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Ch 4 Sec 6: Slide #1 Columbus State Community College Chapter 4 Section 6 Exponents, Order of Operations, and Complex Fractions

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Ch 4 Sec 6: Slide #2 Exponents, Order of Operations, and Complex Fractions 1.Simplify fractions with exponents. 2.Use the order of operations with fractions. 3.Simplify complex fractions.

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Ch 4 Sec 6: Slide #3 Simplifying Fractions with Exponents EXAMPLE 1 Simplifying Fractions with Exponents Simplify. (a) 2 3 – 3 2 3 – 2 3 – 2 3 – 2 3 – 3 = 4 9 2 3 – 8 27 – The base is and the exponent is 3. 2 3 – 3 factors of 2 3 –

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Ch 4 Sec 6: Slide #4 Simplifying Fractions with Exponents EXAMPLE 1 Simplifying Fractions with Exponents Simplify. (b) 2 9 2 3 4 3 = 2 9 2 3 4 3 2 9 3 4 3 4 3 4 2 9 = 2 2 3 3 3 3 3 3 3 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 = 1 48

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Ch 4 Sec 6: Slide #5 Using Your Calculator Try these problems using your calculator. = c A b 23 TI 30X IIS (a) 2 3 – 3 () (-) ^ 3 8 27 –

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Ch 4 Sec 6: Slide #6 Using Your Calculator Try these problems using your calculator. = c A b 23 TI 30 Xa (a) 2 3 – 3 () 3 8 27 – x y + –

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Ch 4 Sec 6: Slide #7 (b) 2 9 2 3 4 3 Using Your Calculator Try these problems using your calculator. = c A b 29 TI 30X IIS () ^ 2 1 48 x c A b 34 () ^ 3 Optional

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Ch 4 Sec 6: Slide #8 Using Your Calculator Try these problems using your calculator. = c A b 29 TI 30 Xa () 2 x y (b) 2 9 2 3 4 3 4 81 c A b 34 () 3 x y 27 64 c A b 481 x c A b 2764 1 48

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Ch 4 Sec 6: Slide #9 Order of Operations Step 1Work inside parentheses or other grouping symbols. Step 2Simplify expressions with exponents. Step 3Do the remaining multiplications and divisions as they occur from left to right. Step 4Do the remaining additions and subtractions as they occur from left to right.

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Ch 4 Sec 6: Slide #10 5 1 3 2 Using the Order of Operations with Fractions EXAMPLE 2 Using the Order of Operations with Fractions Simplify. (a) 5 6 – 2 11 15 1 3 – 5 6 – 2 2 5 11 15 1 3 – = 11 15 – 5 = 6 = 2 5 5 6 – 4 25 = 4 2 5 = 2 2 5 2 5 = 2 15 –

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Ch 4 Sec 6: Slide #11 Using Your Calculator Use your calculator to simplify this expression. = c A b 56 TI 30X IIS () (-) ^ 2 2 15 – 5 6 – 2 11 15 1 3 – c A b 1115 ( ) c A b 13 – x ( Optional )

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Ch 4 Sec 6: Slide #12 + – Using Your Calculator Use your calculator to simplify this expression. = c A b 56 TI 30 Xa 2 2 15 – 5 6 – 2 11 15 1 3 – c A b 1115 c A b 13 – = x y x =

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Ch 4 Sec 6: Slide #13 3 1 2 1 Using the Order of Operations with Fractions EXAMPLE 2 Using the Order of Operations with Fractions Simplify. = 1 6 (b) 3 4 5 8 4 15 + 5 8 4 3 4 1 6 + 3 4 1 6 + = 11 12 11 12 9 2 + =

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Ch 4 Sec 6: Slide #14 Complex Fractions A complex fraction is a fraction in which the numerator and/or denominator contain one or more fractions.

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Ch 4 Sec 6: Slide #15 3 1 Simplifying a Complex Fraction EXAMPLE 3 Simplifying a Complex Fraction Simplify: 4 9 – 1 3 4 9 – 1 3 4 9 – 1 3 = ÷ 4 9 – 3 1 = 4 3 = – = 1 1 3 –

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Ch 4 Sec 6: Slide #16 Exponents, Order of Operations, and Complex Fractions Chapter 4 Section 6 – Completed Written by John T. Wallace

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