https://file.aiquickdraw.com/mathbot/file/1726861605658h6rll7b9.jpg

To solve the addition of mixed numbers \( 4 \frac{5}{9} + 7 \frac{1}{5} \), we need to follow these steps:

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

- For \( 4 \frac{5}{9} \):
  \[
  4 \frac{5}{9} = \frac{4 \times 9 + 5}{9} = \frac{36 + 5}{9} = \frac{41}{9}
  \]

- For \( 7 \frac{1}{5} \):
  \[
  7 \frac{1}{5} = \frac{7 \times 5 + 1}{5} = \frac{35 + 1}{5} = \frac{36}{5}
  \]

### Step 2: Find a common denominator for the fractions.

The denominators are 9 and 5. The least common denominator (LCD) of 9 and 5 is 45.

### Step 3: Convert the fractions to have the same denominator.

- Convert \( \frac{41}{9} \) to a denominator of 45:
  \[
  \frac{41}{9} = \frac{41 \times 5}{9 \times 5} = \frac{205}{45}
  \]

- Convert \( \frac{36}{5} \) to a denominator of 45:
  \[
  \frac{36}{5} = \frac{36 \times 9}{5 \times 9} = \frac{324}{45}
  \]

### Step 4: Add the fractions.

Now that they have the same denominator, add them together:
\[
\frac{205}{45} + \frac{324}{45} = \frac{205 + 324}{45} = \frac{529}{45}
\]

### Step 5: Convert the improper fraction back to a mixed number.

Divide 529 by 45:
\[
529 \div 45 = 11 \text{ remainder } 34
\]
So, \( \frac{529}{45} = 11 \frac{34}{45} \).

### Final Answer:
The sum of \( 4 \frac{5}{9} + 7 \frac{1}{5} \) is \( 11 \frac{34}{45} \).

Let me know if you would like more details or further explanation!

---

Here are 5 related questions:
1. How do you subtract mixed numbers with different denominators?
2. What is the least common denominator and how is it calculated?
3. How do you convert improper fractions back to mixed numbers?
4. What is the best way to simplify a fraction after addition?
5. How do you multiply mixed numbers?

**Tip**: When adding mixed numbers, always convert them to improper fractions first for easier calculation.

Learn how to add mixed numbers, specifically 4 5/9 and 7 1/5, by converting them to improper fractions, finding a common denominator, and solving the sum. Suitable for Grades 5-7.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation