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Chapter 1: Problem 51

Evaluate each of the following expressions, if possible. $$\frac{-20-(8-12)}{-4}$$

Short Answer

Expert verified
4

Step by step solution

01

- Simplify the Inner Expression

Start by simplifying the expression inside the parentheses. In this case, calculate \(8 - 12\) which equals \( -4 \).
02

- Rewrite the Expression

Substitute \( -4 \) back into the original expression: \( \frac{-20 - (-4)}{-4} \).
03

- Simplify the Numerator

Calculate the numerator by resolving the double negative: \(-20 - (-4) = -20 + 4 = -16\).
04

- Perform the Division

Now simplify the entire expression: \( \frac{-16}{-4} \). When dividing two negative numbers, the result is positive: \( \frac{-16}{-4} = 4 \).

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Key Concepts

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

simplifying expressions
Simplifying expressions involves breaking down a complex mathematical phrase into simpler, more manageable parts.
It helps make calculations easier and reveals the underlying structure of the expression. We start by identifying and combining like terms, performing calculations inside parentheses or brackets, and applying mathematical operations in the correct order.
For instance, in the expression \(\frac{-20 - (8 - 12)}{-4}\), we first simplify the parentheses: \8 - 12\, which equals \-4\. This step reduces the complexity of the original expression, paving the way for easier computations.
order of operations
The order of operations is a set of rules that specifies the sequence in which different parts of a mathematical expression should be calculated.
This sequence is often remembered by the acronym PEMDAS, which stands for:
  • Parentheses
  • Exponents
  • Multiplication and Division (left to right)
  • Addition and Subtraction (left to right)
In our given problem \(\frac{-20 - (8 - 12)}{-4}\), we first handle the operation inside the parentheses: \8 - 12\, yielding \-4\.
Next, we substitute this result back into the larger expression, simplifying it step-by-step by resolving operations in the correct order.
negative numbers division
When dividing negative numbers, the signs play a crucial role in determining the result.
Recall that:
  • Negative divided by negative = positive
  • Negative divided by positive = negative
In our example \(\frac{-16}{-4}\), we are dividing \-16\ by \-4\. Both the numerator and denominator are negative, so the result will be positive: \4\.
This principle helps in simplifying expressions accurately and ensures that we reach the correct final answer.

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