Which statement describes how to determine the sign of the sum when adding signed numbers?

• A. The sign of the result equals the sign of the number with the larger magnitude.
• B. The result is always positive.
• C. The result is always negative.
• D. The sign is determined randomly.

Answer: (A)

When adding signed numbers, look at their magnitudes (absolute values) and their signs. If both numbers share the same sign, the sum has that same sign and the magnitudes add. If the signs are different, subtract the smaller magnitude from the larger one and take the sign of the number with the larger magnitude. In other words, the sign of the result matches the sign of the number with the larger magnitude. This works for all cases except when the magnitudes are equal and the signs are opposite, which gives zero.

Examples: 7 + (-5) has larger magnitude on the positive side, so the result is positive (2). -8 + 3 has larger magnitude on the negative side, so the result is negative (-5). 4 + 6 is positive, since both are positive. -4 + -5 is negative, since both are negative. If you have 5 + (-5), the magnitudes are equal, so the sum is zero.