Which statement correctly describes the Subtraction Property?

Which statement correctly describes the Subtraction Property?

• A. If equal quantities are subtracted from equal quantities, the differences are equal.
• B. If equal quantities are subtracted from equal quantities, the quotients are equal.
• C. If equal quantities are subtracted from equal quantities, the sums are equal.
• D. If equal quantities are added to equal quantities, the differences are equal.

Answer: (A)

Subtracting the same amount from both sides of a true equation keeps the two sides equal. In symbols, if a = b, then a − c = b − c for any c. This happens because you’re applying the same operation to both sides, so you remove the same quantity from each side and the equality is preserved. The statement describes exactly that idea: subtracting equal quantities from equal quantities yields equal differences. For example, 10 = 10 implies 10 − 4 = 10 − 4, so 6 = 6. This property is handy for solving equations, and it’s specific to subtraction (the analogous idea for addition is that adding the same amount to both sides preserves equality).

Subtracting the same amount from both sides of a true equation keeps the two sides equal. In symbols, if a = b, then a − c = b − c for any c. This happens because you’re applying the same operation to both sides, so you remove the same quantity from each side and the equality is preserved. The statement describes exactly that idea: subtracting equal quantities from equal quantities yields equal differences. For example, 10 = 10 implies 10 − 4 = 10 − 4, so 6 = 6. This property is handy for solving equations, and it’s specific to subtraction (the analogous idea for addition is that adding the same amount to both sides preserves equality).