3x 2 3 simplified

2 min read 26-02-2025

Understanding how to simplify mathematical expressions is a fundamental skill in algebra and beyond. This article will guide you through simplifying the expression "3 x 2/3," explaining the process clearly and concisely. We'll break down the steps and explore the underlying principles.

Understanding the Expression

The expression "3 x 2/3" involves multiplication and a fraction. We can interpret this as "3 multiplied by two-thirds." Our goal is to find the simplest equivalent form of this expression.

Method 1: Direct Multiplication

One approach is to directly multiply the whole number by the numerator of the fraction:

Multiply the whole number by the numerator: 3 x 2 = 6
Keep the denominator: The denominator remains as 3.
Resulting fraction: This gives us the fraction 6/3.

Method 2: Cancellation Before Multiplication

A more efficient method involves canceling common factors before performing the multiplication. This simplifies the calculation and avoids working with larger numbers.

Rewrite as a multiplication of fractions: We can rewrite 3 as 3/1, making the expression (3/1) x (2/3).
Identify common factors: Notice that both the numerator of the first fraction (3) and the denominator of the second fraction (3) share a common factor of 3.
Cancel the common factors: We can cancel out the 3s: (3/1) x (2/3) simplifies to (1/1) x (2/1).
Simplify the expression: This leaves us with 2/1, which simplifies to 2.

Understanding the Results

Both methods lead to the same simplified result. The fraction 6/3 is equivalent to 2. The second method, using cancellation, is often preferred for its efficiency, especially when dealing with more complex expressions involving larger numbers or multiple fractions.

Why Simplification Matters

Simplifying mathematical expressions is crucial for several reasons:

Clarity: Simplified expressions are easier to understand and interpret.
Efficiency: Simpler expressions are easier and faster to work with in further calculations.
Accuracy: Simplifying reduces the risk of errors in more complex problems.

Practice Problems

Try simplifying these similar expressions using the methods described above:

5 x 4/5
7 x 3/7
10 x 6/20

By mastering the simplification of expressions like "3 x 2/3," you build a strong foundation for more advanced mathematical concepts. Remember to always look for opportunities to cancel common factors to make the process more efficient.