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Section 1.8 Applications and Problem Solving

Learn how to solve problems effectively using the 5-step approach: familiarize, translate, solve, check, and answer. Examples include finding updated balance, calculating distances, and determining total cost.

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Section 1.8 Applications and Problem Solving

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  1. Section 1.8 Applications and Problem Solving • 1. Familiarize yourself with the situation. • a) Carefully read and reread until you understand. • b) Draw a diagram or see if there is a formula to use. • c) Assign a variableto the unknown. • 2. Translateto an equation using the variable. • 3. Solve the equation. • 4. Check the answer. • 5. Answer in a complete sentence with units, if applicable. Section 1.8

  2. Now $112.00 Example (use the 5 step approach) • The balance in Megan’s checking account is $712. She uses her debit card to buy the power saw shown in the ad. Find the new balance in her checking account. Section 1.8

  3. Example (use the 5 step approach) • The captain of a blimp is traveling between two cities that are 745 miles apart. The first day he traveled 375 miles. How much further does he need to travel? Section 1.8

  4. Example (use the 5 step approach) • What is the total cost of 6 calculators if each one costs $326? Section 1.8

  5. Key Words to Translate Section 1.8

  6. Key Words to Translate Section 1.8

  7. Section 1.9 Exponential Notation & Order of Operations Section 1.9

  8. Exponential Notation The 5 is called an exponent (it tells you how many time the base is multiplied by itself) The 4 is the base (it tells you what is being multiplied by itself. Section 1.9

  9. Example Evaluate: 84 and 104 Solution 84 = 8  8  8 8 = 4096 104 = 10  10  10 10 = 10,000 Section 1.9

  10. Order of Operations • 1. Do all calculations in parentheses ( ), brackets [ ], or braces { } before operations outside. • 2. Evaluate all exponential expressions. • 3. Do all multiplications and divisions in order from left to right. • 4. Do all additions and subtractions in order from left to right. Section 1.9

  11. Examples Simplify: It takes a LOT of practice to master this. Section 1.9

  12. Finding the Average Mason has 4 math tests with scores of 76, 85, 92, and 91. Find the average of all four tests. Section 1.9

  13. Parentheses within Parentheses • When parentheses occur within parentheses, we can make them different shapes, such as [ ] (also called “brackets”) and { } (also called “braces”). All of these have the same meaning. When parentheses occur within parentheses, computations in the innermost ones are to be done first. Section 1.9

  14. Example Section 1.9

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