Problem 96 - Prealgebra

Question

Simplify. $$20-8 \cdot 2$$

Step-by-Step Solution

Answer

The simplified expression is 4.

Step 1: Understand the Order of Operations

When simplifying mathematical expressions, the order of operations is crucial. The standard order is Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right). This is often remembered with the acronym PEMDAS.

Step 2: Identify the Operations in the Expression

Our expression is \(20 - 8 \cdot 2\). It involves subtraction and multiplication. According to the order of operations, multiplication should be performed before subtraction.

Step 3: Perform Multiplication

According to PEMDAS, we need to perform the multiplication first. Multiply \(8\) by \(2\) which gives \(16\). Therefore, the expression becomes \(20 - 16\).

Step 4: Perform Subtraction

Now subtract \(16\) from \(20\), which gives us \(4\). Thus, the simplified expression is \(4\).

Key Concepts

PEMDAS

When dealing with mathematical expressions, understanding the order of operations is essential. This sequence is represented by the acronym PEMDAS, which stands for:

• P - Parentheses
• E - Exponents
• M - Multiplication
• D - Division
• A - Addition
• S - Subtraction

To follow PEMDAS properly, address any calculations in parentheses first, then exponents. Next, handle multiplication and division from left to right. Lastly, complete any addition and subtraction from left to right.
PEMDAS helps ensure that everyone performs mathematical operations in a consistent manner, yielding the same result. It clarifies the prioritization of operations, especially when an expression contains multiple operators.

Simplifying Expressions

Simplifying expressions involves reducing them to their simplest form. This typically means performing all operations and reducing the number of terms. For each operations:

• Multiplication and Division: Execute these from left to right. They rank equally, so their order of appearance in the expression determines their execution.
• Addition and Subtraction: Similar to multiplication and division, perform these operations from left to right. They hold the same precedence level and thus are evaluated based on their sequence in the expression.

Performing each mathematical operation, as dictated by PEMDAS, helps to simplify an expression step-by-step until no further reductions are possible. In simpler terms, always break down the expression systematically, completing higher-order operations first before moving down the sequence.

Mathematical Operations

Mathematical operations such as addition, subtraction, multiplication, and division form the bedrock of arithmetic. A solid understanding of these operations is essential for simplifying expressions. Let's explore the operations:

• Addition and Subtraction: These are basic operations that increase or decrease values. Subtraction can also be viewed as adding a negative number.
• Multiplication and Division: Multiplication is repeated addition, while division is the process of determining how many times a number can be subtracted. Division can be understood as multiplying by a reciprocal.

Each operation plays a crucial role in finding accurate solutions when processing expressions. Properly executing these operations through defined rules like PEMDAS ensures consistency in handling complex mathematical problems. By mastering these operations, one can efficiently tackle an array of mathematical challenges.