Question

if $4m = 130$, does $4m \div 4 = 130 \div 4$? explain.

choose the correct answer below.

a. yes. both equations have $4m$ on the left side and $130$ on the right side.

b. no. each side was divided by a different number.

c. no. the second equation is not exactly the same as the first equation, so it cannot be true.

d. yes. each side was divided by the same number.

Explanation:

To determine if \(4m \div 4 = 130 \div 4\) when \(4m = 130\), we use the Division Property of Equality. This property states that if we divide both sides of an equation by the same non - zero number, the two sides of the equation remain equal. In the equation \(4m = 130\), we are dividing the left - hand side (\(4m\)) by 4 and the right - hand side (130) by 4. So, according to the Division Property of Equality, the resulting equation \(4m\div4 = 130\div4\) is also true because we have divided both sides of the original equation by the same number (4).

Let's analyze the other options:

• Option A: The fact that both sides have \(4m\) and 130 is not the reason why the new equation is true. The key is the operation of dividing both sides by the same number, not just the presence of the same expressions on each side.
• Option B: We divided both sides by 4, so each side was divided by the same number, not a different one.
• Option C: The second equation is a valid transformation of the first equation using the Division Property of Equality, so it is true.

Answer:

D. Yes. Each side was divided by the same number.