3 1/2 + 5 3/5 + 2 3/4 + 6 2/3
make the terms into improper fractions
(3 * 2/2 + 1/2) + (5 * 5/5 + 3/5) + (2 * 4/4 + 3/4) + (6 * 3/3 + 2/3)
(6/2 + 1/2) + (25/5 + 3/5) + (8/4 + 3/4) + (18/3 + 2/3)
(7/2) + (28/5) + (11/4) + (20/3)
Factor the denominators to find the Least Common Denominator (LCD)
2 = 2 * 1
5 = 5 * 1
4 = 2 * 2
3 = 3 * 1
LCD = 5 * 2 * 2 * 3 = 60
Get the fractions into a form where they have a common denominator.
(7/2) * ((5 * 2 * 3) / (5 * 2 * 3)) + (28/5) * ((2 * 2 * 3) / (2 * 2 * 3)) + (11/4) * ((5 * 3) / (5 * 3)) + (20/3) * ((5 * 2 * 2) / (5 * 2 * 2))
(7/2) * (30/30) + (28/5) * (12/12) + (11/4) * (15/15) + (20/3) * (20/20)
(210/60) + (336/60) + (165/60) + (400/60)
(210 + 336 + 165 + 400) /60
1111 / 60
Convert back to an improper fraction
18 31/60