Which statement represents the division property of equality?

Which statement represents the division property of equality?

• A. If a = b, then a + c = b + c
• B. If a = b, then a / c = b / c, c ≠ 0
• C. If a = b, then a - c = b - c
• D. If a = b, then ac = bc

Answer: (B)

Dividing both sides by the same nonzero number keeps two equal expressions equal. If a equals b, then dividing both sides by a nonzero c gives a/c = b/c, and the requirement c ≠ 0 is essential because division by zero is not defined. This is exactly what the division property of equality states. Think of it this way: the idea is to apply the same operation to both sides of an equation without changing the truth of the statement. The other basic operations—adding the same number to both sides, subtracting the same number, or multiplying both sides by the same number—also preserve equality, but they are different properties. Here we’re specifically using division by the same nonzero number.

Dividing both sides by the same nonzero number keeps two equal expressions equal. If a equals b, then dividing both sides by a nonzero c gives a/c = b/c, and the requirement c ≠ 0 is essential because division by zero is not defined. This is exactly what the division property of equality states.

Think of it this way: the idea is to apply the same operation to both sides of an equation without changing the truth of the statement. The other basic operations—adding the same number to both sides, subtracting the same number, or multiplying both sides by the same number—also preserve equality, but they are different properties. Here we’re specifically using division by the same nonzero number.