Which of the following is correct?

Question

Accepted Answer

Option 1 is the correct answer: "Dividend = Divisor × Quotient + Remainder." This equation is a fundamental principle of arithmetic division and is known as the division algorithm. It accurately describes the relationship between the dividend, divisor, quotient, and remainder in the division process.

### Explanation for Option 1:

When you divide a number (the dividend) by another number (the divisor), you obtain a quotient and possibly a remainder. The division algorithm states that:

$$ \text{Dividend} = (\text{Divisor} \times \text{Quotient}) + \text{Remainder} $$

This equation ensures that the remainder is always less than the divisor, which is a key property of division. For example, if you divide 17 by 5, the quotient is 3 and the remainder is 2, because:

$$ 17 = (5 \times 3) + 2 $$

This confirms that Option 1 correctly represents the division process.

### Explanation for why the other options are incorrect:

- **Option 2: Dividend = Divisor + Quotient × Remainder**

This option is incorrect because it does not accurately represent the division process. The equation suggests that the dividend is the sum of the divisor and the product of the quotient and remainder, which does not hold true in standard division. For example, using the same numbers as above, $ 17 \neq 5 + (3 \times 2) $.

- **Option 3: Divisor = Dividend × Quotient + Remainder**

This option is incorrect because it misplaces the roles of the numbers involved in division. The divisor cannot be expressed as a combination of the dividend, quotient, and remainder in this manner. For instance, $ 5 \neq 17 \times 3 + 2 $.

- **Option 4: Remainder = Dividend × Divisor + Quotient**

This option is incorrect because it incorrectly defines the remainder. The remainder is the leftover part of the dividend after division, and it cannot be calculated as the product of the dividend and divisor plus the quotient. For example, $ 2 \neq 17 \times 5 + 3 $.

In conclusion, Option 1 is the only option that correctly describes the relationship between the dividend, divisor, quotient, and remainder in the division process.