Solving the Divide and Remainder Problem: A Step-by-Step Guide

When faced with a mathematical problem involving division, quotient, and remainder, it's important to use the correct formula to find the solution. In this guide, we will walk through a detailed example using an actual problem: a number is divided by 13 giving a quotient of 52 and a remainder of 9. We will then explain each step in detail to ensure you fully understand the concept.

Understanding the Problem

The problem is straightforward: we need to find a number that, when divided by 13, gives a quotient of 52 and a remainder of 9. To achieve this, we will use the following formula:

Number Divisor × Quotient Remainder

Applying the Formula

Let's break down the problem using the formula and walk through each step:

Identify the given values: Divisor 13 Quotient 52 Remainder 9 Substitute the values into the formula: Number 13 × 52 9 Calculate the number: Step 1: Calculate 13 × 52 13 × 52 676 Step 2: Add the remainder to the result 676 9 685

Therefore, the number is 685.

Alternative Methods to Solve the Problem

Let's explore other ways to reach the same solution:

Direct Calculation: 13 × 52 676 676 - 9 685 Formula Application: x 13 × 52 9 x 676 9 x 685 Algebraic Approach: Let the number be x x ÷ 13 52 with a remainder of 9 x - 9 52 × 13 x - 9 676 x 676 9 x 685

Verification

To verify our solution, we can use the following proof:

If r 685, then the equation 685 ÷ 13 will yield a quotient of 52 and a remainder of 9. Let's break down the division: 685 ÷ 13 52 R. 9 685 - 9 676 676 ÷ 13 52 This confirms our solution is correct.

Conclusion

Solving problems involving division, quotient, and remainder can be straightforward if you use the correct formula and method. The number is 685, and we have demonstrated three different ways to arrive at this solution. This guide should help you tackle similar problems with confidence and accuracy.

Key takeaways:

Understanding the formula: Number Divisor × Quotient Remainder Step-by-step calculation: Break down the problem into smaller, manageable steps. Verification: Check your solution with the given conditions.