Question

Which factors of the bade would help simplify the expression 16 1/4?
Pick from these answers:
16 = 2 x 2 x 2 x 2
16 = 8 x 8
16 = 4 x 2 x 2
16 = 4 x 4

Answer 1

But which one is best

Answer 2

To simplify the expression \( 16 \frac{1}{4} \), we can first convert it to an improper fraction:

\[
16 \frac{1}{4} = \frac{16 \times 4 + 1}{4} = \frac{64 + 1}{4} = \frac{65}{4}
\]

Now, if we are looking for factors of 16 that help simplify the expression, we should consider the forms of 16 given in the options:

1. \( 16 = 2 \times 2 \times 2 \times 2 \) (This represents \( 16 = 2^4 \))
2. \( 16 = 8 \times 8 \) (This is incorrect, as \( 8 \times 8 = 64 \))
3. \( 16 = 4 \times 2 \times 2 \) (This is correct, as \( 4 \times 2 \times 2 = 16 \))
4. \( 16 = 4 \times 4 \) (This is also correct, as \( 4 \times 4 = 16 \))

The options that provide valid factorization of 16, which could help in simplifying or understanding the expression, are:

- \( 16 = 2 \times 2 \times 2 \times 2 \)
- \( 16 = 4 \times 2 \times 2 \)
- \( 16 = 4 \times 4 \)

So, the relevant factors of 16 that would assist in simplification are:

- \( 16 = 2 \times 2 \times 2 \times 2 \)
- \( 16 = 4 \times 2 \times 2 \)
- \( 16 = 4 \times 4 \)

The option \( 16 = 8 \times 8 \) should be disregarded as it is not correct.

Answer 3

To determine which factorization is the **best** for simplifying the expression \( 16 \frac{1}{4} \), let's analyze each option:

1. **\( 16 = 2 \times 2 \times 2 \times 2 \) (or \( 2^4 \))**:
- This representation is useful for converting \( 16 \) into its prime factorization, but it doesn't directly relate to simplifying \( \frac{65}{4} \).

2. **\( 16 = 8 \times 8 \)**:
- This option is incorrect because \( 8 \times 8 = 64 \), not 16.

3. **\( 16 = 4 \times 2 \times 2 \)**:
- This method shows a combination of smaller factors. It could be useful for breaking down calculations, though it's not strictly necessary.

4. **\( 16 = 4 \times 4 \)**:
- This is the best option for simplification, as it directly shows \( 16 \) as a product of two equal factors. This representation can help when performing certain calculations involving square roots or when simplifying fractions, as in dividing \( 16 \) by another number.

### Best Factorization:

Given the context and looking for the most straightforward representation that ties into simplification, **the best factorization for understanding and potentially simplifying** would be:

**\( 16 = 4 \times 4 \)**

This is because it clearly shows that 16 can be expressed as the square of a smaller number, helping in various mathematical contexts (including geometry and algebraic factoring).