91Ó°ÊÓ

Simplifying expressions is about making a complex mathematical expression easier to understand or work with.
The goal is to reduce it to its simplest form without changing its value.

For example, in our original exercise, the expression \( \frac{-44-16+80}{-5} \) gets simplified step by step.

First, we simplify the numerator: \(-44 - 16 + 80\).
To tackle this, break it down into smaller parts:
\[ -44 - 16 = -60 \]
Combine the negative numbers first and then add:
\[ -60 + 80 = 20 \]
Now, the numerator is simplified to 20.
Simplifying expressions often requires basic arithmetic and an understanding of the order of operations. Stay patient and tackle one part of the expression at a time!

Understanding integer division is crucial for solving expressions involving complex numbers.

In our exercise, after we simplify the numerator to 20, we need to divide it by -5 to get our final answer: \( \frac{20}{-5} \).

Here's how you can approach integer division:

• A positive number divided by a negative number results in a negative number.
• A negative number divided by a positive number also results in a negative number.
• Both positive and negative integers divided by themselves (except zero) give a result of 1 or -1.

So, \( 20 \div -5 = -4 \).
The result of this division operation is -4 because 20 is positive and -5 is negative, leading to a negative quotient.

The order of operations is the sequence in which different mathematical operations should be performed.
It ensures that everyone solves the problem the same way and gets the same result.

The commonly accepted sequence can be remembered by the acronym PEMDAS:

• P: Parentheses first
• E: Exponents (i.e., powers and roots)
• M and D: Multiplication and Division (from left to right)
• A and S: Addition and Subtraction (from left to right)

In our original exercise, we start by solving inside the numerator since it's within an implied parentheses: \(-44 - 16 + 80\).
We then follow with division,
as seen here: \ \frac{20}{-5} = -4 \.
Correct application of the order of operations is essential to evaluate expressions accurately!