Solving Division Sum Problems: A Detailed Breakdown

Division problems form a fundamental part of arithmetic. One interesting type of division problem involves complex relationships between the divisor, quotient, and remainder. In this article, we will explore such a problem in detail, providing a step-by-step breakdown.

Understanding the Problem

Consider the following division sum: the divisor is 20 times the quotient and 10 times the remainder. Given that the remainder is 92, we are to find the value of the dividend.

Variables and Equations

To start, we will denote the variables as follows:

Divisor as d Quotient as q Remainder as r

The problem provides us with the following relationships:

The divisor is 20 times the quotient: d 20q The divisor is 10 times the remainder: d 10r

Substituting the Given Remainder

We are given that the remainder r is 92. Substituting this into the second equation gives us:

d 10 times 92 920

Finding the Quotient

Now that we have the value of the divisor, we can substitute it back into the first equation to find the quotient:

920 20q

Solving for q:

q 920 / 20 46

Calculating the Dividend

The relationship between the dividend D, divisor d, quotient q, and remainder r is given by the formula:

D d times q r

Substituting the known values:

D 920 times 46 92

First, calculate 920 times 46:

920 times 46 42320

Now, adding the remainder:

D 42320 92 42412

Thus, the value of the dividend is:

boxed{42412}

Summary and Recap

Here's a quick summary of the steps we followed to solve this problem:

Identified the variables: divisor d, quotient q, and remainder r. Determined the relationships between the variables: d 20q and d 10r. Substituted the given remainder r 92 into the second equation to find d 920. Substituted d 920 back into the first equation to find q 46. Used the formula D d times q r to calculate the dividend, D 42412.

Conclusion

Division sum problems, such as the one discussed here, can be solved systematically by breaking down the given information and using algebraic equations to find the unknowns. By understanding the relationships between the divisor, quotient, and remainder, one can easily find the value of the dividend. This method can be applied to various similar problems in mathematics, making it a valuable skill to develop.

Frequently Asked Questions (FAQs)

Q: What is the dividend in this problem?

A: The value of the dividend in this problem is 42412.

Q: What is the relationship between the divisor, quotient, and remainder?

A: In a division problem, the relationship is given by the formula D d times q r, where D is the dividend, d is the divisor, q is the quotient, and r is the remainder.

Q: How do we find the quotient when the divisor and remainder are known?

A: First, we use the relationship given: the divisor is 10 times the remainder. Then, using the second relationship, we find the divisor by dividing the product of the divisor and quotient. Finally, we solve for the quotient using the divisor value.

Related Articles

Solving Other Division Sum Problems Understanding the Ratio Between Divisor and Quotient Exploring the Concept of Remainder in Division