The multiplication \(\frac{1}{3} \times 27 = 9\) can be understood by considering the following steps:

### Understanding the Fraction \(\frac{1}{3}\):
- The fraction \(\frac{1}{3}\) means "one-third," or 1 divided by 3. It represents a part of a whole that is divided into 3 equal parts.

### Multiplication by a Fraction:
- When you multiply a number by a fraction, you're essentially finding that fraction of the number. In this case, you're finding one-third of 27.

### Calculation:
- To find \(\frac{1}{3}\) of 27, you divide 27 by 3:
  \[
  \frac{27}{3} = 9
  \]
- This means that 27 divided into three equal parts gives you 9 in each part. Therefore, \(\frac{1}{3} \times 27 = 9\).

### Conceptual Explanation:
- Imagine you have 27 objects. If you want to group these objects into 3 equal groups, each group would have 9 objects. Hence, multiplying by \(\frac{1}{3}\) gives you the size of one of these groups, which is 9.

Would you like more details or have any questions?

Here are some related questions to consider:

1. How would the result change if you multiplied by \(\frac{2}{3}\) instead of \(\frac{1}{3}\)?
2. What happens if you multiply a number by a fraction greater than 1?
3. Can you explain why \(\frac{2}{3} \times 27\) is equal to 18?
4. How does multiplying by a fraction compare to dividing by a whole number?
5. What would the result be if you multiplied by \(\frac{1}{2}\) instead of \(\frac{1}{3}\)?
6. Can you apply this concept to decimals instead of fractions?
7. How would you explain this multiplication to someone learning fractions for the first time?
8. What happens if you multiply by \(\frac{3}{3}\) or \(\frac{4}{3}\)?

**Tip:** Multiplying by a fraction is the same as dividing by its denominator, which helps break down the operation into simpler steps.

Explore how to multiply fractions and understand the equation 1/3 × 27 = 9 step-by-step. This problem covers fundamental concepts in fractions and multiplication. Suitable for students in Grades 4-6.

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