"Thinking backwards"-starting at the end of the problem and using reverse operations-can help you solve certain problems at different grade levels.
Upper Elementary and Middle School:
A certain number is doubled. That answer is tripled. Finally, that answer is quadrupled and the answer is 60. What is the original number?
When we quadruple a number, we multiply it by 4. As division is the inverse of multiplication, 60 ÷ 4 = 15. Tripling a number means "multiply by 3," so 15 ÷ 3 = 5. Finally, doubling a number means "multiply by 2," thus, 5 ÷ 2 = 2.5, or 2 ½.
A certain number is quadrupled. 3 is added to the answer. That answer is then tripled. Finally, when that answer is cut in half, the answer is 12.