In a division, the Quotient = (Dividend – Remainder) ÷ Divisor
The Correct Answer and Explanation is:
In division, the relationship between the quotient, dividend, remainder, and divisor can be expressed using the formula:
Quotient = (Dividend – Remainder) ÷ Divisor
This formula is derived from the basic division rule. To understand this formula, let’s break down the components:
- Dividend: This is the number that is being divided.
- Divisor: This is the number by which the dividend is being divided.
- Remainder: This is what is left over after the division.
- Quotient: This is the result of the division, excluding the remainder.
When we divide a number, say 17, by 5, the result will be:
- Division: 17 ÷ 5 = 3 with a remainder of 2.
- Here, the dividend is 17, the divisor is 5, the quotient is 3, and the remainder is 2.
The formula can now be applied:
- Dividend = Quotient × Divisor + Remainder
So, in our example, we can verify:- 17 = (3 × 5) + 2, which simplifies to 17 = 15 + 2. This is correct!
Now, using the formula you provided:
- Quotient = (Dividend – Remainder) ÷ Divisor
- Quotient = (17 – 2) ÷ 5 = 15 ÷ 5 = 3.
So, by subtracting the remainder from the dividend and then dividing by the divisor, we get the quotient, which confirms that the quotient of 17 ÷ 5 is indeed 3.
This formula is essentially an alternative representation of the standard division algorithm, and it can help in understanding how the quotient and remainder are related to the original division. It’s important to note that this formula holds only when there is a remainder after division (i.e., the division isn’t exact).
