https://file.aiquickdraw.com/mathbot/file/1727802838060vv7ai6lt.jpg

The image shows the sum of two mixed numbers:

\[
6 \frac{2}{3} + 6 \frac{4}{7}
\]

To solve this, let's break it down:

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

- For \( 6 \frac{2}{3} \):
  \[
  6 \frac{2}{3} = \frac{6 \times 3 + 2}{3} = \frac{18 + 2}{3} = \frac{20}{3}
  \]

- For \( 6 \frac{4}{7} \):
  \[
  6 \frac{4}{7} = \frac{6 \times 7 + 4}{7} = \frac{42 + 4}{7} = \frac{46}{7}
  \]

### Step 2: Find a common denominator.

The least common denominator (LCD) of 3 and 7 is 21.

- Convert \( \frac{20}{3} \) to have a denominator of 21:
  \[
  \frac{20}{3} = \frac{20 \times 7}{3 \times 7} = \frac{140}{21}
  \]

- Convert \( \frac{46}{7} \) to have a denominator of 21:
  \[
  \frac{46}{7} = \frac{46 \times 3}{7 \times 3} = \frac{138}{21}
  \]

### Step 3: Add the fractions.

Now that both fractions have the same denominator, we can add them:
\[
\frac{140}{21} + \frac{138}{21} = \frac{140 + 138}{21} = \frac{278}{21}
\]

### Step 4: Simplify the result.

Divide \( \frac{278}{21} \):
\[
278 \div 21 \approx 13 \text{ remainder } 5
\]

So, \( \frac{278}{21} = 13 \frac{5}{21} \).

### Final Answer:
\[
6 \frac{2}{3} + 6 \frac{4}{7} = 13 \frac{5}{21}
\]

Let me know if you'd like more details or have any questions!

Here are 5 related questions:
1. How can you subtract mixed numbers with different denominators?
2. What is the general method for multiplying mixed numbers?
3. Can you convert improper fractions back into mixed numbers?
4. How do you simplify improper fractions?
5. What is the process to solve a word problem involving mixed numbers?

**Tip:** Always convert mixed numbers to improper fractions first when performing addition or subtraction for easier calculation.

Learn how to add mixed numbers like 6 2/3 and 6 4/7 by converting them into improper fractions, finding the least common denominator, and performing fraction addition. The solution simplifies the final answer to a mixed number, 13 5/21. Suitable for Grades 5-7 students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation