3. Lei and Narvey wanted to establish a business but they have no enough money for their start up capital. They agreed to include Drew into the partnership. If Lei will invest 1/2 and Narvey will invest 1/8 of the needed capital respectively, what fractional share will Drew need to invest to come up with the needed capital?

To determine what fractional share Drew needs to invest, we start by considering the total capital needed for the business. Let's denote the total capital required as $ C $.

- Lei will invest $\frac{1}{2}$ of $ C $, which is $\frac{C}{2}$.
- Narvey will invest $\frac{1}{8}$ of $ C $, which is $\frac{C}{8}$.

The sum of Lei's and Narvey's investments is:

\[
\frac{C}{2} + \frac{C}{8}
\]

To add these fractions, they need a common denominator. The least common denominator of 2 and 8 is 8. Therefore:

\[
\frac{C}{2} = \frac{4C}{8}
\]

Now, adding the fractions:

\[
\frac{4C}{8} + \frac{C}{8} = \frac{5C}{8}
\]

So, Lei and Narvey together will invest $\frac{5C}{8}$ of the total capital.

Drew needs to invest the remaining portion to make up the full capital $ C $:

\[
\text{Drew's investment} = C - \frac{5C}{8} = \frac{8C}{8} - \frac{5C}{8} = \frac{3C}{8}
\]

Thus, Drew needs to invest $\frac{3}{8}$ of the total capital.

### Summary
Drew needs to invest $\frac{3}{8}$ of the total capital to complete the partnership's required startup capital.

Would you like more details on this explanation or have any other questions?

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Here are 5 related questions:

1. If the total capital required was $80,000, how much would each partner invest in dollar terms?
2. What if Narvey decided to invest $\frac{1}{4}$ instead of $\frac{1}{8}$? How much would Drew need to invest then?
3. What percentage of the total capital does Drew's investment represent?
4. If Drew only invested $\frac{2}{8}$ of the total capital, how much more would be needed to reach the required capital?
5. How would the investment fractions change if Lei decided to invest $\frac{1}{3}$ of the total capital?

**Tip:** When dealing with fractions, always find a common denominator to simplify addition or subtraction.

Learn how to calculate Drew's fractional share in a business partnership where Lei and Narvey have already invested fractions of the needed capital. This problem involves basic arithmetic with fractions and is suitable for students in Grades 5-7.

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