To find the multiplicative inverse of \( \frac{2}{3} - \frac{5}{6} \), follow these steps:

### Step 1: Perform the subtraction
We need to subtract \( \frac{5}{6} \) from \( \frac{2}{3} \). To do this, first get a common denominator.

\[
\frac{2}{3} = \frac{4}{6} 
\]

Now subtract \( \frac{5}{6} \) from \( \frac{4}{6} \):

\[
\frac{4}{6} - \frac{5}{6} = \frac{-1}{6}
\]

### Step 2: Find the multiplicative inverse
The multiplicative inverse of a number \( x \) is \( \frac{1}{x} \). So, the multiplicative inverse of \( \frac{-1}{6} \) is:

\[
\frac{1}{\frac{-1}{6}} = -6
\]

### Final Answer:
The multiplicative inverse of \( \frac{2}{3} - \frac{5}{6} \) is \( -6 \).

Would you like further clarification or details?

Here are five related questions you might find helpful:
1. What is the multiplicative inverse of other fractions like \( \frac{4}{5} \)?
2. How do you find the additive inverse of a number or fraction?
3. How do you perform operations with fractions that have different denominators?
4. Can the multiplicative inverse of 0 exist? Why or why not?
5. How do multiplicative and additive inverses relate in solving equations?

**Tip:** Always simplify fractions and expressions before finding the inverse to make the process easier.

Learn how to find the multiplicative inverse of the fraction 2/3 - 5/6. This detailed step-by-step solution covers key concepts such as subtracting fractions and finding the multiplicative inverse. Suitable for students in Grades 6-8.

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