Problem 44 - Prealgebra

Question

Evaluate each expression. $$8 \div 2 \cdot 4$$

Step-by-Step Solution

Answer

The evaluated expression is 16.

Step 1: Understand the Order of Operations

To evaluate the expression \(8 \div 2 \cdot 4\), we need to follow the order of operations, often remembered by the acronym PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).

Step 2: Perform Division

According to the order of operations, we perform division and multiplication from left to right. First, we divide 8 by 2: \[ 8 \div 2 = 4 \]

Step 3: Perform Multiplication

Next, we use the result from Step 2 to perform the multiplication. Multiply 4 by 4: \[ 4 \cdot 4 = 16 \]

Key Concepts

PEMDAS

In mathematics, understanding the correct order to perform operations is crucial for solving expressions accurately. This order is memorized by the acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division (from left to right), Addition, and Subtraction (from left to right). These rules are essential because they determine how we simplify and solve expressions. Without following PEMDAS, different interpretations could lead to different results.
PEMDAS helps in avoiding confusion and ensures consistency in how mathematical problems are solved. It's important to remember that multiplication and division should be handled from left to right. The same rule applies to addition and subtraction. This left-to-right rule is sometimes where students make mistakes, so practice is key to mastering its application.

division

Division is the process of splitting a number into equal parts. In the expression given, division is one of the operations we perform. According to PEMDAS, division and multiplication are performed simultaneously, based on their order from left to right. In this specific example, the expression is "8 divided by 2".
When you divide 8 by 2, you are essentially asking, "How many twos are in eight?" This calculation yields a result of 4. Division is a key operation in many areas of mathematics and appears frequently in algebra, calculus, and beyond. One trick to remember is that division is the process of finding how many times one number is contained within another.

multiplication

Multiplication is a mathematical operation that indicates scaling a number by a certain factor. Once we perform division in our expression, the next step following PEMDAS is to multiply. From our earlier division result of 4, the expression continues with multiplication: "4 times 4".
The operation "4 times 4" results in the number 16. Multiplication can be thought of as repeated addition. In this case, it means you add the number 4 together four times (4 + 4 + 4 + 4). Understanding multiplication deeply aids in solving complex problems that involve equations and functions, making it an essential skill for aspiring mathematicians.

step-by-step solution

A step-by-step approach is invaluable when solving mathematical expressions, especially when ensuring adherence to PEMDAS. Let's revisit the expression given:

• First, identify and understand the order of operations using the acronym PEMDAS.
• Next, perform operations in their order of appearance from left to right, starting with division: calculate 8 divided by 2 to get 4.
• Finally, carry out multiplication: multiply the result 4 by 4 to obtain the final answer of 16.

Breaking down complex expressions into simpler steps helps prevent mistakes and build confidence. Practicing this method enhances understanding and ensures accurate computations, a critical aspect for anyone looking to master mathematics. Each step builds upon the previous one, leading to a clear solution and aiding comprehension for future, more challenging problems.