find  2 3/10 + 4 2/5 in two different ways

To find the sum of \( 2 \frac{3}{10} + 4 \frac{2}{5} \), I will solve it in two different ways.

### Method 1: Converting to Improper Fractions
1. Convert each mixed number to an improper fraction:
   - \( 2 \frac{3}{10} = \frac{2 \times 10 + 3}{10} = \frac{23}{10} \)
   - \( 4 \frac{2}{5} = \frac{4 \times 5 + 2}{5} = \frac{22}{5} \)

2. Find a common denominator. The least common denominator (LCD) of 10 and 5 is 10.
   - \( \frac{22}{5} = \frac{22 \times 2}{5 \times 2} = \frac{44}{10} \)

3. Add the fractions:
   \[
   \frac{23}{10} + \frac{44}{10} = \frac{23 + 44}{10} = \frac{67}{10}
   \]

4. Convert back to a mixed number:
   \[
   \frac{67}{10} = 6 \frac{7}{10}
   \]

### Method 2: Adding Whole Numbers and Fractions Separately
1. Add the whole numbers: 
   \[
   2 + 4 = 6
   \]

2. Add the fractional parts:
   - \( \frac{3}{10} + \frac{2}{5} \)
   - Convert \( \frac{2}{5} \) to have a denominator of 10:
     \[
     \frac{2}{5} = \frac{4}{10}
     \]
   - Now add:
     \[
     \frac{3}{10} + \frac{4}{10} = \frac{7}{10}
     \]

3. Combine the whole number and the fraction:
   \[
   6 + \frac{7}{10} = 6 \frac{7}{10}
   \]

In both methods, the result is \( 6 \frac{7}{10} \).

Would you like further details on any step? Here are five related questions for deeper understanding:

1. How do you find the least common denominator for fractions?
2. Can you explain how to convert between improper fractions and mixed numbers?
3. What is the importance of converting fractions to have a common denominator?
4. How can we subtract mixed numbers instead of adding them?
5. How do you multiply mixed numbers together?

**Tip:** When adding fractions, always make sure their denominators are the same before proceeding with the addition.

find 2 3/10 + 4 2/5 in two different ways

Learn how to add mixed numbers like 2 3/10 and 4 2/5 using two different methods: converting to improper fractions and adding fractions separately. Understand the process of finding a common denominator and converting results back into mixed numbers. Suitable for Grades 5-7.

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