Question

At a plant nursery, 5/8 of the plants for sale are flowers and another 1/3 of the plants are shrubs. What fraction of the plants are either flowers or shrubs?
Responses

Answer 1

To find the fraction of the plants that are either flowers or shrubs, we need to add the fractions representing each type of plant.

Given:
- Fraction of plants that are flowers: \( \frac{5}{8} \)
- Fraction of plants that are shrubs: \( \frac{1}{3} \)

To add these fractions, we need a common denominator. The least common multiple (LCM) of the denominators 8 and 3 is 24.

Next, we convert each fraction to have a denominator of 24:

1. For flowers:
\[
\frac{5}{8} = \frac{5 \times 3}{8 \times 3} = \frac{15}{24}
\]

2. For shrubs:
\[
\frac{1}{3} = \frac{1 \times 8}{3 \times 8} = \frac{8}{24}
\]

Now we can add the two fractions:
\[
\frac{15}{24} + \frac{8}{24} = \frac{15 + 8}{24} = \frac{23}{24}
\]

Thus, the fraction of the plants that are either flowers or shrubs is \( \frac{23}{24} \).