The smiths are sending out a batch of holiday cards. emily signed 2/5 of the cards. then josh signed 1/9 of the remaining cards. tatiana signed 20% of what josh had left. if there were 75 cards in all, how many cards are left to be signed?

There were 75 cards in all.

Emily: 2/5 of 75 = 2/5 * 75 = 30
Emily signed 30 cards, and left 75 - 30 = 45

Josh: 1/9 * 45 = 45/9 = 5
Josh signed 5 cards and left 45 - 5 = 40

Tatiana: 20% * 40 = 0.2 * 40 = 8
Tatiana signed 8 cards and left 40 - 8 = 32

There are 32 cards left to sign.