Which factors of the base would help simplify the expression 16 1/4

Question

16
1
4
?(1 point)
Responses

16=4⋅2⋅2
16
=
4
⋅
2
⋅
2
16 equals 4 times 2 times 2

16=8⋅8
16
=
8
⋅
8
16 equals 8 times 8

16=4⋅4
16
=
4
⋅
4
16 equals 4 times 4

16=2⋅2⋅2⋅2

Answer 1

To simplify the expression \( 16 \frac{1}{4} \), we can first rewrite it as \( 16 + \frac{1}{4} \) or multiply \( 16 \times \frac{1}{4} \) depending on what is needed.

First, let's consider the value of \( 16 \):

• \( 16 = 2^4 \)
• \( 16 = 8 \times 2 \)
• \( 16 = 4 \times 4 \)
• \( 16 = 4 \times 2 \times 2 \)

The simplest and most useful factorization for further calculations, especially in terms of simplification of fractions or products involving \( 16 \), would be \( 16 = 4 \times 4 \) or \( 16 = 2 \times 2 \times 2 \times 2 \).

To decide which representations would help in simplifying \( 16 \frac{1}{4} \), here’s how you can use \( 16 = 4 \times 4 \):

• If you're trying to express \( 16 \frac{1}{4} \) in a different way, this representation could help.

Overall, any of the factorizations could be used, but the one that might provide the most straightforward simplification related to fractions (like converting the mixed number) would likely be \( 16 = 4 \times 4 \) because it connects with the \( \frac{1}{4} \) term nicely.

So in response to your question, either \( 16 = 4 \cdot 4 \) or \( 16 = 2 \cdot 2 \cdot 2 \cdot 2 \) would be particularly useful for simplification.