91Ó°ÊÓ

Simplifying an expression is an essential skill in prealgebra. It involves reducing an expression to its simplest form.
Simplifying makes complex calculations more manageable and helps us understand the problem better.
To simplify, you should follow these steps:

• Identify and solve any operations within parentheses first
• Perform any multiplication or division from left to right
• Then, handle addition or subtraction from left to right

In our exercise, simplifying the expression inside the parentheses was the first step.
The expression inside was \(8 \cdot 6 - 3\). You start with multiplication, and then subtraction,
which gives us 45. This simplification was crucial to solve the expression efficiently.

The order of operations is a set of rules that tells the sequence in which calculations should be done to ensure accurate results.
This is often remembered using the acronym PEMDAS:

• P: Parentheses first
• E: Exponents (ie powers and roots, etc.)
• MD: Multiplication and Division (from left to right)
• AS: Addition and Subtraction (from left to right)

In our example, we began by evaluating the terms inside the parentheses \(8 \cdot 6 - 3\).
According to the order of operations, multiplication precedes subtraction.
Similarly, in the denominator \(5 \cdot 4 - 5\), multiplication is performed first, followed by subtraction.
Applying the order of operations ensures that each step of our calculation is correct and consistent.

Fractions represent a part of a whole and are written as one number over another, separated by a division line.
In our exercise, we were given the fraction \(\frac{60-(8 \cdot 6-3)}{5 \cdot 4-5}\) to simplify.
Fractions involve a numerator (top number) and a denominator (bottom number).To simplify a fraction, first simplify both the numerator and the denominator separately.
In this case, the numerator reduced to 15, and the denominator also simplified to 15.
Once both parts are simplified, the fraction itself can be simplified by dividing both the numerator and denominator by the greatest common factor, if possible.Here, dividing 15 by 15 gives us a simplified result of 1.
This process of simplifying helps make the fraction easier to work with and comprehend.