a certain requires 4 1/5 cups of flour and 2 3/7 cups of sugar.
a) if 4/9 of the recipe is to be made, how much sugar is needed?
b) if the above ingredients are required for one batch, find the amount of flour needed for a triple batch.

In this item, we are given with the amounts of both the flour and sugar. 

Part A:
First, we determine the total amount of recipes needed for the batch.
    total amount = (4 1/5 cup) + (2 3/7 cup)
     total amount = 232/35 cup

To determine the total amount of sugar needed for 4/9 of the recipe, we multiply the given amount of sugar by 4/9. That is,
            amount of sugar = (4/9)(2 3/7) 
            amount of sugar = 68/63 cups of sugar

Part B: To determine the amount of flour needed is 3 times the given amount for each batch.

      amount of flour = (3)(4 1/5 cups of flour)
     amount of flour = 63/5 cups or 12.6 cups of flour