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?

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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 \( \frac{23}{24} \).