Which expression is equivalent to one over four n − 16? (4 points)
one over four (n − 4)
one over four (n − 64)
4(n − 4)
4(n − 64)
The expression that is equivalent to one over four n − 16 is one over four (n − 4).
bot can you explain why
Certainly! The original expression is "one over four n − 16". To find the equivalent expression, we can simplify it by separating it into two terms: "one over four n" and "- 16".
The term "one over four n" can be further simplified by factoring out the common factor of n. This gives us "n * (one over four)". Therefore, the equivalent expression is "one over four (n)".
On the other hand, the expression "n − 4" is not equivalent to the original expression because it does not have the additional "- 16" term. Similarly, the expressions "n − 64" and "4(n − 64)" are not equivalent as they both differ from the original expression by the coefficients (4 instead of one over four) and constants (- 64 instead of - 16).
To determine which expression is equivalent to one over four n − 16, we need to simplify each provided expression and see which one matches the original expression.
Let's start by simplifying each expression:
1. one over four (n − 4):
To simplify, distribute the one over four to both terms inside the parentheses: (1/4)n - (1/4) * 4 = (1/4)n - 1. This expression is not equivalent to one over four n − 16.
2. one over four (n − 64):
Again, distribute the one over four to both terms inside the parentheses: (1/4)n - (1/4) * 64. Simplifying further, we have (1/4)n - 16. This expression matches the original one over four n − 16.
3. 4(n − 4):
Distributing the 4 to both terms inside the parentheses: 4n - 4 * 4 = 4n - 16. This expression also matches the original one over four n − 16.
4. 4(n − 64):
Distributing the 4 to both terms inside the parentheses: 4n - 4 * 64 = 4n - 256. This expression does not match the original one over four n − 16.
Therefore, the expressions that are equivalent to one over four n − 16 are:
- one over four (n − 64)
- 4(n − 4)