Why is it important to keep the two sides of an equation balanced when solving? What other properties do we use to rewrite expressions and equations?

Amber had 1/6 of a pie left after the bake sale. rihanna had 3/8 of a pie left. what fraction of a pie did they have altogether?

Each of the walls of a room with square dimensions has been built with two pieces of sheetrock, a smaller one and a larger one. the length of all the smaller ones is the same and is stored in the variable small. similarly, the length of all the larger ones is the same and is stored in the variable large. write a single expression whose value is the total area of this room. do not use any method invocations.

Ahiking trail is 6 miles long. it has 4 exercise stations, spaced evenly along the trail. what is the distance between each exercise station?