To solve the expression \( 7 \frac{12}{7} \div 7 \frac{4}{7} \), we need to first convert the mixed numbers into improper fractions.

### Step 1: Convert mixed numbers to improper fractions.
1. \( 7 \frac{12}{7} = \frac{7 \times 7 + 12}{7} = \frac{49 + 12}{7} = \frac{61}{7} \)
2. \( 7 \frac{4}{7} = \frac{7 \times 7 + 4}{7} = \frac{49 + 4}{7} = \frac{53}{7} \)

### Step 2: Perform the division.
Now divide the two improper fractions:
\[
\frac{61}{7} \div \frac{53}{7}
\]
Dividing fractions is equivalent to multiplying by the reciprocal:
\[
\frac{61}{7} \times \frac{7}{53} = \frac{61 \times 7}{7 \times 53} = \frac{61}{53}
\]

So, \( 7 \frac{12}{7} \div 7 \frac{4}{7} = \frac{61}{53} \), which is the simplified form.

Let me know if you'd like further details, or if you have any questions.

Here are some related questions to explore:
1. How do you convert between mixed numbers and improper fractions?
2. What is the process for multiplying fractions?
3. Can you always simplify a fraction after dividing?
4. How can you verify if two fractions are equivalent?
5. What are some real-world examples where fraction division is used?

**Tip:** When dividing fractions, always multiply by the reciprocal of the divisor.

Learn how to solve the division problem involving mixed numbers: 7 12 ÷ 7 4. This step-by-step solution demonstrates the conversion of mixed numbers to improper fractions and the process of dividing fractions by multiplying with the reciprocal. Suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation