Finding a Number Given Its Quotient and Remainder When Divided by 29
When working with division in mathematics, one common scenario is finding the original number given the quotient and remainder. In this article, we will explore how to find the number when it is divided by 29 with a quotient of 134 and a remainder of 11, using the division formula.
The Mathematical Formula
The formula for finding a number based on the quotient and remainder when the number is divided by a specific divisor is:
N D × Q R
Where:
N is the number you are trying to find. D is the divisor (the number by which the number is divided). Q is the quotient (the result of the division). R is the remainder (the amount left over after the division).Applying the Formula to Our Problem
In this specific scenario, we are given:
The divisor (D) is 29. The quotient (Q) is 134. The remainder (R) is 11.Plugging these values into the formula, we get:
N 29 × 134 11
Let's break down the calculation step by step:
Step 1: Multiply the Divisor by the Quotient
29 × 134 3886
Step 2: Add the Remainder to the Result
3886 11 3897
Thus, the number is 3897.
Converting the Process into an Equation
Another way to express the same process mathematically is:
x 134 × 29 11
Calculating this step by step:
Step 1: Calculate 134 × 29
134 × 29 3886
Step 2: Add the Remainder to the Result
3886 11 3897
Therefore, the number is 3897.
Conclusion
By using the division formula and following the step-by-step process, we were able to find that the number, when divided by 29 with a quotient of 134 and a remainder of 11, is 3897. This method can be applied to similar problems to find the original number based on the given quotient and remainder.
Understanding and applying the division formula is crucial in various mathematical computations. If you need to solve similar problems or understand the steps in more detail, this article provides a comprehensive guide on how to do so. Remember to follow the formula and break down the calculations step-by-step to ensure accuracy.