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1.1 Expressions and Formulas

1.1 Expressions and Formulas. Algebra 2 Mrs. Spitz Fall 2006. Objectives. Use the order of operations to evaluate expressions Use formulas. Order of Operations. Simplify the expressions inside the grouping symbols, such as parentheses, brackets, and fraction bars. Evaluate all powers.

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1.1 Expressions and Formulas

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  1. 1.1 Expressions and Formulas Algebra 2 Mrs. Spitz Fall 2006

  2. Objectives • Use the order of operations to evaluate expressions • Use formulas

  3. Order of Operations • Simplify the expressions inside the grouping symbols, such as parentheses, brackets, and fraction bars. • Evaluate all powers. • Do all multiplications and divisions from left to right. • Do all additions and subtractions from left to right.

  4. 5 + 82 ÷ 4 · 3 = 5 + 64 ÷ 4 · 3 = 5 + 16 · 3 = 5 + 48 = 53 Evaluate all powers Do all multiplications and divisions left to right Do all additions and subtractions left to right. Example 1 Find the value of 5 + 82 ÷ 4 · 3. Grouping symbols can be used to change or clarify the order of operations. Frequently used groping symbols are parentheses, ( ), and brackets, [ ]. When calculating the value of an expression, you should begin with the operation in the innermost set of grouping symbols.

  5. [(4 + 8)2 ÷ 9] · 5= [(12)2 ÷ 9] · 5 = [144 ÷ 9] · 5 =[16] · 5 = 80 First add 4 and 8 Then find 122 Now divide 144 by 9 Multiply 16 by 5 Example 2 Find the value of [(4 + 8)2 ÷ 9] · 5. Algebraic expressions contain at least one variable. You can evaluate an algebraic expression by replacing each variable with a value and then applying the rules for the order of operations.

  6. 4x2 + 3xy = 4(-3)2 + 3(-3)(5) = 4(9) + 3(-3)(5) =36 + (-45) = -9 Replace x by -3 and y by 5. Find (-3)2 Multiply left to right. Add Example 3 Evaluate 4x2 + 3xy if x = -3 and y = 5 A formula is a mathematical sentence that expresses the relationship between certain quantities. If you know a value for every variable in the formula except one, you can find the value for that remaining variable.

  7. V = 4/3∏r3 = 4/3 ∏ (7.6)3 Enter 4 ÷ 3 x ∏ x 7.6 yx 3 = 1838.78 cubic centimeters Write the formula Substitute values Key into your calculator Round to the nearest hundredth. Example 4 The volume of a sphere is calculated by using the formula V = 4/3∏r3. In the formula, r represents the measure of the radius. Use a calculator to find the volume of a sphere with a radius of 7.6 centimeters. Use the ∏ key on your calculator.

  8. I = prt = 6000(0.12)(2) Enter 6000 x .12 x 2 =$1,440 Write the formula Substitute values Key into your calculator Round to the nearest dollar. Example 5 You are about to buy a new car. The sales associate offers you a simple interest loan to finance it. Simple interest is calculated by using the formula I = prt. In the formula, p represents the principal in dollars, r represents the annual interest rate, and t represents the time in years. Find the amount of interest you would pay for a two-year loan if the principal is $6,000 and the rate is 12%.

  9. C = 5(F – 32) = 5(787.1 – 32) =419.5 Write the formula Substitute value of F Do order of operations with what is in parentheses first. Then multiply that by 5. Finally divide what you get by 9. Example 6 The boiling point of the metal zinc if 787.1° on the Fahrenheit scale. Change the temperature to its equivalent on the Celsius scale. Note: The relationship between Celsius temperature, C, and Fahrenheit temperature, F, is given by C = 5(F – 32) 9 9 9 The Celsius temperature is 419.5°.

  10. Assignment • Worksheet 1.1 • SHOW ALL WORK OR IT DOESN’T COUNT!!! • Bring your questions and/or problems you were unable to solve with you next time we meet.

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