Key takeaways
- Addition combines two numbers into one total: Sum = a + b.
- Line up digits by place value before adding multi-digit numbers.
- If a column adds to 10 or more, carry the extra 1 to the next column.
- Order doesn't matter: a + b always equals b + a.
In this guide
What is addition?
Addition combines two or more numbers into one total. If you have 3 apples and someone gives you 2 more, addition tells you how many you have altogether: 5.
Why does addition matter?
You add numbers dozens of times a day without noticing: totaling a bill, counting points in a game, or working out how many days until a trip. Every other math skill, from multiplication to algebra, is built on top of addition.
Multiplication is really just fast, repeated addition — 4 × 3 is just 3 + 3 + 3 + 3 in disguise.
The formula
| Symbol | What it means | Example |
|---|---|---|
| Sum | The total after combining the numbers | 83 |
| a | The first number | 45 |
| b | The second number | 38 |
How to add step by step
- 1Write down the two numbers. Stack them so the ones digit is under the ones digit, tens under tens.
- 2Add the ones column first. If the total is 10 or more, write down the last digit and carry the 1 to the tens column.
- 3Add the tens column, including any digit you carried, then move on to hundreds and beyond the same way.
- 4Read off the final sum from top to bottom of your columns.
Try changing the numbers in the calculator below to see every carrying step laid out for you.
Try it yourself
Pre-filled with the example — change any value.
Common mistakes to avoid
- Misaligning digits. Lining up a 2-digit number under a 3-digit number in the wrong place makes the whole sum wrong.
- Losing track of a carried digit. Write the carried 1 above the next column so you don't forget it.
- Mixing up addition with [subtraction](/calculator/subtraction-basic). Adding finds a total; subtracting finds what's left.
Tips and tricks
- Estimate first by rounding each number to the nearest ten, so you can spot a typo in your final answer.
- Check your work by adding the columns in reverse order (bottom to top) — you should get the same sum.
- Comfortable with addition? Multiplying numbers is the natural next step.
Where you'll use it in real life
- Shopping: totaling the price of everything in your cart before you reach the register.
- Sports: adding up points, goals, or laps across a game or a season.
- Saving money: combining several weeks of savings into one running total.
- Cooking: adding ingredient amounts when you double a recipe.
Quick summary
To add two numbers, line them up by place value, add each column starting from the ones, and carry any extra ten into the next column. Addition is commutative, so the order never changes the answer. Use the calculator above to check your work with every step shown.
Worked example
You saved $45 in the first week of the month and $38 in the second week. How much have you saved in total so far?
- 01Sum = a + b
- 02Sum = 45 + 38
- 03Sum = 83
These numbers are pre-filled in the calculator above.
Frequently asked questions
What is the easiest way to add large numbers?
Line the numbers up by place value (ones, tens, hundreds), add column by column from right to left, and carry over any digit of 10 or more into the next column.
Does the order of the numbers change the sum?
No. Addition is commutative, meaning a + b always equals b + a. 5 + 3 gives the same answer as 3 + 5.
How do I add more than two numbers?
Add any two of them first to get a partial sum, then add the next number to that result, and repeat until every number has been included.
What does it mean to "carry" a number in addition?
When a column adds up to 10 or more, you write down only the last digit in that column and move (carry) the extra 1 into the next column to the left.
