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Chapter 7

Chapter 7. Pre-Algebra. Bell Ringer. Get out yesterday’s homework assignment (7.4) Think of any clarifying questions you may have about 7.1-7.4 Write an equation for the following word problem:

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Chapter 7

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  1. Chapter 7 Pre-Algebra

  2. Bell Ringer • Get out yesterday’s homework assignment (7.4) • Think of any clarifying questions you may have about 7.1-7.4 • Write an equation for the following word problem: • The perimeter of the classroom is 100 feet. The length is 10 feet greater than the width. Find the length and the width. Width: Length: Equation:

  3. Quiz Review

  4. QUIZ TOMORROW!! • Sections 7.1-7.4 • Homework: Page 393-394, 8-23 • Study: • 7.1-7.4 Homework • Notes • Problems from today’s review

  5. Bell Ringer (7.5) • Get out your notebook and prepare to take notes on Section 7.5 • Prepare to ask questions about the 7-1-7.4 quiz

  6. 7.5 – Solving Equations With Variables on Both Sides (Page 371) • Essential Question: • How is solving an equation with the variable appearing twice on the same side of the equals sign different from solving an equation with the variable appearing on both sides of the equals sign?

  7. 7.5 cont. Steps in Solving Equations 1. Remove ( ) 2. Remove fractions or decimals by multiplication 3. Combine like terms 4. Isolate variables to one side 5. Undo + or - 6. Undo x or / 7. Check!! • 4. Isolate variables to one side

  8. 7.5 cont. • Example 1: CHECK!!

  9. 7.5 cont. • Example 2: CHECK!!

  10. 7.5 cont. 7.5 cont. • Example 3: CHECK!! Example 3:

  11. 7.5 cont. • Example 4: CHECK!!

  12. 7.5 cont. • Example 5:

  13. 7.5 - Closure • How is solving an equation with the variable appearing twice on the same side of the equals sign different from solving an equation with the variable appearing on both sides of the equals sign? • Twice on same side: • Combine terms using the operation shown • On both sides: • Combine terms using inverse operations

  14. 7.5 - Homework Page 373-374, 4-22 even, 28, 30

  15. Bell Ringer (7.6) • Get out your 7.5 homework assignment • Get out your notebook and prepare to take notes on Section 7.6 • Solve the following equation for x:

  16. 7.6 – Solving Two- Step Inequalities (Page 377) • Essential Question: • How is solving two-step inequalities different from solving two-step equations?

  17. 7.6 cont. • Graphing Inequalities: • We can use the number line to solve inequalities containing < , ≤ , > , and ≥ . • = ≤, ≥ • = <, >

  18. 7.6 cont. • Example 1: • Solve and graph .

  19. 7.6 cont. • Example 2: • Solve . **Remember to reverse the direction of the inequality symbol when you multiply or divide by a negative number**

  20. 7.6 cont. • Example 3: • Dale has $25 to spend at a carnival. If the admission to the carnival is $4 and the rides cost $1.50 each, what is the greatest number of rides Dale can go on? Therefore, the greatest number of rides Dale can ride is 14.

  21. 7.6 - Closure • How is solving two-step inequalities different from solving two-step equations? • Same except when you multiply or divide each side of an inequality by a negative number, you must also reverse the inequality symbol.

  22. 7.6 - Homework Page 379, 4-24 even, 34, 35

  23. Bell Ringer (7.7) • Get out your 7.6 homework assignment • Get out your notebook and prepare to take notes on Section 7.7 • Solve the following inequality for y:

  24. 7.7 – Transforming Formulas (Page 382) • Essential Question: • What does it mean to “solve a formula for a given variable”?

  25. 7.7 cont. • Formula: • An equation that shows a relationship between quantities that are represented by variables NOT THE RACE CAR BRENDEN!! BEITZ RACING

  26. 7.7 cont. • Transforming in One Step: • Example 1: Solve the area formula for length.

  27. 7.7 cont. • Transforming in More Than One Step: • Example 2: Solve the perimeter formula for width.

  28. 7.7 cont. • Transforming Temperatures: • Example 3: Convert to by solving for F, then substituting.

  29. 7.7 - Closure • What does it mean to “solve a formula for a given variable”? • Expressing one variable in terms of the other variables used in the formula

  30. 7.7 - Homework Page 384, 4-26 even

  31. Bell Ringer (7.8) • Get out your 7.7 homework assignment • Get out your notebook and prepare to take notes on Section 7.8 • What does the term “interest” mean in mathematics?

  32. 7.8 – Simple and Compound Interest (Page 386) • Essential Question: • What is the difference between simple interest and compound interest?

  33. 7.8 cont. • New Vocabulary: • Principal – initial amount of an investment or loan • Interest - fee charged by a lender to a borrower for the use of borrowed money • Interest Rate – percentage of the balance that an account or investment earns in a fixed period of time

  34. 7.8 cont. • New Vocabulary: • Simple Interest – interest paid only on the principal

  35. 7.8 cont. • Example 1: • Suppose you deposit $1,000 in a savings account that earns 6% interest per year. Find the interest earned in 2 years. Find the total principal plus interest. • SIMPLE INTEREST PROBLEM!! ONLY INTEREST!!

  36. 7.8 cont. • Balance – principal plus earned interest • Interest Period – length of time over which interest is calculated • Can be a year or less than a year

  37. 7.8 cont. • Compound Interest – interest paid on both the principal and the interest earned in previous interest periods

  38. 7.8 cont. • Example 2: • Suppose you deposit $400 in an account that earns 5% interest compounded annually. The balance after the first four years is $486.20. What is the balance in your account after another 4 years, a total of 8 years? • COMPOUND INTEREST PROBLEM!! OR

  39. 7.8 cont.

  40. 7.8 cont. • Example 3: • Find the balance on a deposit of $2,500 that earns %3 interest compounded semiannually for 4 years.

  41. 7.8 cont.

  42. 7.8 - Closure • What is the difference between simple interest and compound interest? • Simple Interest: • Paid only on the principal • Compound Interest: • Paid on both the principal and the previously earned interest

  43. 7.8 - Homework Page 389, 2-18 even

  44. Bell Ringer • Get out your homework assignment • Think of any clarifying questions you may have about Chapter • Find the balance on a deposit of $1000 that earns 4% interest compounded semiannually for 5 years.

  45. Steps for Solving Equations: 1. Remove ( ) 2. Remove fractions or decimals by 3. Combine like terms 4. Isolate variables to one side 5. Undo or 6. Undo or 7. Check!!

  46. 7.1 - Review (Page 393)

  47. 7.2, 7.3 - Review (Page 393)

  48. 7.4 - Review (Page 394)

  49. 7.5 - Review (Page 394)

  50. 7.6 - Review (Page 394-395)

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