Solving Division Problems: Finding the Dividend Given the Divisor and Quotient
Division problems often require a bit of algebraic manipulation to solve. One such common problem is finding the dividend given the divisor and quotient. This article will walk you through the process of solving such problems step-by-step, using a straightforward example and providing a detailed explanation for each step.
Understanding the Problem Statement
To find the number that should be divided by 12 to get a quotient of 4, follow the formula: (frac{x}{12} 4).
Setting Up the Equation
When you encounter a division problem where you need to find the dividend, organize the information into an equation. In this problem, we need to find the value of x such that when divided by 12, it yields a quotient of 4. The equation can be set up as follows:
[frac{x}{12} 4]Solving for the Dividend
To isolate x, we need to eliminate the denominator on the left side of the equation. This is done by multiplying both sides of the equation by 12:
[frac{x}{12} times 12 4 times 12]Simplifying the left side, we have:
[x 4 times 12]Carrying out the multiplication, we get:
[x 48]Therefore, the number that should be divided by 12 to get a quotient of 4 is 48.
Verification and Proof
To verify our answer, we can substitute the value of x back into the original equation:
Using our solution:
[frac{48}{12} 4]This confirms that our answer is correct, as the quotient is indeed 4.
Additional Examples
Here are a few more examples to illustrate the process of solving similar problems:
What number should be divided by 15 to get a quotient of 5? To find the number, we set it up as: (frac{x}{15} 5). Solving for x, we get: [x 5 times 15 75]. Verification: [frac{75}{15} 5].Another example:
What number should be divided by 9 to get a quotient of 6? Solving for x, we get: [x 6 times 9 54]. Verification: [frac{54}{9} 6].Conclusion
Solving division problems like these is a fundamental concept in mathematics. Understanding and being able to solve such problems accurately helps in a wide range of real-world applications, such as budgeting, calculating proportions, and more. Whether you're a student or a professional, these skills can be invaluable.