Understanding Division by 999 with a Quotient of 366 and Remainder of 103
In mathematical terms, division involves several components: the dividend, which is the number to be divided; the divisor, which is the number by which we divide; the quotient, which is the result obtained from the division; and the remainder, which is the number left over after the division. Understanding these components can help us solve complex division problems.
Given Problem: Division by 999 with a Specific Quotient and Remainder
Consider the following problem: to find a number such that when divided by 999, the quotient obtained is 366, and the remainder is 103. The formula to find such a number can be expressed as:
Number Quotient × Divisor - Remainder
Step-by-Step Solution
Let's walk through the solution step by step:
Identify the given values from the problem statement: Quotient 366 Divisor 999 Remainder 103 Substitute these values into the division formula: Number 366 × 999 - 103 Calculate the multiplication first: 366 × 999 365634 Now, subtract the remainder from the result of the multiplication: Number 365634 - 103 365737 Verify the solution by performing the division: 365737 ÷ 999 366 remainder 103The number we have determined is 365737, which satisfies the given conditions of the division problem.
Understanding the Components of Division
In division, the relationship between the dividend, divisor, quotient, and remainder can be succinctly expressed by the formula:
Dividend Divisor × Quotient Remainder
This formula is fundamental and can be applied to solve various division problems. For the given example, the formula can be written as:
999 x × 366 103
Solving for the divisor (x), we get:
x (999 - 103) ÷ 366
Simplifying:
x 896 ÷ 366 ≈ 2.448
This confirms that the divisor is approximately 2.448, although in practical problems, we typically work with whole numbers for the divisor.
Understanding these mathematical concepts will not only help in solving similar problems but also in verifying the correctness of your solutions through the application of the division formula.