Question

Marc, Steven, and Daniel entered into a Subway sandwich shop partnership. Marc owns 1/9

of the shop and Steven owns 1/4

of the partnership.

What part of this business deal does Daniel own?

Answer 1

To find out how much of the business Daniel owns, we first need to calculate the total ownership that Marc and Steven have together.

Marc owns \( \frac{1}{9} \) of the partnership, and Steven owns \( \frac{1}{4} \).

To add these two fractions, we first need a common denominator. The least common multiple (LCM) of 9 and 4 is 36.

Now, we can convert each fraction:

1. Marc's ownership:
\[
\frac{1}{9} = \frac{1 \times 4}{9 \times 4} = \frac{4}{36}
\]

2. Steven's ownership:
\[
\frac{1}{4} = \frac{1 \times 9}{4 \times 9} = \frac{9}{36}
\]

Now we can add Marc's and Steven's ownership together:
\[
\frac{4}{36} + \frac{9}{36} = \frac{4 + 9}{36} = \frac{13}{36}
\]

Since the total ownership of the partnership must equal 1 (or \( \frac{36}{36} \)), we can find Daniel's ownership by subtracting the sum of Marc's and Steven's ownership from the total:
\[
\text{Daniel's ownership} = 1 - \frac{13}{36} = \frac{36}{36} - \frac{13}{36} = \frac{36 - 13}{36} = \frac{23}{36}
\]

Thus, Daniel owns \( \frac{23}{36} \) of the partnership.