To divide two mixed numbers like \( 1 \frac{3}{7} \) by \( 1 \frac{1}{4} \), follow these steps:

### Step 1: Convert both mixed numbers to improper fractions.

\[
1 \frac{3}{7} = \frac{7 \times 1 + 3}{7} = \frac{10}{7}
\]
\[
1 \frac{1}{4} = \frac{4 \times 1 + 1}{4} = \frac{5}{4}
\]

### Step 2: Perform the division by multiplying the first fraction by the reciprocal of the second.

\[
\frac{10}{7} \div \frac{5}{4} = \frac{10}{7} \times \frac{4}{5} = \frac{10 \times 4}{7 \times 5} = \frac{40}{35}
\]

### Step 3: Simplify the resulting fraction.
\[
\frac{40}{35} = \frac{8}{7}
\]

So, \( 1 \frac{3}{7} \div 1 \frac{1}{4} = \frac{8}{7} \), or \( 1 \frac{1}{7} \) as a mixed number.

Would you like further details or clarification?

Here are five related questions to explore this further:
1. How do you multiply fractions with different denominators?
2. How do you add mixed numbers?
3. Can you convert improper fractions back to mixed numbers?
4. How do you simplify fractions?
5. How does the reciprocal of a fraction work in division?

**Tip:** Always simplify fractions to their lowest terms to get the most reduced answer.

Learn how to divide mixed numbers like 1 3/7 by 1 1/4 with this detailed step-by-step solution. This guide covers converting mixed numbers to improper fractions, using the reciprocal in division, and simplifying fractions. Suitable for students in Grades 6-8.

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