Problem 90 - Prealgebra

Question

Divide. $$24 \div 4$$

Step-by-Step Solution

Answer

24 divided by 4 equals 6.

Step 1: Set Up the Division

First, identify the numbers involved in the division problem. The number 24 is the dividend, which is the number being divided, and 4 is the divisor, which is the number you are dividing by.

Step 2: Perform the Division

Divide the dividend by the divisor. Here, divide 24 by 4 to determine how many times 4 fits into 24. You can calculate this by determining what number multiplied by 4 gives you 24.

Step 3: Calculate the Result

Since 4 multiplied by 6 equals 24, the result of the division is 6. This means that 4 fits into 24 exactly 6 times without any remainder.

Key Concepts

Dividend

The concept of a dividend in mathematics often refers to the number you intend to divide in a division problem. In the exercise you are working on, the number 24 is the dividend. Understanding the role of the dividend is crucial for mastering division. Here’s why:

• It represents the "total" or "whole" amount that is to be divided into parts.
• The size of the dividend will influence the outcome of the division greatly.
• Choosing the correct dividend is essential, as it sets the stage for solving the entire problem accurately.

In practical terms, if you think of the dividend as a cake, it’s the entire cake you want to slice into pieces. The division operation will show how many pieces you get when you cut it into smaller sections.

Divisor

The divisor is a key player in any division operation. It is the number by which the dividend will be divided. In this scenario, the number 4 is the divisor. Here are a few important aspects of the divisor to keep in mind:

• The divisor determines the size of each group when you divide the dividend.
• A larger divisor generally results in a smaller quotient, as fewer groups will fit into the dividend.
• If the divisor is 1, the dividend remains unchanged because dividing by 1 leaves the number as is.

Think of the divisor as the knife in the cake analogy, deciding how thick each slice or piece should be. A careful choice of the divisor ensures a correct and meaningful distribution of the dividend.

Quotient

The quotient is the result you get from dividing one number by another. In our exercise, dividing 24 by 4 gives a quotient of 6. Let's explore what quotient represents:

• It shows how many times the divisor can "fit" into the dividend perfectly.
• The quotient will often tell you how many groups of a certain size can be made from the dividend, determined by the divisor.
• If there is no remainder, as in this example, the division is perfectly clean, meaning the dividend is perfectly split by the divisor.

Therefore, in our metaphor, the quotient is like the number of complete slices you get from cutting the cake into pieces of the size determined by the divisor.