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Understanding Expressions and Formulas: Order of Operations in Algebra

This section delves into the order of operations essential for solving algebraic expressions and formulas. It includes concepts such as the use of parentheses, brackets, and braces, as well as exponents, and multiplication/division in sequence before addition/subtraction. Various examples illustrate how to apply these rules effectively. Additional discussions cover variable representation, algebraic expressions, and real-world applications like calculating the volume of a cone and converting temperature from Fahrenheit to Celsius. Test your understanding with practical problems!

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Understanding Expressions and Formulas: Order of Operations in Algebra

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  1. Section 1.1 Expressions and Formulas

  2. Order of Operations • Parenthesis, brackets, braces, and fraction bars • Exponents, powers • Multiplication/Division • Addition/Subtraction • Try this: • Ex. 1 [384 – 3(7-2)³] /3

  3. [384 – 3(7-2)³] / 3 • [384- 3(5)³] / 3 • [384 – 3(125)] / 3 • [384 – 375] / 3 • 9 / 3 • 3

  4. Variable – symbols, usually letters, used to represent unknown quantities. • Algebraic expressions - expressions that contain at least one variable. • Example 2: a – b (a² - b) if a=2 and b=3.4. 2 – 3.4 (2² - 3.4) 2 – 3.4 (4 – 3.4) 2 – 3.4 (0.6) 2 – 2.04 -.04

  5. Example 3: 8xy + z³ y² + 5 if x = 5, y = -2 and z = -1 8(5)(-2) + (-1)³ (-2)² + 5 -80 – 1 4 +5 -81 9 -9

  6. Formula – a mathematical sentence that expresses the relationship between certain quantities. • Look at example 4 from page 8.

  7. Word Problems • Example 4: The formula for the volume of a cone is V = 1/3 ii r²h. Find the approximate volume of a cone that has a radius of 75 meters and is 225 meters high.

  8. Example 5: The formula C = 5(F -32) 9a) Can be used to convert temperatures in degrees Fahrenheit to degrees Celsius. • Room temperature commonly ranges from 64 F to 73 F. Determine the room temperature range in degrees Celsius.

  9. Example 5 cont’d • B) The normal average human body temperature is 98.6 F. A temperature above this indicates a fever. If your temperature is 42 C, do you have a fever? Explain your answer.

  10. Example 6: The radius of the earth’s orbit is 93,000,000 miles. • A)Find the circumference of the Earth’s orbit assuming that the orbit is a circle. The formula for the circumference of a circle is C = 2iir.

  11. B) Earth travels at a speed of 66,698 miles per hour around the sun. Use the formula T = c v where T is the time in hours, C is the circumference, and V is the velocity, to find the number of hours it takes the Earth to revolve around the sun.

  12. C) Did you prove that it takes one year for the earth to go around the sun? Explain your answer.

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