**Simplifying Fractions: 1 4/5 x 2/3**

In this article, we will explore how to simplify the fraction 1 4/5 x 2/3. We will break down the steps to multiply these mixed numbers and express the result as a simplified fraction.

**Step 1: Convert Mixed Numbers to Improper Fractions**

To multiply these mixed numbers, we need to convert them into improper fractions. An improper fraction is a fraction where the numerator is greater than or equal to the denominator.

**1 4/5**

To convert 1 4/5 into an improper fraction, we multiply the whole number part (1) by the denominator (5) and then add the numerator (4).

**1 × 5 = 5**
**5 + 4 = 9**

So, 1 4/5 is equivalent to **9/5**.

**2/3**

The second mixed number is already an improper fraction, so we don't need to convert it.

**Step 2: Multiply the Fractions**

Now that we have our improper fractions, we can multiply them together.

**9/5 × 2/3**

To multiply fractions, we multiply the numerators (9 and 2) and multiply the denominators (5 and 3).

**9 × 2 = 18**
**5 × 3 = 15**

So, the result of multiplying the fractions is **18/15**.

**Step 3: Simplify the Fraction**

We can simplify the fraction **18/15** by dividing both the numerator and denominator by their greatest common divisor (GCD).

The GCD of 18 and 15 is **3**. Therefore, we can divide both numbers by 3.

**18 ÷ 3 = 6**
**15 ÷ 3 = 5**

The simplified fraction is **6/5**.

**Conclusion**

In conclusion, the result of multiplying 1 4/5 and 2/3 is **6/5**. We can simplify fractions by converting mixed numbers to improper fractions, multiplying them together, and then simplifying the resulting fraction.