To add the mixed numbers $1 \frac{4}{7}$ and $3 \frac{2}{5}$, let's follow these steps:

Step 1: Convert the mixed numbers to improper fractions

• For $1 \frac{4}{7}$: $1 \frac{4}{7} = \frac{1 \times 7 + 4}{7} = \frac{7 + 4}{7} = \frac{11}{7}$

• For $3 \frac{2}{5}$: $3 \frac{2}{5} = \frac{3 \times 5 + 2}{5} = \frac{15 + 2}{5} = \frac{17}{5}$

Step 2: Find a common denominator

The denominators are 7 and 5. The least common denominator (LCD) is 35.

• For $\frac{11}{7}$, multiply both the numerator and denominator by 5: $\frac{11}{7} = \frac{11 \times 5}{7 \times 5} = \frac{55}{35}$

• For $\frac{17}{5}$, multiply both the numerator and denominator by 7: $\frac{17}{5} = \frac{17 \times 7}{5 \times 7} = \frac{119}{35}$

Step 3: Add the fractions

Now that the fractions have the same denominator, we can add them: $\frac{55}{35} + \frac{119}{35} = \frac{55 + 119}{35} = \frac{174}{35}$

Step 4: Convert the improper fraction back to a mixed number

To convert $\frac{174}{35}$ to a mixed number, divide 174 by 35: $174 \div 35 = 4 \text{ with a remainder of } 34$

Thus, $\frac{174}{35} = 4 \frac{34}{35}$.

Final Answer:

$1 \frac{4}{7} + 3 \frac{2}{5} = 4 \frac{34}{35}$

Would you like further details or have any questions on this process?

Additional questions to explore:

1. How do you add fractions with different denominators?
2. Can you simplify the fraction before converting to a mixed number?
3. What is the process for subtracting mixed numbers?
4. How do you convert a fraction to a decimal?
5. What’s the difference between an improper fraction and a mixed number?

Tip:

When adding mixed numbers, it can be helpful to first convert them to improper fractions. This simplifies the process and avoids confusion during addition!