two-third of three-fifth of fifth-sixth of what percentage of number

Let's break down the expression step by step to solve for "what percentage of a number." We're calculating a series of fractions:

We want to find **two-thirds of three-fifths of five-sixths of a percentage of a number**.

Let the number be **\( x \)%**. The steps are as follows:

1. First, take **five-sixths** of the number:  
   \[ \frac{5}{6} \times x \]

2. Next, take **three-fifths** of the result from step 1:  
   \[ \frac{3}{5} \times \left( \frac{5}{6} \times x \right) = \frac{3}{5} \times \frac{5}{6} \times x = \frac{15}{30} \times x = \frac{1}{2} \times x \]

3. Finally, take **two-thirds** of the result from step 2:  
   \[ \frac{2}{3} \times \left( \frac{1}{2} \times x \right) = \frac{2}{3} \times \frac{1}{2} \times x = \frac{2}{6} \times x = \frac{1}{3} \times x \]

Therefore, the entire expression simplifies to:

\[
\frac{1}{3} \times x
\]

This means the final value is **one-third** of the original number \( x \). If you're asking for the percentage of a number, it would be **one-third** of that percentage.

Would you like to go into more detail or ask anything else?

### Related questions:
1. What is the concept of taking fractions of fractions?
2. How do we simplify complex fractions involving multiple steps?
3. How can you apply this process to real-world problems?
4. Can the same approach be used for fractions with larger numerators and denominators?
5. How do percentages work with fractional calculations?

### Tip:
Always simplify fractions step by step to avoid confusion in complex operations!

Learn how to simplify and solve a multi-step fraction problem: two-thirds of three-fifths of five-sixths of a percentage of a number. This explanation covers key concepts in fractions and percentage calculations, suitable for students in Grades 6-8.

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