Which statement reflects the Division Property applied to a = b and c = d ≠ 0?

Which statement reflects the Division Property applied to a = b and c = d ≠ 0?

• A. If a = b and c = d ≠ 0, then a + c = b + d.
• B. If a = b and c = d ≠ 0, then a/c = b/d.
• C. If a = b and c = d ≠ 0, then a - c = b - d.
• D. If a = b and c = d ≠ 0, then a × c = b × d.

Answer: (B)

Dividing equal quantities by the same nonzero number keeps them equal. If a = b and c = d ≠ 0, start with a = b and divide both sides by c (allowed because c ≠ 0) to get a/c = b/c. Since c = d, the right-hand side b/c equals b/d. Therefore a/c = b/d. This shows the Division Property in action: equal numerators with equal nonzero denominators yield equal quotients. (The same premises would also imply other straightforward equalities like a+c = b+d or a×c = b×d, but the division statement specifically demonstrates how division preserves equality when using equal nonzero denominators.)

Dividing equal quantities by the same nonzero number keeps them equal. If a = b and c = d ≠ 0, start with a = b and divide both sides by c (allowed because c ≠ 0) to get a/c = b/c. Since c = d, the right-hand side b/c equals b/d. Therefore a/c = b/d. This shows the Division Property in action: equal numerators with equal nonzero denominators yield equal quotients. (The same premises would also imply other straightforward equalities like a+c = b+d or a×c = b×d, but the division statement specifically demonstrates how division preserves equality when using equal nonzero denominators.)