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Equations, Formulas, and the Problem-Solving Process

This guide explores the foundational concepts of equations and formulas in mathematics. It defines expressions and equations, differentiating between them while emphasizing the importance of verifying solutions. It explains how to use formulas to solve practical problems, such as calculating perimeter, area, and volume. The document also presents how to check solutions by substituting values to confirm accuracy. Real-world examples, like calculating dimensions for a pool, demonstrate the application of these concepts.

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Equations, Formulas, and the Problem-Solving Process

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  1. 2.1 Equations, Formulas, and the Problem-Solving Process 1. Verify solutions to equations. 2. Use formulas to solve problems.

  2. What’s the difference? Expression Equation Simplified Solved Equation: Two expressions set equal. False True Solution: A number that makes an equation true when it replaces the variable in the equation.

  3. To Check a Possible Solution • Replace the variable in the equation with the value. • If the resulting equation is true, the value is a solution.

  4. Solutions Is a = 12 a solution? Use parentheses! NO

  5. Solutions Is a solution? Yes

  6. Determine which of the following is a solution for the equation. a) –5 b) – 1 c) 2 d) 4 2.1

  7. Determine which of the following is a solution for the equation. a) –5 b) – 1 c) 2 d) 4 2.1

  8. Formula: An equation that describes a mathematical relationship. Perimeter: The distance around a figure. Area: The total number of square units that fill a figure. The total number of cubic units that fill a space. Volume: Circumference: The distance around a circle. Radius: The distance from the center of a circle to any point on the circle. Diameter: The distance across a circle through its center.

  9. Formulas See page 95!!!! Area: w Perimeter: l Area: h b Area: r Circumference:

  10. Formulas Perimeter, Area or Volume? Filling a pool with water? Volume Cover for a pool? Area Tile around a pool? Perimeter Fencing? Perimeter Laying carpet? Area Putting up a wallpaper border? Perimeter

  11. Formulas Suppose you have a rectangular pool that is 12 feet wide and 20 feet long. The pool has a constant depth of 4 feet. Find the perimeter, the area and the volume. Perimeter: feet

  12. Formulas Suppose you have a rectangular pool that is 12 feet wide and 20 feet long. The pool has a constant depth of 4 feet. Find the perimeter, the area and the volume. Area: square feet or ft2

  13. Formulas Suppose you have a rectangular pool that is 12 feet wide and 20 feet long. The pool has a constant depth of 4 feet. Find the perimeter, the area and the volume. Volume: cubic feet or ft3

  14. A thermometer reads 30° C: what is this temperature in degrees Fahrenheit? a) 34F b) 49F c) 86F d) 112F 2.1

  15. A thermometer reads 30° C: what is this temperature in degrees Fahrenheit? a) 34F b) 49F c) 86F d) 112F 2.1

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