Divided fraction to lowest term What is 3/4 of 2/5 divided by 27? Find? Given? Solution?

To solve this problem, let's carefully go through each step. 

### Given
- You need to find what \( \frac{3}{4} \) of \( \frac{2}{5} \) is, and then divide that result by 27.

### Step-by-Step Solution

1. **Calculate \( \frac{3}{4} \) of \( \frac{2}{5} \):**
   - Multiplication of fractions:  
   \[
   \frac{3}{4} \times \frac{2}{5} = \frac{3 \times 2}{4 \times 5} = \frac{6}{20}
   \]
   - Simplify \( \frac{6}{20} \) to its lowest terms by dividing the numerator and the denominator by their greatest common divisor, which is 2:  
   \[
   \frac{6 \div 2}{20 \div 2} = \frac{3}{10}
   \]

2. **Divide the result by 27:**
   - Dividing \( \frac{3}{10} \) by 27 can be written as:  
   \[
   \frac{3}{10} \div 27 = \frac{3}{10} \times \frac{1}{27} = \frac{3 \times 1}{10 \times 27} = \frac{3}{270}
   \]
   - Simplify \( \frac{3}{270} \) to its lowest terms by dividing the numerator and the denominator by their greatest common divisor, which is 3:  
   \[
   \frac{3 \div 3}{270 \div 3} = \frac{1}{90}
   \]

### Final Answer
\[
\frac{1}{90}
\]

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#### Related Questions:
1. What is \( \frac{2}{5} \) of \( \frac{3}{4} \)?
2. How to simplify fractions to their lowest terms?
3. What are the properties of multiplication and division of fractions?
4. How to find the greatest common divisor (GCD) of two numbers?
5. What is the difference between multiplying and dividing fractions?

#### Tip:
When dividing by a number, you can multiply by its reciprocal to simplify the calculation.

Learn how to simplify the expression 3/4 of 2/5 divided by 27 with a detailed step-by-step solution. This problem covers key fraction concepts such as multiplication, division, and simplification, making it suitable for students in Grades 5-6.

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