Problem 93 - Prealgebra

Question

Simplify. $$36-6+12$$

Step-by-Step Solution

Answer

The simplified result is 42.

Step 1: Understand the Problem

We are given the expression \(36 - 6 + 12\) and we need to simplify it. Simplifying an expression means performing the operations to condense it into a single numerical value.

Step 2: Perform Subtraction First

Start with the first operation in the expression: subtraction. Calculate \(36 - 6\) which equals \(30\).

Step 3: Perform Addition

Now, take the result from Step 2, which is \(30\), and add \(12\) to it: \(30 + 12 = 42\).

Key Concepts

Simplifying Expressions

Simplifying expressions is an essential part of prealgebra practice. In essence, it involves reducing an expression to its simplest form by performing all the arithmetic operations it contains. This process is aimed at making expressions easier to understand and work with.

When we simplify an expression, our goal is to condense it into a single number or a simpler form, especially useful when dealing with more complex problems. In the exercise provided, the expression is simplified by following the order of operations. It's crucial to recognize the operations involved and ensure accuracy at each step.

• Identify each arithmetic operation in the expression: Add, subtract, multiply, or divide.
• Perform each operation step-by-step, adhering to the rules of order of operations.
• Continue until you consolidate the entire expression into a single value.

Order of Operations

The order of operations is a fundamental principle in mathematics that dictates the sequence in which arithmetic operations should be performed. This is especially important for simplifying expressions accurately. The standard convention is often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).

For instance, in the expression given, there are only two operations: subtraction and addition. According to the order of operations:

• Perform subtraction first: Calculate \(36 - 6\).
• Once complete, proceed to addition: Add \(12\) to the result.

Adhering to this order is crucial for obtaining the correct result. Omitting or misapplying these rules can lead to incorrect answers, as some operations might change the outcome if performed out of order.

Basic Arithmetic Operations

Understanding basic arithmetic operations is the cornerstone of effectively working with expressions. Arithmetic operations consist of addition, subtraction, multiplication, and division. These operations are the building blocks for simplifying expressions and solving equations.

Each operation has its unique function:

• Addition combines quantities to achieve a sum (e.g., \(a + b\)).
• Subtraction finds the difference between numbers, effectively removing a value from another (e.g., \(a - b\)).
• Multiplication counts up the total in a specified number of groups (e.g., \(a \times b\)).
• Division splits a number into equal parts (e.g., \(a \div b\)).

In the problem at hand, performing the subtraction first and then the addition gave us a clearer path to the solution. Understanding these operations and knowing which comes first when ordered properly is crucial in simplifying expressions efficiently.