Problem 71 - Basic College Mathematics

Question

Divide. $$ 0 \div 22 $$

Step-by-Step Solution

Answer

0

Step 1: Understand Division

Division is the process of determining how many times one number (the divisor) is contained within another number (the dividend). In this exercise, 0 is the dividend and 22 is the divisor.

Step 2: Division by Nonzero Number

Any number divided by another nonzero number follows the general division rule. Specifically, for any number a, if a is 0, then it follows that 0 divided by any number is always 0.

Step 3: Apply the Rule

Here, since the dividend is 0 and the divisor (22) is a nonzero number, apply the rule: 0 divided by any nonzero number is 0.

Key Concepts

dividend

In the context of division, the dividend is the number being divided. It represents what you start with before you split it into parts. For example, in our exercise, 0 is the dividend. To visualize this, imagine you have 0 candies and want to share them with some friends. In reality, you can't give out any candies because there are none to begin with. This fundamental principle always applies, regardless of how many groups you divide into.

divisor

The divisor is the number by which the dividend is divided. In simpler terms, it's the number of parts or groups we are dividing the dividend into. For the given exercise, the divisor is 22. Think of it as wanting to divide 0 candies among 22 friends. Even though the divisor is 22, since the dividend is 0, each friend would still get 0 candies. This concept highlights another basic rule of division: the nature of the divisor doesn't change the outcome when the dividend is 0.

division by zero

Division by zero is a special case in mathematics and is undefined. This means you cannot divide any number by zero. To understand why let's explore some scenarios:

• When you try to split a nonzero number into zero parts, it's unclear what each part should be.
• From a practical standpoint, you can't distribute something into no groups—it's simply nonsensical.

However, dividing 0 by any nonzero number (as in our exercise with 0 divided by 22) is always 0. This is an exception to the undefined nature of division by zero, due to the unique property of zero having no quantity to be distributed.