# Quotient

A quotient is the result of a division problem. In other words, it is the solution to the question "how many times does a number (the divisor) go into another (the dividend)?" A division problem can be structured in a number of different ways, as shown below.

There are other symbols used to indicate division as well, such as 12 / 3 = 4. In all the cases, the problem is the same, and the quotient is 4.

Examples

Identify the quotient in the following division problems.

1. 32 ÷ 2 = 16; the quotient is 16.

2. = 4; the quotient is 4.

3. James has 64 apples and wants to share them with his 3 friends. He wants everyone (including himself) to have an equal number of apples, so he gives each person 16 apples. What is the quotient?; the quotient is 16.

It is important to understand the various parts of a division sentence (and equations in general) to be able to understand and communicate mathematics. However, it is also important to understand division as a concept. One way to conceptualize division is to think of it in terms of a given number of objects being broken up into a number of groups containing an equal number of objects. For example, in 8 ÷ 2 = 4, there are a total of 8 objects that are broken into 4 groups. In order for each group to have an equal number of objects, each group would have to have 2 objects, as in the figure below.

The dividend in the figure above is represented by the 8 red circles.