They married in Coatbridge/Old Monkland in 1887.
The 1891 census shows them in Portland Street, Coatbridge:
Alexander, 26, manager drapery department of store.
Amelia, 28,
William, 3,
Amelia, 1
The 1901 census shows them in Almondbank Terrace, Edinburgh:
Alexander Fraser, 35, draper (manager), b Slamannan, Stirlingshire (contradicted by 1871 census),
Amelia, 37, b. Coatbridge,
William, 13, scholar, b. Coatbridge,
Amelia, 11, scholar, b. Coatbridge,
Agnes, 8, schgolar, b. Coatbridge
The 1871 census shows Alexander with his parents at "Houses E of Burnfoot, New Monkland":
William Gardner, 36, blacksmith, b. Slamannan, Stirlingshire,
Agnes Stevenson, wife, 30, b. Muiravonside, Stirlingshire,
Andrew Gardner, 10, scholar, b. Muiravonside, Stirlingshire,
William Gardner, 8, scholar, b. Muiravonside, Stirlingshire,
Robert Gardner, 6, b. New Monkland,
Alexander Gardner, 4, b. New Monkland,
Charlotte A. Gardner, 1, b. New Monkland,
Margaret Nimmo, 15, general servant
The 1881 census shows Alexander with his parents at Ballencrieff Toll, Bathgate, W. Lothian:
William Gardner, 46, blacksmith,
Agnes, 39,
William, 18, scholar,
Alexander, 14, draper's apprentice,
Charlotte "N.", 11, scholar,
Margaret M., 9,
Agnes S., 7,
Marion M., 4,
Mary, 2
The four youngest children are born in Bathgate.