3x 2 3 simplified

Daniel Parker

2 min read

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25-02-2025

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This article will guide you through simplifying the expression 3 x (2/3). We'll break down the process step-by-step, making it easy to understand, even if you're new to fractions and multiplication. Understanding how to simplify this type of expression is crucial for mastering basic arithmetic and algebra.

Understanding the Problem: 3 x 2/3

The expression "3 x 2/3" means we're multiplying the whole number 3 by the fraction 2/3. This is a common type of problem encountered in elementary math and beyond. Knowing how to simplify it efficiently is key to solving more complex equations later on.

Method 1: Multiplying First, Then Simplifying

One way to approach this problem is to multiply the whole number by the numerator of the fraction first.

Step 1: Multiply the whole number by the numerator.

3 x 2 = 6

Step 2: Keep the denominator the same.

Our result now looks like this: 6/3

Step 3: Simplify the fraction.

6/3 simplifies to 2 because 3 goes into 6 two times. Therefore, 3 x 2/3 = 2.

Method 2: Canceling Before Multiplying (The Efficient Way)

This method utilizes the concept of canceling common factors. It's a more efficient approach, especially when dealing with larger numbers or more complex fractions.

Step 1: Rewrite the whole number as a fraction.

We can rewrite the whole number 3 as the fraction 3/1. Our expression now becomes (3/1) x (2/3).

Step 2: Identify common factors in the numerator and denominator.

Notice that we have a '3' in both the numerator (of the first fraction) and the denominator (of the second fraction).

Step 3: Cancel the common factors.

We can cancel out the 3 from the numerator and the denominator. This leaves us with:

(1/1) x (2/1)

Step 4: Multiply the remaining numbers.

1 x 2 = 2

Therefore, using this method, we also arrive at the answer: 3 x 2/3 = 2

Why is Simplification Important?

Simplifying fractions is crucial because it makes working with numbers easier. A simplified fraction is easier to understand and use in further calculations. In more advanced math, simplifying expressions early on can prevent errors and save time.

Practice Problems

Try simplifying these expressions using the methods outlined above:

• 5 x 4/5
• 7 x 3/7
• 12 x (1/12)

Remember, always look for opportunities to cancel common factors before multiplying to make the process quicker and less prone to errors. Practice makes perfect, so keep working through examples!