Division (mathematics)

Division is one of the four basic operations of arithmetic, along with addition, subtraction, and multiplication. It helps us share things equally or figure out how many times one number fits into another. For example, if you have 20 apples and want to share them evenly among 4 friends, division tells you that each friend gets 5 apples.

When dividing, the number being split is called the dividend, the number we divide by is the divisor, and the answer we get is the quotient. Division can be simple, like sharing whole apples, or more complex when we need to deal with parts of numbers.

To always get a single answer without leftovers, we use numbers that include parts of numbers, called rational numbers or real numbers. This lets us say that dividing 21 apples among 4 people means each person gets 5 and a quarter apples, with no apples left over. However, there are some rules, like we can't divide by zero, because that doesn't make sense in mathematics.

Introduction

Division is one of the four basic math operations, along with addition, subtraction, and multiplication. It tells us how many times one number fits into another. For example, if you have 20 apples and want to share them equally among 5 friends, each friend gets 4 apples. We write this as 20 ÷ 5 = 4. Here, 20 is the dividend (the number being divided), 5 is the divisor (the number we are dividing by), and 4 is the quotient (the result).

Sometimes, numbers don’t divide evenly. For instance, when you divide 10 by 3, you get 3 groups of 3 with 1 apple left over. This leftover amount is called a remainder. We can express this as a fraction (like 3 and 1/3) or as a decimal (about 3.33). Division is different from multiplication and addition because changing the order changes the result. For example, 8 ÷ 2 is 4, but 2 ÷ 8 is only 0.25.

Notation

Further information: Division sign

Division can be shown in a few different ways. One common way is to write the number being divided above the number you are dividing by, with a line in between. For example, "a divided by b" can be written as a fraction:

a/b

Another way is to write the number being divided, then a slash, then the number you are dividing by, like this:

a / b

This is how division is often shown in computer programming because it is easy to type. Some computer programs let you write the number you are dividing by first and then use a backslash, like this:

b \ a

You can also use the division sign (÷), which you might see on calculators. In some countries, a colon (:) is used to show division, like this:

a : b

These different ways of writing division all mean the same thing—they just look a little different!

Computing

Main articles: Long division and Division algorithm

Division can be learned by sharing things equally, like splitting candies among friends. One way to do this is called "chunking," where you take away groups until everything is shared.

For bigger numbers, people use methods like short division or long division. These can be done with pencil and paper.

Today, calculators and computers can do division quickly. They might use methods like long division or even faster ways, especially in modular arithmetic and with real numbers. Some of these methods use a special number to help make division easier for computers.

Division in different contexts

Main article: Euclidean division

Division is one of the four basic math operations, along with addition, subtraction, and multiplication. When we divide, we split a number into equal parts based on another number. The number we split is called the dividend, and the number we split by is called the divisor. The answer we get is called the quotient.

We can use division with different types of numbers. For whole numbers, Euclidean division shows how many times one number fits into another and what is left over. With fractions, dividing one fraction by another is the same as multiplying by its reciprocal. For real numbers, division works as long as we do not divide by zero. Division can also be used in more complex math, but these topics are usually studied in advanced classes.

Division by zero

Main article: Division by zero

Dividing any number by zero is not possible in regular math. This is because zero times any number is always zero. Most calculators will show an error if you try this. In some special math systems, like the zero ring, division by zero can have a meaning, but it works differently.