Which statement represents the addition property of equality?

Which statement represents the addition property of equality?

• A. If a = b, then a + c = b + c
• B. If a = b, then ac = bc
• C. (a + b) + c = a + (b + c)
• D. Ax + By = C

Answer: (A)

The addition property of equality says that if two quantities are equal, you can add the same value to both sides and they remain equal. The statement “If a = b, then a + c = b + c” is a direct expression of that rule: you’re adding the same number c to both sides, which keeps the equality true for any a, b, and c. For a quick check, if a and b are both 4 and you add 7 to each side, you get 11 on both sides, so the equality holds. This is why that option is the best choice: it captures the idea of preserving equality when the same addition is performed to both sides. The other options describe a different concept: multiplying both sides, associativity of addition, and a general linear equation form, none of which state the addition property of equality.

The addition property of equality says that if two quantities are equal, you can add the same value to both sides and they remain equal. The statement “If a = b, then a + c = b + c” is a direct expression of that rule: you’re adding the same number c to both sides, which keeps the equality true for any a, b, and c.

For a quick check, if a and b are both 4 and you add 7 to each side, you get 11 on both sides, so the equality holds.

This is why that option is the best choice: it captures the idea of preserving equality when the same addition is performed to both sides. The other options describe a different concept: multiplying both sides, associativity of addition, and a general linear equation form, none of which state the addition property of equality.