To make a batch of
fruit punch, steve needs 2 2/3 cups
blackberry juice. if he wants to make 2 ¾ batches of punch, how many cups of
blackberry juice will he need?

Steve wants to make 2+3/4 batches=2*4/4+3/4=11/4. He needs 2+2/3 cups=2*3/3+2/3=8/3. 11/4*8/3=88/12. You can see both have a factor 2, so 88/12=44/6 and again 44/6=22/3. 22 cannot be devided by 3 but division with rest gives 22/3 = 7 + 1/3.