https://file.aiquickdraw.com/mathbot/file/1726183546941enbsftw1.jpg

The problem you're solving involves dividing two fractions:

\[
\frac{6 \frac{1}{7}}{3 \frac{5}{7}}.
\]

Let's break this down step by step.

### Step 1: Convert mixed numbers to improper fractions.
- \(6 \frac{1}{7}\) can be written as an improper fraction. Multiply the whole number (6) by the denominator (7) and add the numerator (1):
  \[
  6 \frac{1}{7} = \frac{6 \times 7 + 1}{7} = \frac{42 + 1}{7} = \frac{43}{7}.
  \]

- \(3 \frac{5}{7}\) can also be converted to an improper fraction:
  \[
  3 \frac{5}{7} = \frac{3 \times 7 + 5}{7} = \frac{21 + 5}{7} = \frac{26}{7}.
  \]

### Step 2: Division of two fractions.
Dividing two fractions is equivalent to multiplying by the reciprocal of the second fraction:
\[
\frac{\frac{43}{7}}{\frac{26}{7}} = \frac{43}{7} \times \frac{7}{26}.
\]

### Step 3: Simplify.
When multiplying, we can cancel out the common factor of 7:
\[
\frac{43}{\cancel{7}} \times \frac{\cancel{7}}{26} = \frac{43}{26}.
\]

### Step 4: Simplify the fraction (if needed).
Since 43 and 26 have no common factors, the fraction \(\frac{43}{26}\) is already in its simplest form. As a mixed number, this is:
\[
43 \div 26 = 1 \frac{17}{26}.
\]

So, the quotient is \(1 \frac{17}{26}\).

Would you like further details or clarification? Here are five related questions you could explore:

1. How do you multiply two fractions?
2. What is the process for converting improper fractions to mixed numbers?
3. What are some strategies for simplifying fractions?
4. Can you explain why dividing by a fraction is the same as multiplying by its reciprocal?
5. How do you check whether a fraction is in its simplest form?

**Tip:** When dividing fractions, always remember to "flip" (find the reciprocal of) the second fraction and then multiply.

Learn how to divide mixed numbers by converting them to improper fractions. This step-by-step guide explains how to find the quotient of (6 1/7) ÷ (3 5/7) using reciprocal multiplication. Ideal 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