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Simplifying Numerical Expressions and Order of Operations

This guide covers the essential principles of numerical expressions. A numerical expression consists of numbers and operation symbols. Learn how to simplify expressions using the Order of Operations: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction (PEMDAS). Explore examples, such as simplifying expressions without parentheses or exponents and solving problems involving multiple operations. Practice problems are included for reinforcement. Prepare for upcoming quizzes and do your homework diligently to master the concepts of numerical expressions.

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Simplifying Numerical Expressions and Order of Operations

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  1. Do Now • 93 2.) 112 3.) 12,4540 4.) 23.1 + 14.07 729 121 1 27.17

  2. 12/9/2013 5-1 A Numerical Expressions

  3. Numerical Expression- a mathematical phrase that includes only numbers and operation symbols Examples: 4 + 8 ÷ 2 × 6 371 – 203 + 2 5,006 × 19

  4. Simplify- to find the value of a numerical expression • Synonyms: Solve Evaluate

  5. Order of Operations- a rule for evaluating numerical expressions • Perform operations in parentheses • Find the values of numbers withexponents • Multiply orDivide from left to right as ordered in the problem • Add orsubtract from left to right as ordered in the problem

  6. A little trick… Please Parentheses ExcuseExponents My/Dear Multiply/Divide Aunt/Sally Add/Subtract PEM/DA/S

  7. Ex. 1 Simplify the expression 9 + 12 × 2 9 + 12 × 2There are no parentheses or exponents 9 + 24Multiply 33 Add

  8. Ex. 2 33 + 8 – 16 33 + 8 - 16There are no parenthesis 27 + 8 - 16Find the values of numbers with exponents 35 - 16 Add 19 Subtract

  9. Ex. 3 Find the value of 90 ÷ 3 + (3 – 2) – 20. 90 ÷ 3 + (3 – 2) – 20 90 ÷ 3 + 1 – 20 30 + 1 – 20 31 – 20 11

  10. Ex. 4 7– 3[10 –2(6 – 3)] ÷ 2 7 – 3 [10 -2 (3)] ÷ 2 7 – 3 [10 – 6] ÷ 2 7 – 3 [4] ÷ 2 7 – 12 ÷ 2 7 – 6 1

  11. Ex. 5 George, Jill, and Avery need to buy sporting equipment. Each person buys a ball, a pair of shin guards, and a pair of cleats. Write an expression for the total cost of the equipment they buy. Then find the total cost.

  12. 3 × $15 + 3 × $18 + 3 × $25 $45 + 3 × $18 + 3 × $25 $45 + $54 + 3 × $25 $45 + $54 + $75 = $174

  13. Create an expression using multiple operations. Solve the problem on the back. Then switch with your neighbor.

  14. Exit Ticket

  15. [(3 + 2) × (6 - 4) + 2] × 4 3.) 16 – 3(8 – 3)2 ÷ 5 • 9 + (21 ÷ 7) × 5 4.) 24 + 6 × 4 • Mr. Kellett bought 6Itunes albums for $4 each and 5 albums for $3 each. Write an expression to find the amount Mr. Kellett spent on the albums.

  16. Homework! • Pg. 272 #1-28 Evens • SHOW ALL OF YOUR WORK • Remember PEM/DA/S • Quiz on Wednesday (12/11)

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