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Answer :
- Add the whole numbers: $6 + 2 = 8$.
- Find a common denominator and add the fractions: $\frac{38}{45} + \frac{5}{9} = \frac{38}{45} + \frac{25}{45} = \frac{63}{45}$.
- Simplify the fraction: $\frac{63}{45} = \frac{7}{5} = 1 \frac{2}{5}$.
- Add the whole and fractional parts: $8 + 1 \frac{2}{5} = \boxed{9 \frac{2}{5}}$.
### Explanation
1. Problem Analysis
We are asked to add two mixed numbers: $6 \frac{38}{45}$ and $2 \frac{5}{9}$. The final answer must be a mixed number in simplest form.
2. Adding Whole Numbers
First, let's add the whole number parts: $6 + 2 = 8$.
3. Finding Common Denominator
Next, we need to add the fractional parts: $\frac{38}{45} + \frac{5}{9}$. To do this, we need a common denominator. The least common multiple of 45 and 9 is 45. So we rewrite $\frac{5}{9}$ as $\frac{5 \times 5}{9 \times 5} = \frac{25}{45}$.
4. Adding Fractions
Now we can add the fractions: $\frac{38}{45} + \frac{25}{45} = \frac{38+25}{45} = \frac{63}{45}$.
5. Simplifying Fraction
Now we simplify the fraction $\frac{63}{45}$. Both 63 and 45 are divisible by 9. So, $\frac{63}{45} = \frac{63 \div 9}{45 \div 9} = \frac{7}{5}$.
6. Converting to Mixed Number
Now we convert the improper fraction $\frac{7}{5}$ to a mixed number: $\frac{7}{5} = 1 \frac{2}{5}$.
7. Adding Whole and Fractional Parts
Finally, we add the whole number parts: $8 + 1 \frac{2}{5} = 9 \frac{2}{5}$.
8. Final Answer
Therefore, $6 \frac{38}{45} + 2 \frac{5}{9} = 9 \frac{2}{5}$.
### Examples
Mixed number addition is useful in everyday situations such as cooking, where you might need to combine fractional amounts of ingredients. For example, if a recipe calls for $6 \frac{38}{45}$ cups of flour and you want to double the recipe, you would need to add $6 \frac{38}{45} + 6 \frac{38}{45}$ cups of flour. Similarly, if you are measuring wood for a project, you might need to add lengths given in mixed numbers to determine the total length of wood needed.
- Find a common denominator and add the fractions: $\frac{38}{45} + \frac{5}{9} = \frac{38}{45} + \frac{25}{45} = \frac{63}{45}$.
- Simplify the fraction: $\frac{63}{45} = \frac{7}{5} = 1 \frac{2}{5}$.
- Add the whole and fractional parts: $8 + 1 \frac{2}{5} = \boxed{9 \frac{2}{5}}$.
### Explanation
1. Problem Analysis
We are asked to add two mixed numbers: $6 \frac{38}{45}$ and $2 \frac{5}{9}$. The final answer must be a mixed number in simplest form.
2. Adding Whole Numbers
First, let's add the whole number parts: $6 + 2 = 8$.
3. Finding Common Denominator
Next, we need to add the fractional parts: $\frac{38}{45} + \frac{5}{9}$. To do this, we need a common denominator. The least common multiple of 45 and 9 is 45. So we rewrite $\frac{5}{9}$ as $\frac{5 \times 5}{9 \times 5} = \frac{25}{45}$.
4. Adding Fractions
Now we can add the fractions: $\frac{38}{45} + \frac{25}{45} = \frac{38+25}{45} = \frac{63}{45}$.
5. Simplifying Fraction
Now we simplify the fraction $\frac{63}{45}$. Both 63 and 45 are divisible by 9. So, $\frac{63}{45} = \frac{63 \div 9}{45 \div 9} = \frac{7}{5}$.
6. Converting to Mixed Number
Now we convert the improper fraction $\frac{7}{5}$ to a mixed number: $\frac{7}{5} = 1 \frac{2}{5}$.
7. Adding Whole and Fractional Parts
Finally, we add the whole number parts: $8 + 1 \frac{2}{5} = 9 \frac{2}{5}$.
8. Final Answer
Therefore, $6 \frac{38}{45} + 2 \frac{5}{9} = 9 \frac{2}{5}$.
### Examples
Mixed number addition is useful in everyday situations such as cooking, where you might need to combine fractional amounts of ingredients. For example, if a recipe calls for $6 \frac{38}{45}$ cups of flour and you want to double the recipe, you would need to add $6 \frac{38}{45} + 6 \frac{38}{45}$ cups of flour. Similarly, if you are measuring wood for a project, you might need to add lengths given in mixed numbers to determine the total length of wood needed.
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