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Chapter 1: Problem 76

Evaluate each of the following expressions, if possible. $$-72-\frac{88-120}{8-12}$$

Short Answer

Expert verified
-80

Step by step solution

01

- Simplify the Numerator

First, simplify the numerator of the fraction by evaluating the expression inside the parentheses: 88 - 120 = -32.
02

- Simplify the Denominator

Next, simplify the denominator of the fraction by evaluating the expression inside the parentheses: 8 - 12 = -4.
03

- Divide the Numerator by the Denominator

Now, divide the simplified numerator by the simplified denominator: i.e., \( \frac{-32}{-4} = 8 \).
04

- Evaluate the Entire Expression

Finally, substitute the result from Step 3 back into the original expression and complete the calculation: i.e., \( -72 - 8 = -80 \).

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Key Concepts

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

evaluating expressions
Let's delve into evaluating expressions, a critical skill in algebra. The given expression is $$-72 - \frac{88-120}{8-12}$$. Evaluating this expression involves breaking it down step-by-step.First, handle any operations within parentheses, next complete any division, and finally, simplify the entire expression. The goal is to follow the correct order of operations (PEMDAS/BODMAS): Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). This ensures we get the right result every time.
numerator simplification
Numerator simplification is crucial in evaluating expressions with fractions. The numerator is the top part of the fraction. In our example, we start with $$88 - 120$$. Here鈥檚 how we simplify it:
  • Calculate the value inside the parentheses first: $$88 - 120$$.
  • Perform the subtraction which gives us: $$-32$$.
    • This simplified numerator, $$-32$$, is then used in the next steps.
denominator simplification
Next, let's focus on denominator simplification, which involves simplifying the bottom part of the fraction. For our given problem, the expression inside the denominator is $$8 - 12$$. We simplify it as follows:
  • First, handle the arithmetic operation inside the parentheses: $$8 - 12$$.
  • Perform the subtraction, which results in $$-4$$.
    • This simplified denominator, $$-4$$, is now ready for the division. Breaking down the numerator and denominator helps in accurate calculations.
fraction division
Fraction division is a key step in simplifying expressions like ours. After simplifying the numerator ($$-32$$) and the denominator ($$-4$$), we need to divide them:
  • Use the fraction $$\frac{-32}{-4}$$.
  • Divide the numerator by the denominator: $$\frac{-32}{-4} = 8$$.
    • Division of two negative numbers results in a positive quotient. Finally, use this result in the remaining expression. In our example, the last step is substituting 8 back into the expression, leading to $$ -72 - 8 = -80$$. Hence, the evaluated expression is $$-80$$.

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