How do you do this problem multiplying fractions: lily has 30 messages on her phone. of those messages, 1/5 are picture messages and 7/8 of the remainder are text messages. how many text messages does she receive?

so, she has 30 messages, and 1/5 of those are pictures, now, a whole will be 5/5, so if 1/5 are pictures, then the other 4/5 are the remainder.

how much is 4/5 of 30?  well, is just their product, 30(4/5) => 24.

now, of the remainder, 7/8 are text messages, well the remainder is 24, how much is 7/8 of 24?  same, is their product, 24(7/8) => 21.

δabc ≅ δdcb by sas because

db ≅ ac . . given (side)

bc ≅ bc . . reflexive property (side)

∠dbc ≅ ∠ acb . . alternate interior angles where transversal bc crosses parallel lines bd and ac (included angle)