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An area in front of the tub was soft so I cut it out. It is not rotted out under the tub. As you can see in the pics the edges next to the tub aren't a very clean cut. Didn't have a sawzall so the cuts are jagged. Am I going to have to nail or screw some boards perpendicular to the floor boards under the tub for more support or do you think it is OK the way it is? The jagged edge goes back about 3/4" in some areas. I'm not sure how these garden tubs are supported. I stuck my finger under one edge of the tub and it was hollow.

You will need perpendicular blocking under the tub, and under the edge of the existing floor to provide a support for the replacement floor. The tub itself is supported by the center section, the edge you see provides only minimal support.

Is it ok to use 2 x 4's or do I have to use 2 x 6's? It's not going to be easy adding boards to the 2 x 6's on the ends. Any suggestions?

I think I would have tried to take the tub out in order to replace it all. Are you sure the floor holding the tub up is in good shape?

I run my blocking "flat" so that the 4 or 6" side is flat, it gives a little more for the sub floor to sit on instead of just 3/4". They don't really need to support a lot because the floor joists will do most of the supporting, they are mainly for if someone was to step right on the edge in the middle of two floor joists. You can cut the blocking and then start the screws on an angle from the bottom to toe "nail" into the joists. You can also buy some metal brackets to screw them in. I call them simpson brackets but that is just a name of one brand that makes them. The box stores like HD and lowes will have them. Just need an angle plate that you can pre screw to the blocking and then slide the blocking in and then screw the plate to the joists. Plates will probably be the easiest since you won't have to screw at weird angles. The stores have plates for just about any setup you can think of so check them out and find one that will work good for your situation. Screw the edges of the sub floor good and also make sure you screw the existing floor joists good and it will be strong.