Which statement describes the Division Property?

Which statement describes the Division Property?

• A. If equal quantities are divided by equal nonzero quantities, the sums are equal.
• B. If equal quantities are divided by equal nonzero quantities, the products are equal.
• C. If equal quantities are divided by equal nonzero quantities, the quotients are equal.
• D. If equal quantities are divided by zero, the quotients are equal.

Answer: (C)

Dividing equal quantities by equal nonzero quantities preserves equality. If two numerators are equal (say a = b) and you divide each by the same nonzero number (say c = d ≠ 0), the quotients are the same: a/c = b/d. This is why the statement describes the Division Property—it guarantees that replacing equal inputs into a division keeps the results equal, as long as the divisors aren’t zero. For example, if a = b = 12 and the common divisor is 4, then 12/4 = 12/4 = 3. The caveat is that you can’t divide by zero, which is why the divisor must be nonzero.

Dividing equal quantities by equal nonzero quantities preserves equality. If two numerators are equal (say a = b) and you divide each by the same nonzero number (say c = d ≠ 0), the quotients are the same: a/c = b/d. This is why the statement describes the Division Property—it guarantees that replacing equal inputs into a division keeps the results equal, as long as the divisors aren’t zero. For example, if a = b = 12 and the common divisor is 4, then 12/4 = 12/4 = 3. The caveat is that you can’t divide by zero, which is why the divisor must be nonzero.