order of Operations? • A numerical expression is a phrase which represents a number: 25 increased by 33 → 25 + 33 = 8 50 decreased by 34 → 50 – 34 = 16 Two-thirds of 12 → 2/3 x 12 = 8 • Some numerical expressions may require more than one operation: 6 x (20 – 13) = 43 33 – (81 ÷ 9) = 18 • Evaluating a numerical expression requires applying an order of operations: o Work from left to right o Complete the operations inside the parentheses o Simplify all exponents o Multiply or divide from left to right o Add or subtract from left to right © Copyright NewPath Learning. All Rights Reserved. Permission is granted for the purchaser to print copies for non-commercial educational purposes only. Visit us at www.NewPathLearning.com.
How to evaluate numerical expressions using order of operations: • Numerical expressions often require more than one step, for instance, 5 X (18 ÷ 3). • Work from left to right to solve a multi-step problem. 124 ÷ 4 – 15 → 31 – 15 = 16 • Simplify all operations inside parentheses first: 135 – (42 x 3) → 135 – 126 = 9 • Working from left to right, simplify all exponents, complete operations inside parentheses, and then solve: 632 – (232 + 3) → 632 – (529 +3) → 632 – 532 =100 • Clear parentheses and exponents, perform multiplication, and then division from left to right. Lastly, perform addition and subtraction: 53 ÷ (14 – 9) – 18 →125 ÷ 5 – 18 → 25 – 18 = 7 Try This! 102 x (54 ÷ 9) __________________________________________ 125 - (2 + 9) - 4 ________________________________________ (32 x 6) ÷ 3 ____________________________________________ 56 ÷ 8 -9 _________________________________________ 72 - (49 ÷ 7) ___________________________________________ © Copyright NewPath Learning. All Rights Reserved. Permission is granted for the purchaser to print copies for non-commercial educational purposes only. Visit us at www.NewPathLearning.com.
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