Final answer:
The equation 3 x n/3 = 3 x n/3 simplifies to just n. This occurs because multiplying and then dividing by the same number cancels each other out, which is a basic algebraic principle of inverse operations.
Step-by-step explanation:
If 3 x n/3 = 3 x n/3, then both sides of the equation are equal, which means that no matter what the value of n is, after the operation is performed, the result will be the same on both sides. This is a straightforward algebraic equation. In mathematics, when we see an equation like this, we understand that it simplifies to n because the threes cancel out. So, if we multiply n by 3 and then divide by 3, we are left with n. This is akin to saying that one half of one-half is one quarter. The principle lies in understanding how multiplication and division are inverse operations and can cancel each other out.
In other scenarios resembling the concept of equations, similar principles apply. For instance, if we have an equality such as 1 yd = 3 ft, we can divide or multiply both sides by the same number, and the resulting expressions will retain equality. This maintains the balance of the equation and is a fundamental aspect of algebra.
In conclusion, the original equation 3 x n/3 = 3 x n/3 simplifies to just n. This is because the multiplicative factor of 3 on both sides cancels out with the division by 3, leaving us with the original number, n.