Which expression is equivalent to ⅜ (y + 16)?

Question

3(8y + 128)

3(1/8y+2)

3/8y + 6

3/8y + 2

⅛ (3y + 48)

Answer 1

To find an expression equivalent to \( \frac{3}{8} (y + 16) \), we can distribute \( \frac{3}{8} \) to both terms inside the parentheses.

\[ \frac{3}{8} (y + 16) = \frac{3}{8} y + \frac{3}{8} \times 16 \]

Calculating the second term:

\[ \frac{3}{8} \times 16 = \frac{3 \times 16}{8} = \frac{48}{8} = 6 \]

So, this simplifies to:

\[ \frac{3}{8} y + 6 \]

Now let's check the options given:

1. \( 3(8y + 128) \) = \( 24y + 384 \) (not equivalent)
2. \( 3\left(\frac{1}{8}y + 2\right) = \frac{3}{8}y + 6 \) (equivalent)
3. \( \frac{3}{8}y + 6 \) (equivalent)
4. \( \frac{3}{8}y + 2 \) (not equivalent)
5. \( \frac{1}{8}(3y + 48) = \frac{3}{8}y + 6 \) (equivalent)

Thus, the expressions that are equivalent to \( \frac{3}{8} (y + 16) \) are:

• \( 3\left(\frac{1}{8}y + 2\right) \)
• \( \frac{3}{8}y + 6 \)
• \( \frac{1}{8}(3y + 48) \)

Among the options listed, the correct expressions equivalent to \( \frac{3}{8} (y + 16) \) are:

• \( 3\left(\frac{1}{8}y + 2\right) \)
• \( \frac{3}{8}y + 6 \)
• \( \frac{1}{8}(3y + 48) \)

If only one option must be selected based on the provided list, the most directly equivalent option is \( \frac{3}{8}y + 6 \).