The division is a fundamental mathematical operation that allows us to distribute or partition a quantity into equal parts. In this article, we will explore division by delving into the specific calculation of 72 divided by 9. We will break down the process step by step, discuss its real-life applications, and highlight the importance of division in mathematics.

The Concept of Division

Before we dive into the specific calculation, let’s briefly review the concept of division. The division is the process of dividing a number (the dividend) into equal parts or groups using a divisor. The result of division is called the quotient.

Understanding 72 Divided by 9

Divisibility Rule

To understand division better, it’s essential to know that not all numbers are divisible by each other. However, in our case, 72 and 9 have a unique relationship. A number is divisible by 9 if the sum of its digits is also divisible by 9. In this case, 7 + 2 equals 9, which is divisible by 9. Therefore, 72 is divisible by 9.

Long Division Method

One common method to calculate division is the long division method. It involves a series of steps to determine the quotient and remainder. Let’s apply this method to 72 divided by 9.

Quotient and Remainder

In division, we obtain two important results: the quotient and the remainder. The quotient represents how many times the divisor can be subtracted from the dividend, leaving no remainder. The first Number 72 is called Dividend and on the other hand second number is called Divisor.

Real-Life Applications

Division is not just a mathematical concept; it has numerous real-life applications. From dividing resources among a group of people to calculating prices per unit, division plays a crucial role in everyday scenarios.

Mathematical Properties

Commutative Property

One important property of division is the commutative property. It means that the order of numbers in a division operation does not affect the result. For example, 72 divided by 9 is the same as 9 divided by 72.

Associative Property

The associative property of division states that when dividing more than two numbers, the grouping of the numbers does not change the result. This property can be helpful in solving complex division problems.

Dividing 72 by 9: Step by Step

Let’s apply the long division method to calculate 72 divided by 9 step by step.

• Write down the dividend (72) and the divisor (9).
• Determine how many times the divisor (9) can be subtracted from the leftmost digits of the dividend (7). In this case, it can be subtracted 8 times.
• Write the quotient (8) above the dividend.
• Multiply the quotient (8) by the divisor (9) and write the result (72) below the dividend.
• Subtract the result (72) from the dividend (72), leaving no remainder.
• The final result is the quotient (8).

So, 72 divided by 9 equals 8.

Alternative Methods

Multiplication Approach

Another way to calculate division is by using the inverse operation of multiplication. You can find the quotient by asking how many times the divisor can fit into the dividend.

Mental Math

For simple division problems like 72 divided by 9, you can also use mental math techniques to quickly find the answer.

Importance of Division

Division is essential in mathematics because it helps us distribute and allocate resources, solve problems, and understand the relationships between numbers. It is a foundational concept that is used extensively in various fields, including science, engineering, and economics.

Common Mistakes to Avoid

When performing division, it’s crucial to avoid common mistakes, such as dividing by zero or incorrectly calculating the quotient. Always double-check your work to ensure accuracy.

Practice Problems

To solidify your understanding of division, try solving some practice problems. This will help you gain confidence and proficiency in this fundamental mathematical operation.

Conclusion

In conclusion, division is a fundamental mathematical operation that allows us to divide quantities into equal parts. We’ve explored the specific example of 72 divided by 9, using both the long division method and alternative approaches. The division plays a crucial role in mathematics and everyday life, making it a valuable skill to master.

Frequently Asked Questions

FAQ 1: What is the result of 72 divided by 9?

The result of 72 divided by 9 is 8.

FAQ 2: Can you simplify the division of 72 by 9?

No further simplification is needed for the division of 72 by 9, as the result is already a whole number, which is 8.

FAQ 3: How can I check if 72 is divisible by 9?

You can check if a number is divisible by 9 by adding up its digits. If the sum is divisible by 9, then the number itself is divisible by 9.

FAQ 4: Are there any shortcuts for division?

Yes, there are various mental math shortcuts for division, especially for simple problems like 72 divided by 9. These shortcuts can help you quickly find the answer.

FAQ 5: Why is division important in mathematics?

Division is important in mathematics because it allows us to distribute resources, solve problems, and understand the relationships between numbers. It is a fundamental operation used in various fields and everyday life.