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Ch. R - Review of Basic Concepts
Lial - College Algebra 13th Edition
Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook
All textbooksLial 13th EditionCh. R - Review of Basic ConceptsProblem 97
Chapter 1, Problem 97

Evaluate each expression. −8+(−4)(−6)÷124−(−3)\(\frac{-8 + (-4)(-6) \div 12}{4 - (-3)}\)

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1
Start by simplifying the expression inside the numerator brackets: \([-8 + (-4)(-6)/12]\). First, calculate the product \((-4)(-6)\).
Next, divide the product from the previous step by 12, so compute \(\frac{(-4)(-6)}{12}\).
Add the result of the division to -8 inside the numerator brackets to simplify the entire numerator.
Now simplify the denominator brackets: \([4 - (-3)]\). Remember that subtracting a negative number is the same as adding its positive counterpart.
Finally, divide the simplified numerator by the simplified denominator to evaluate the entire expression.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Order of Operations

The order of operations is a set of rules that dictate the sequence in which mathematical operations should be performed to correctly evaluate expressions. It is commonly remembered by the acronym PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right). Following this order ensures consistent and accurate results.
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Operations with Negative Numbers

Understanding how to handle negative numbers in arithmetic operations is essential. Multiplying two negative numbers results in a positive number, while multiplying a positive and a negative number results in a negative number. Similarly, subtracting a negative number is equivalent to adding its positive counterpart.
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Simplifying Complex Fractions

Simplifying complex fractions involves evaluating the numerator and denominator separately before performing the division. This process requires careful application of arithmetic operations and order of operations to avoid errors and to reduce the expression to its simplest form.
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