Question: how much of South Dakota is west of the longest river in North America?

Context paragraphs:
South Dakota's 2nd congressional district: South Dakota's 2nd congressional district is an obsolete district.  It was created after the 1910 census and abolished after the 1980 census.  Members were elected at-large until the formation of individual districts after the 1910 Census.  From 1913 until 1933, the 2nd District covered much of northeastern South Dakota, including the cities of Aberdeen, Brookings, Huron, and Watertown.  When South Dakota's 3rd congressional district was eliminated after the 1930 Census, the 2nd District was relocated to cover all of the counties in South Dakota west of the Missouri River.  Population changes eventually moved the district's boundaries further east.  During the 97th Congress, it covered all but the 21 easternmost counties in the state.

Pipestone Creek (Big Sioux River): Pipestone Creek is a 53.2 mi river in southwestern Minnesota, having a center branch as well as branches named "North" and "South".  The creek (center branch) begins about 3 mi north of Holland (the high point of its watershed actually being underneath the north branch's watershed) and flows southwesterly, roughly following MN State Highway 23 for much of its early existence (also being known as County Ditch Number 1).  The creek approaches the town of Pipestone from the east, but turns northwesterly just before Highway 23 meets U.S. Highway 75, with the creek going under both highways in rapid succession.  Flowing through Pipestone National Monument, the creek passes over Winnewissa Falls, and then enters the adjacent State DNR controlled "Pipestone Wildlike Management Area" where a small "impoundment" (dam) forms "Indian Lake".  The creek continues northwesterly until turning southwesterly just east of County Road 53.  On the west side of County Rd 53, and on the North side of Country Rd 5, it is joined by the North branch, and on the south side of the same road, the South branch joins.  The creek continues southwesterly, and crosses the state line in South Dakota above the road known as 81st Street in Minnesota and 236th A Street in South Dakota.  It does not travel far into South Dakota, but loops back into Minnesota, flowing into Split Rock Creek within a mile of the state line, this confluence about 3 miles north of Sherman, South Dakota, also being 3 miles south of Jasper, Minnesota.  Split Rock Creek itself is a tributary of the Big Sioux River, which in turn flows via the Missouri River and Mississippi River to the Gulf of Mexico.

Charles A. West: Charles A. "Jack" West (c. 1890 – October 29, 1957) was an American football, Canadian football, and basketball coach and college athletics administrator.  He served as the head football coach at South Dakota State College of Agricultural and Mechanic Arts—now South Dakota State University—from 1919 to 1927 and at the University of North Dakota from 1928 to 1941 and again in 1945, compiling a career college football record of 134–55–14.  West was also the head basketball coach at South Dakota State from 1919 to 1926 and at North Dakota during the 1944–45 season, amassing a career college basketball record of 74–66.  He coached football teams to 11 North Central Conference titles, three at South Dakota State and eight at North Dakota.  In addition, he served as North Dakota's athletic director from 1928 to 1946.  West left the college ranks in 1946 to become head coach of the Winnipeg Blue Bombers, then of the Western Interprovincial Football Union, now a division of the Canadian Football League.  He died at the age of 67 on October 29, 1957 at his home in Grand Forks, North Dakota.

South Dakota Highway 45: South Dakota Highway 45 is a state route that runs north to south across much of central South Dakota.  The northern terminus is at the North Dakota border as a continuation of North Dakota Highway 3, and runs south to South Dakota Highway 44 at Platte.  It is 198 mi in length.

Mackenzie River: The Mackenzie River (Slavey language: Deh-Cho [tèh tʃʰò], "big river" or Inuvialuktun: Kuukpak [kuːkpɑk], "great river") is the largest and longest river system in Canada, and is exceeded only by the Mississippi River system in North America.  It flows through a vast, isolated region of forest and tundra entirely within the country's Northwest Territories, although its many tributaries reach into four other Canadian provinces and territories.  The river's mainstem runs 1738 km in a northerly direction to the Arctic Ocean, draining a vast area nearly the size of Indonesia.  It is the largest river flowing into the Arctic from North America, and with its tributaries is one of the longest rivers in the world.

South Dakota Highway 75: South Dakota Highway 75 (SD 75) is a state route located in northwest South Dakota.  The southern terminus is at South Dakota Highway 20 west of Bison, and the route runs northerly to the North Dakota border, becoming North Dakota Highway 8.  It is 28 miles (45 kilometers) in length.

West River (South Dakota): West River is the portion of the state of South Dakota located west of the Missouri River with well over one-half of the land area and between one-quarter and one-third of the population of the state.

Missouri River: The Missouri River is the longest river in North America.  Rising in the Rocky Mountains of western Montana, the Missouri flows east and south for 2341 mi before entering the Mississippi River north of St. Louis, Missouri.  The river takes drainage from a sparsely populated, semi-arid watershed of more than half a million square miles (1,300,000 km), which includes parts of ten U.S. states and two Canadian provinces.  When combined with the lower Mississippi River, it forms the world's fourth longest river system.

The Standing Rock Rural Water System: The Standing Rock Rural Water System (RWS) is a $30 million water system funded by the American Recovery and Reinvestment Act in 2009 for about 10,000 residents of the Standing Rock Sioux reservation in North Dakota.  The RWS includes the Standing Rock Water Treatment and the "Indian Memorial Intake Pump Station, a raw water pipeline, two transmission pipelines and Kline Butte Storage Reservoir."  The main regulation reservoir of the Standing Rock Rural Water System is the $3.6 million Kline Butte Storage Reservoir, located southwest of Kenel, South Dakota, which consists of a 5 million gallon ground storage reservoir.  Currently, (in December 2016) the intake valve for the water system is "located in a shallow part of the Missouri River near Fort Yates, North Dakota, roughly 20 miles from the planned river crossing of the controversial Dakota Access Pipeline also known as the Bakken pipeline.  The Bakken oil pipeline Dakota line is to be "buried 92 feet below the riverbed in hard clay."  A new valve came online in 2016 in Mobridge, South Dakota which is seventy miles south of the proposed Bakken Pipeline Missouri River crossing.  This Mobridge intake valve is intended to service the entire Standing Rock Sioux reservation.

South Dakota Highway 25: South Dakota Highway 25 is a state route that runs north to south across a large portion of South Dakota.  It is divided into two segments.  The main segment begins at the North Dakota border, with the junction of North Dakota Highway 18 north of Claire City.  Its southern terminus is at the junction of South Dakota Highway 42 south of Emery.  This segment is 191 mi long.  The second segment begins at a junction with U.S. Highway 18 west of Olivet, and extends south to South Dakota Highway 50 northwest of Tabor.  It is 22 mi in length.  The total length of SD 25 is just over 201 mi in length.

Supporting paragraphs: West River (South Dakota) Missouri River
Answer: over one-half of the land area