No:
1 US liquid quart = 0.946352946 litres
1 US dry quart = 1.101220942715 litres
1 Imperial quart = 1.1365225 litres
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Convert to same units and then can compare. Based on your spelling of liter, I guess you are American: 1 liter ≈ 2.11 US pints 1 quart = 2 pints → 1 liter is greater than 1 quart. If you are a European who can't spell litre or is stuck with an American dictionary: 1 litre ≈ 1.76 imp pints 1 quart = 2 pints → 1 litre is less than 1 quart.
They are equal because 1 quart is equal to 4 cups
There can be no answer. A quart can be expressed as a fraction only in the context of another quantity of volume.
2 pints is equal to 1 quart.
A quart is 1/4 of a gallon. A gallon is 3.785 liters, so a quart would be 3.785/4 liters.