To divide means to separate into parts. Given the problem 12 ÷ 6, which is read as "twelve divided by six," we can think of division as "how many groups of 6 can we separate 12 into?" The solution, also referred to as the quotient, is 2. Similarly, 12 ÷ 2 = 6, meaning that 12 can be separated into 6 groups of 2. Below is a figure showing these two division problems using objects.
On the left, we can see that 12 ÷ 2 results in 6 groups of 2 stars each. On the right, 12 ÷ 6 results in 2 groups of 6 stars each. For smaller values, this approach can be a helpful way to get a grasp of division. Eventually, it helps to memorize the multiplication facts, which are the 100 multiplication problems formed by all the combinations of one-digit numbers. 2 × 6 = 12 is a multiplication fact, as is 6 × 2. Memorizing these is helpful because division is the inverse of multiplication. Knowing the above multiplication facts would've allowed us to solve the above example very quickly.
To learn how to perform long division, refer to the long division page. Long division is an algorithm that can be used to systematically divide any number, including larger numbers as well as numbers that involve decimal places.
There are a number of ways to express division using different symbols. The following are all examples of the same division problem:
The first two simply use different division symbols, "÷" and "/". The third is a fraction, or a ratio, that can also be looked at as a division problem, and the last is the format used for long division.