Problem 15 - Prealgebra

Question

Find the value of each expression. $$3 \cdot 6-4$$

Step-by-Step Solution

Answer

The value of the expression is 14.

Step 1: Understand the Expression

The given expression is \(3 \cdot 6 - 4\). It consists of a multiplication followed by a subtraction.

Step 2: Perform Multiplication

First, calculate the multiplication part of the expression: \(3 \cdot 6\). This means multiplying 3 by 6, which results in 18.

Step 3: Perform Subtraction

Next, take the result from the multiplication, which is 18, and subtract 4 from it. So, \(18 - 4 = 14\).

Key Concepts

Understanding Multiplication in Arithmetic

Multiplication is one of the four basic operations in arithmetic. It represents repeated addition, making calculations more efficient when dealing with large numbers. For instance, multiplying 3 by 6, as seen in the expression \(3 \cdot 6 - 4\), is similar to adding 3 together six times: \(3 + 3 + 3 + 3 + 3 + 3 = 18\).

• Terminology: The numbers being multiplied are called 'factors.' In this example, 3 and 6 are the factors.
• Result: The result of multiplication is called the 'product.' Here, 18 is the product of the multiplication step.

Remembering these terms and concepts can help solidify the fundamental role multiplication plays in arithmetic operations.
When evaluating arithmetic expressions, it's important to perform multiplication before moving on to other operations such as addition or subtraction.

The Role of Subtraction in Arithmetic

Subtraction is another fundamental operation in arithmetic. It involves finding the difference between numbers, often representing situations of taking away or decreasing amounts. In the given expression \(3 \cdot 6 - 4\), the subtraction step occurs after multiplication.

• Identifying Parts: In subtraction, the number from which you subtract is called the 'minuend' and the number you subtract is the 'subtrahend.' In the step \(18 - 4\), 18 is the minuend, and 4 is the subtrahend.
• Outcome: The result of a subtraction is called the 'difference.' Thus, 14 is the difference in this example.

Understanding the steps encourages precision. Perform operations in sequence to ensure all calculations are accurate.

Evaluating Arithmetical Expressions

Arithmetical expressions involve various numbers and operations like addition, subtraction, multiplication, and division. To correctly evaluate these expressions, a systematic approach following the 'order of operations' is necessary.
When looking at an expression like \(3 \cdot 6 - 4\), order matters significantly. The widely accepted rule is PEMDAS:

• P: Parentheses first (anything inside brackets)
• E: Exponents (powers and roots)
• M/D: Multiplication and Division from left to right
• A/S: Addition and Subtraction from left to right

In our problem, multiplication comes before subtraction, ensuring that \(3 \cdot 6\) is calculated prior to subtracting 4.
By remembering and applying these rules, students can work through arithmetical expressions confidently and accurately, obtaining the correct results.