To add the mixed numbers \( 4 \frac{2}{3} \) and \( 3 \frac{5}{9} \), we first convert them to improper fractions.
-
For \( 4 \frac{2}{3} \): \[ 4 \frac{2}{3} = 4 \times 3 + 2 = 12 + 2 = 14 \quad \text{(improper fraction: } \frac{14}{3}\text{)} \]
-
For \( 3 \frac{5}{9} \): \[ 3 \frac{5}{9} = 3 \times 9 + 5 = 27 + 5 = 32 \quad \text{(improper fraction: } \frac{32}{9}\text{)} \]
Next, we need a common denominator to add these two fractions. The denominators are 3 and 9. The least common denominator (LCD) is 9.
Now, we convert \( \frac{14}{3} \) to a fraction with a denominator of 9: \[ \frac{14}{3} = \frac{14 \times 3}{3 \times 3} = \frac{42}{9} \]
Now we can add the two fractions: \[ \frac{42}{9} + \frac{32}{9} = \frac{42 + 32}{9} = \frac{74}{9} \]
Now we convert \( \frac{74}{9} \) back to a mixed number:
- Divide 74 by 9:
- \( 74 \div 9 = 8 \) (whole number),
- Remainder = \( 74 - (9 \times 8) = 74 - 72 = 2 \).
So, we can write: \[ \frac{74}{9} = 8 \frac{2}{9} \]
Therefore, the answer in mixed number form is: \[ 8 \frac{2}{9} \]
The whole number is \( 8 \). So, the final answer is:
Whole number: \( 8 \)
1 answer