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

Let's solve the problem step by step:

### **Given:**
- We need to find \( \frac{3}{4} \) of \( \frac{2}{5} \) divided by 27.

### **Find:**
- The result of \( \left(\frac{3}{4} \times \frac{2}{5}\right) \div 27 \).

### **Solution:**

1. **Multiply the fractions:**
   \[
   \frac{3}{4} \times \frac{2}{5} = \frac{3 \times 2}{4 \times 5} = \frac{6}{20}
   \]
   Simplify \( \frac{6}{20} \) by dividing both the numerator and denominator by their greatest common divisor, which is 2:
   \[
   \frac{6}{20} = \frac{3}{10}
   \]

2. **Divide the fraction by 27:**
   \[
   \frac{3}{10} \div 27 = \frac{3}{10} \times \frac{1}{27} = \frac{3 \times 1}{10 \times 27} = \frac{3}{270}
   \]
   Simplify \( \frac{3}{270} \) by dividing both the numerator and denominator by 3:
   \[
   \frac{3}{270} = \frac{1}{90}
   \]

### **Final Answer:**
The result is \( \frac{1}{90} \).

Would you like any further details or explanations?

Here are 5 related questions to explore:

1. What is the result of \( \frac{5}{6} \) of \( \frac{3}{7} \) divided by 18?
2. How do you multiply two fractions and simplify the result?
3. What is the process of dividing one fraction by another?
4. How would the answer change if the original division was by 54 instead of 27?
5. Can you generalize the method used here to any fractions and a divisor?

**Tip:** When multiplying fractions, always simplify the result if possible to make further calculations easier.

Discover how to solve the problem of finding 3/4 of 2/5 divided by 27 with a detailed step-by-step guide. This explanation covers multiplying and dividing fractions, simplifying the result, and is perfect for students in Grades 5-7.

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