3 1/2 + 1 2/3
To solve this problem, we need to first convert the mixed numbers into improper fractions.
To convert 3 1/2 into an improper fraction, we multiply the whole number (3) by the denominator (2) and add the numerator (1):
3 x 2 + 1 = 7
The new numerator is 7, and the denominator remains the same (2). Therefore, 3 1/2 as an improper fraction is 7/2.
To convert 1 2/3 into an improper fraction, we follow the same steps:
1 x 3 + 2 = 5
The new numerator is 5, and the denominator remains the same (3). Therefore, 1 2/3 as an improper fraction is 5/3.
Now that we have converted both mixed numbers into improper fractions, we can add them together.
7/2 + 5/3
To add these fractions, we need to find a common denominator. The least common multiple of 2 and 3 is 6.
We can then convert both fractions to have a denominator of 6:
7/2 = (7/2) x (3/3) = 21/6
5/3 = (5/3) x (2/2) = 10/6
Now that both fractions have a denominator of 6, we can add them together:
21/6 + 10/6 = 31/6
Therefore, 3 1/2 + 1 2/3 = 31/6.