If you are working out a budget, checking a bill, claiming a benefit or work expenses, determining the distance between two places by car, or many other everyday calculations, you will probably need to add some numbers together. Consider the following questions.

• How much is the bill altogether?
• How much will your vacation cost now that the total price of your airfare has increased by \$50 due to fuel surcharges?
• Five more people want to come on the trip: What is the total number of people booked on the bus now?
• What is the cost plus sales tax? All the questions above involve addition to work out the answer. The key or “trigger” words that indicate addition have been bolded. The process of adding numbers together may also be referred to more formally as finding the sum of a set of numbers.

When you are adding two numbers together, it does not matter in which order you add them together, so gives the same answer as . In mathematical terms, we say that addition is commutative. Not every operation will possess this property (for example ).