Addition facts for kids

Adding 3 apples and 2 apples gives a total of 5 apples.

Addition is one of the four basic operations in arithmetic, along with subtraction, multiplication, and division. We use the plus sign (+) to show addition. When you add two numbers, the result is called the sum.

For example, if you have 3 apples and you get 2 more apples, you have 5 apples in total. We write this as a math problem: 3 + 2 = 5. This is read as "three plus two equals five."

Addition isn't just for counting things you can see. It also works with all kinds of numbers, like integers (positive and negative whole numbers), real numbers, and even more abstract things in algebra like vectors and matrices.

Addition has some simple but important rules. For example, the order you add numbers in doesn't change the answer (this is called being commutative). Also, when you add zero to a number, the number stays the same. Learning to add is one of the first steps in math, and even modern computers are designed to perform addition very quickly.

How to Write Addition

The plus sign is used for addition.

Addition is written using the plus sign (+) between the numbers you are adding. The answer is shown with an equals sign (=). For example: ("one plus two equals three")

The numbers being added together are called addends or terms. The final answer is called the sum. In the example above, 1 and 2 are the addends, and 3 is the sum.

Sometimes, you might see a whole number and a fraction written together, like . This is a mixed number and means , or 3.5.

The Rules of Addition

Addition follows a few simple rules that make it easy to work with.

Order Doesn't Matter (Commutative Property)

4 + 2 gives the same result as 2 + 4.

Addition is commutative, which means you can switch the order of the numbers and still get the same answer. For example, 4 + 2 gives you the same sum as 2 + 4. Both equal 6.

Grouping Doesn't Matter (Associative Property)

When adding 2, 1, and 3, it doesn't matter if you add (2+1) first or (1+3) first.

Addition is associative. This means that when you add three or more numbers, it doesn't matter how you group them. For example, if you are adding 1, 2, and 3, you can add 1 and 2 first, or you can add 2 and 3 first. The final sum will be the same.

Adding Zero (Identity Property)

Adding zero to a number doesn't change its value.

When you add zero to any number, the number doesn't change. Zero is called the identity element for addition. For example, 5 + 0 = 5.

Adding with Units

To add physical amounts, they must have the same units. For example, you can add 50 milliliters to 150 milliliters to get 200 milliliters. But you can't add 3 meters to 4 square meters because the units are different and measure different things (length vs. area).

How We Add Numbers

Learning to Add by Counting

Most children first learn to add by counting. If you ask a young child to solve 2 + 3, they might use their fingers or draw objects to count the total.

A common strategy is "counting-on." To find 2 + 3, a child might start at 2 and then count three more numbers: "three, four, five." As they get better, they learn to start with the bigger number to count less. For 2 + 3, they would start at 3 and count: "four, five."

Mastering Single-Digit Addition

To add bigger numbers, you first need to know how to add single-digit numbers (0 through 9). These are often learned using an addition table.

Instead of memorizing the whole table, students often learn patterns to find the answers faster, like "doubles" (6 + 6 = 12) or "making ten" (8 + 6 = 8 + 2 + 4 = 10 + 4 = 14).

Adding Bigger Numbers: The Carry Method

An example of adding with a "carry".

To add numbers with more than one digit, you can line them up vertically. You add each column, starting from the right (the ones place). If a column's sum is 10 or more, you "carry" the extra digit over to the next column on the left.

For example, to add 27 + 59:

• In the ones column, 7 + 9 = 16. You write down the 6 and carry the 1 to the tens column.
• In the tens column, you add the carried 1 to 2 and 5. So, 1 + 2 + 5 = 8.
• The final answer is 86.

Adding Decimals

To add numbers with decimal points, you follow a similar process.

1. Line up the numbers so their decimal points are in the same column.
2. If one number has fewer decimal places, you can add zeros to the end to make them the same length.
3. Add the columns just like with whole numbers.
4. Place the decimal point in the answer directly below the other decimal points.

As an example, 45.1 + 4.34 can be solved as follows:
4 5 . 1 0
+
0 4 . 3 4
————————————
4 9 . 4 4

How Computers Add

Part of Charles Babbage's Difference Engine, an early mechanical calculator that could perform addition.

Addition is a basic task for computers. Early calculating tools like the abacus helped people add for thousands of years. In 1642, Blaise Pascal invented a mechanical calculator that could add numbers.

Modern digital computers perform addition using binary arithmetic (using only 0s and 1s). They have special electronic circuits called adders that are designed to add binary numbers very quickly. The speed of addition is very important for a computer's overall performance, because it's used in almost everything a computer does, from complex calculations to finding information in its memory.

Sometimes, if the result of an addition is too large for the computer to store, an error called an arithmetic overflow can happen. This was a cause of the Year 2000 problem, where some computers couldn't handle the change from the year 1999 to 2000.

How Addition Connects to Other Math

Addition is closely connected to other basic math operations.

• Subtraction is the inverse, or opposite, of addition. Adding a number and then subtracting the same number gets you back to where you started. For example, (10 + 5) - 5 = 10.
• Multiplication can be seen as repeated addition. For example, 3 × 4 is the same as adding 4 to itself 3 times (4 + 4 + 4 = 12).
• Division is the inverse of multiplication. It is more distantly related to addition, but they are all part of the basic set of arithmetic operations.

Images for kids

• 

  An illustration from a 15th-century English math book.

• 

  An electronic circuit called an operational amplifier, which can be used to add voltages.

• 

  A diagram of a "full adder" circuit, which computers use to add two binary digits.

• 

  A circular slide rule, an old tool that could be used for multiplication and division.

Related pages

• Identity element
• Order of operations

See also

In Spanish: Adición (matemática) para niños

• Mental arithmetic
• Parallel addition (mathematics)
• Verbal arithmetic (also known as cryptarithms), puzzles involving addition