how did you do the first step this is my first time doing a division of two fractions so explain every small detail;

Sure! Let's break down the first step in detail, focusing on dividing two fractions.

### Expression:
\[
\left(\frac{\frac{a}{b}}{c}\right)
\]

### Understanding the Expression:
This expression involves dividing the fraction \(\frac{a}{b}\) by the number \(c\). When dividing fractions, you can think of the number \(c\) as a fraction with a denominator of 1, i.e., \(\frac{c}{1}\). The division of two fractions is the same as multiplying the first fraction by the reciprocal of the second fraction.

### Step-by-Step Division:

1. **Original Problem:**
   \[
   \frac{\frac{a}{b}}{c}
   \]

2. **Convert \(c\) to a Fraction:**
   We can write \(c\) as \(\frac{c}{1}\), so the expression becomes:
   \[
   \frac{\frac{a}{b}}{\frac{c}{1}}
   \]

3. **Dividing by a Fraction:**
   Dividing by a fraction is equivalent to multiplying by its reciprocal. The reciprocal of \(\frac{c}{1}\) is \(\frac{1}{c}\). So, we multiply \(\frac{a}{b}\) by \(\frac{1}{c}\):

   \[
   \frac{a}{b} \div \frac{c}{1} = \frac{a}{b} \cdot \frac{1}{c}
   \]

4. **Multiply the Fractions:**
   When multiplying two fractions, you multiply the numerators together and the denominators together:

   \[
   \frac{a}{b} \cdot \frac{1}{c} = \frac{a \cdot 1}{b \cdot c}
   \]

   This simplifies to:

   \[
   \frac{a}{bc}
   \]

### Final Result:
So, \(\frac{\frac{a}{b}}{c} = \frac{a}{bc}\).

This is how we obtained the result for the first step. The key idea here is that dividing by a fraction is the same as multiplying by its reciprocal.

Would you like any more details or explanations on this topic?

### Related Questions:

1. What does the reciprocal of a number mean?
2. How do you find the reciprocal of a fraction?
3. Why is dividing by a fraction equivalent to multiplying by its reciprocal?
4. Can you provide an example with numbers for dividing fractions?
5. How do you handle division when there are variables in the fractions?
6. What are some common mistakes to avoid when dividing fractions?
7. How can we verify the result of a division of fractions?
8. What is the relationship between division and multiplication in the context of fractions?

### Tip:
Always remember that dividing by a fraction (or a whole number) is equivalent to multiplying by its reciprocal. This rule is fundamental in simplifying expressions involving division of fractions.

Learn how to divide fractions step-by-step with a detailed explanation. This guide covers fundamental concepts such as fractions, division of fractions, and reciprocals. Suitable for students in Grades 5-8.

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