**7 over 15 divided by 3 over 10: Understanding Fraction Operations**

In this article, we will explore the operation of dividing two fractions: 7 over 15 divided by 3 over 10. We will break down the steps to solve this problem and provide a clear explanation of the process.

**The Problem: 7/15 ÷ 3/10**

To evaluate this expression, we need to follow the order of operations (PEMDAS):

- Divide the two fractions
- Simplify the result

**Step 1: Divide the Fractions**

To divide two fractions, we need to invert the second fraction (i.e., flip the numerator and denominator) and then multiply:

`(7/15) ÷ (3/10) = (7/15) × (10/3)`

**Step 2: Multiply the Fractions**

Now, we need to multiply the numerators (numbers on top) and multiply the denominators (numbers on the bottom):

`(7 × 10) / (15 × 3) = 70 / 45`

**Simplifying the Result**

To simplify the fraction, we need to find the greatest common divisor (GCD) of 70 and 45, which is 5. Then, we can divide both numbers by 5:

`70 ÷ 5 = 14`

`45 ÷ 5 = 9`

So, the simplified result is:

`7/15 ÷ 3/10 = 14/9`

**Conclusion**

In conclusion, the result of dividing 7 over 15 by 3 over 10 is 14 over 9. By following the steps of inverting the second fraction, multiplying, and simplifying, we can evaluate this expression accurately.