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Chapter 1: Problem 77

Perform each indicated operation. $$ \frac{8(-1)-|(-4)(-3)|}{-6-(-1)} $$

Short Answer

Expert verified
The result is 4.

Step by step solution

01

Simplify the numerator

First, break down the numerator by performing the operations separately. Start with the multiplication: \ \( 8(-1) = -8 \), \ and \ \( (-4)(-3) = 12 \). \ Next, find the absolute value: \ \( |-12| = 12 \). \ Then subtract these two results: \ \( -8 - 12 = -20 \).
02

Simplify the denominator

Simplify the expression in the denominator: \ \( -6 - (-1) \). \ The subtraction of a negative number is equivalent to adding the positive number: \ \( -6 + 1 = -5 \).
03

Divide the simplified numerator by the simplified denominator

Now divide the simplified numerator by the simplified denominator: \ \( \frac{-20}{-5} \). \ Division of two negative numbers results in a positive number: \ \( \frac{-20}{-5} = 4 \).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Simplification
Simplification is the process of reducing an expression to its simplest form. This means breaking down the equation step by step. Here鈥檚 how it works in our example:

**Numerator:** \begin{itemize} \begin{itemize}
  • Start with multiplying. We have: \(8(-1) = -8\) and \((-4)(-3) = 12\)
  • Calculate the absolute value of 12, which is just 12 because the absolute value represents the distance from zero.
  • Subtract the results: \-8 - 12 = -20.
    • \br>
    Keep the process orderly and clear, solving one step at a time.
    Absolute Value
    The absolute value of a number is its distance from zero, regardless of whether it is positive or negative. It's indicated by vertical bars. For instance, \(|-4| = 4\).

    Let鈥檚 use our example:
    \begin{itemize}
  • The product, \((-4)(-3) = 12\), results in a positive number because multiplying two negatives makes a positive.
  • Then, find the absolute value of 12: \(|12| = 12 \). Since 12 is already positive, its absolute value remains the same.
    • \br>
    Absolute value helps keep calculations straightforward, focusing on magnitude instead of negative signs.
    Division of Integers
    Dividing integers can be straightforward as long as you keep the rules in mind. Here is a step-by-step breakdown:

    \begin{itemize}
  • If both integers are positive or negative, the result is positive.
  • If one is positive and the other is negative, the result is negative.

    • Let鈥檚 divide using our example:
    \begin{itemize}
  • First, simplify the denominator: \(-6 - (-1) = -6 + 1 = -5\).
  • Then, divide the numerator and denominator: \(\frac{-20}{-5}\).
  • Since both numbers are negative, the result is positive, so \(\frac{-20}{-5} = 4\).
    • \br>
    Keep these rules handy for error-free division of integers.

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    Most popular questions from this chapter

    Simplify each expression. $$ -\frac{4}{3}+2 t+\frac{1}{3} t-8-\frac{8}{3} t $$

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    Simplify each expression. $$ -4(-3 x+3)-(6 x-4)-2 x+1 $$
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