Question

In order to make the expression below equivalent to 1/2x+6, which additional operation should be included in the expression?
5/6x + 6 +____

Answer 1

To make the expression \( \frac{5}{6}x + 6 + \_\_\_ \) equivalent to \( \frac{1}{2}x + 6 \), we need to determine what addition we need to add in place of the blank.

First, let's express \( \frac{1}{2} \) as a fraction with a denominator of 6 for easier comparison:

\[
\frac{1}{2} = \frac{3}{6}
\]

Now we want \( \frac{5}{6}x + 6 + \_\_\_ \) to equal \( \frac{3}{6}x + 6 \).

Now, let's set up the equation:

\[
\frac{5}{6}x + 6 + \_\_ = \frac{3}{6}x + 6
\]

To isolate the unknown, we can subtract \( 6 \) from both sides:

\[
\frac{5}{6}x + \_\_ = \frac{3}{6}x
\]

Now, subtract \( \frac{5}{6}x \) from both sides:

\[
\_\_ = \frac{3}{6}x - \frac{5}{6}x
\]

Now, perform the subtraction:

\[
\_\_ = \frac{3 - 5}{6}x = -\frac{2}{6}x = -\frac{1}{3}x
\]

So, the additional operation that should be included in the expression is:

\[
-\frac{1}{3}x
\]

Therefore, the complete expression is:

\[
\frac{5}{6}x + 6 - \frac{1}{3}x
\]

This will make it equivalent to \( \frac{1}{2}x + 6 \).