WASHINGTON – Five big-state primaries Tuesday will try to clarify the math and momentum of a presidential ­campaign that has mocked conventional wisdom.

The survival of as many as three candidates — one Democrat and two Republicans — is on the line.

Together with contests on either side of the Mississippi in Illinois and Missouri, primaries in Florida, Ohio and North Carolina will make up the second-biggest single-day ­delegate prize of the campaign in both parties.

For Democrats, former Secretary of State Hillary Clinton's grind-it-out strategy over surprise challenger Vermont Sen. Bernie Sanders would get a momentum boost if, as polls suggest, she sweeps the five states, which have 792 delegates, roughly a third of the total necessary to win the nomination.

If Sanders blunts her momentum with wins or even close losses, the grind of proportional fights over delegates would continue in primaries and caucuses into late spring.

For Republicans, it is all about the math — and whether billionaire Donald Trump and Texas Sen. Ted Cruz finally get the two-man race each has been clamoring for.

Florida and Ohio will be the first GOP winner-take-all states in 2016, and together they add up to about 13 percent of all delegates necessary to win the nomination. If Trump wins both and adds delegates awarded proportionally in Missouri, Illinois and North Carolina, his path to the GOP nomination would be virtually unstoppable.

A St. Louis Post-Dispatch poll of Missouri conducted by the Docking Institute of Public Affairs at Fort Hays State University in Kansas showed Trump with a small lead over Cruz among Republicans, 36 percent to 29 percent, with a margin of error of plus or minus 7 percent.

In other polls leading into the weekend, Trump led favorite son John Kasich in Ohio and favorite son Marco Rubio in Florida. Trump also was ahead in polls in Illinois and North Carolina.

Without victories in their home states, Rubio and Kasich would face immediate decisions on whether to continue.

Among Democrats, Clinton wins in five big, disparate states would begin pleas for the party to rally around her.

But by pulling off late-surge victories, any one of the three — Rubio, Kasich or Sanders — could emerge as central players in new theatrics amid a campaign in which anger against the establishment has been a driving force.

Among Republicans, a widely split verdict Tuesday would greatly increase the likelihood that no candidate would gather the 1,237 delegates necessary to win the nomination before arriving in Cleveland for the July convention.

If Trump has a good night, the story line would be, "He is the presumptive nominee," said David Robertson, chair of the Department of Political Science at the University of Missouri, St. Louis. But if Trump loses multiple states, Robertson said, the takeaway would be: "Long, tough slog ahead — advantage still Trump."

Trump and Clinton have racked up decisive, but not yet conclusive, leads in delegates in their respective parties, and each has won a solid majority of the primaries and caucuses since Feb. 1.

Cruz has emerged as Trump's primary challenger.

"There are two of us that can" get to 1,237 delegates, Trump said during a debate Thursday night, "and two of us that can't. … That is a mathematical fact."

As of Friday, Real Clear Politics had Trump ahead of Cruz, 458-359, followed by Rubio at 151 and Kasich at 54.

Clinton had a wider lead over Sanders among Democrats, with Real Clear Politics showing her having procured about half the 2,383 delegates necessary to win the nomination, and leading Sanders by a margin of more than 2-1. But that tally distorts the closeness of the campaign so far, because it includes Clinton's overwhelming 461-25 advantage in "superdelegates" — party free-agent luminaries who can vote for whomever they want at the convention.

Sanders' surprise win over Clinton in Michigan on Tuesday has his strategists hoping for a carry-over in fellow Midwestern states Missouri, Illinois and Ohio.

"I do think, for example the issue of trade, which we focused on in Michigan, is a powerful issue in Illinois and Missouri and Ohio," Sanders senior adviser Tad Devine said.

Clinton is leading in polls in all five states. But polls before Michigan gave Clinton a more than 20-point edge. Sanders won by about 18,000 votes out of nearly 1.2 million cast.

"We will compete in all five states again, with the goal of building our delegate lead," said Clinton campaign manager Robbie Mook. "All signs point to Sen. Sanders competing especially in … Ohio, Illinois and Missouri. And it is true that the demographics in those states are similar to Michigan."