Answer:
49/9 = 5 4/9
Explanation:
To add the fractions 4 2/3 and 7/9, we first need to convert the mixed number 4 2/3 into an improper fraction. To do this, we multiply the whole number (4) by the denominator of the fraction (3) and then add the numerator (2) to get the new numerator. The denominator remains the same.
4 * 3 = 12
12 + 2 = 14
So, 4 2/3 is equivalent to the improper fraction 14/3.
Now, we can add the fractions:
14/3 + 7/9
To add fractions, we need a common denominator. In this case, the least common multiple (LCM) of 3 and 9 is 9.
Now, let's convert the fractions to have a common denominator of 9:
14/3 = (14 * 3)/(3 * 3) = 42/9
7/9 = (7 * 1)/(9 * 1) = 7/9
Now, we can add the fractions:
42/9 + 7/9 = (42 + 7)/9 = 49/9
The sum of 4 2/3 and 7/9 is 49/9 = 5 4/9.