What is a situation, or mathematical problem, in which being able to complete various steps mentally can be helpful?
There are many every day situations in which it is convenient to be able to complete mathematical processes mentally.
Consider any time you undertake a long drive, such as a multi-state family vacation. As you travel, you will probably monitor the gas mileage you get by dividing the number of miles traveled by the number of gallons of gas you put in the gas tank. Based on that number, you will formulate predictions concerning how far you will be able to drive before needing to refill again. You may estimate the total cost for gas on your trip by dividing the total number of miles you anticipate traveling by the miles per gallon figure you computed. All this figuring is more quickly and easily completed if done mentally.
When shopping, being able to keep a mental running total of the costs of the items you have in your cart can help you remain within your budget for the trip. Multiplying the number of pieces of pizza that each person at a gathering might eat by the number of probable attendees, and dividing that number by the number of slices in a given size of pizza can help you decide how many pizzas to have delivered. Being able to mentally adjust all ingredients in a recipe by the same proportion allows you to increase or decrease the size of a recipe while reading from the cookbook.