Basic College Mathematics (10th Edition)

Published by Pearson
ISBN 10: 0134467795
ISBN 13: 978-0-13446-779-5

Chapter 9 - Basic Algebra - Summary Exercises - Operations with Signed Numbers - Page 656: 45



Work Step by Step

RECALL: The order of operations follow the PEMDAS rule: First Priority: P - parentheses or grouping symbols Second Priority: E - exponents Third Priority: M/D - multiplication or division, whichever comes first from the left Fourth Priority: A/S - addition or subtraction, whichever comes first from the left Using the PEMDAS rule above gives: Perform the ones inside the parentheses first to obtain: $$=\dfrac{5-|2-4\cdot 4|+(-5)^2\div 5^2}{-9 \div 3(0) -(-8)}$$ Simplify within the absolute value by performing the multiplication first followed by subtraction to obtain: $$=\dfrac{5-|2-16|+(-5)^2\div 5^2}{-9 \div 3(0) -(-8)} \\=\dfrac{5-|-14|+(-5)^2\div 5^2}{-9 \div 3(0) -(-8)} \\=\dfrac{5-14+(-5)^2\div 5^2}{-9 \div 3(0) -(-8)}$$ Apply the exponents to obtain: $$=\dfrac{5-14+25 \div 25}{-9 \div 3(0) -(-8)}$$ Perform the divisions to obtain: $$=\dfrac{5-14+1}{-3(0)-(-8)}$$ Perform the multiplication in the denominator to obtain: $$=\dfrac{5-14+1}{0-(-8)}$$ Do the subtractions to obtain: $$=\dfrac{-9+1}{0+8}$$ Simplify the numerator and the denominator to obtain: $$=\dfrac{-8}{8}$$ Divide $-8$ by $8$. Note that the quotient of two numbers with different signs is negative: $$=-1$$
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