I mentioned CARS, which was an Army-wide reorganization of the combat arms which began in the late 1950's. Under CARS, what had once been Battery B, 34th Field Artillery Battalion became Headquarters & Headquarters Battery, 2d Battalion, 34th Field Artillery. In researching USA, AUS, ARNG & USAR units, it's very important to consider CARS in that units were consolidated, reorganized and/or redesignated so that a unit you're researching almost certainly has a different designation - in many cases, completely different than that prior to CARS.
During World War II, an infantry division was assigned four battalions of artillery - one battalion of 155 millimeter howitzers and three battalions of 105 millimeter howitzers. Typically, three of the 155 batteries provided fire support to to the division's three regiments, a battery to each regiment, and the fourth provided general support - extra support whenever and wherever needed. Each of the 105 battalions supported an infantry regiment. A battery of each battalion supporting an infantry battalion and the fourth battery of each battalion providing general support for its respective regiment. The 34th was the 9th Infantry Division's 155 battalion so figure it out based on the above.
Assuming you're researching - or researching for - an individual. An individual's campaign credits would, of course, be based on his OWN service; he MUST have been present for duty within the prescribed area of operations during the specified time frame to be credited. If the individual participated in the action for which the battalion was awarded the PUC, he may wear the award (ribbon) permanently. If not, he may wear the award only while assigned to the unit. The Belgian Fourragere was awarded to units that had been cited at least twice in Belgian Army Orders. The Belgian award differs from the French Fourragere in that there was no provision allowing for temporary display. An individual MUST have participated in BOTH actions for which the unit was cited to be eligible to wear the award.