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3. Riley planted flowers in some of her garden. Then, she planted vegetables in \( \frac{2}{8} \) of her garden. Now, \( \frac{7}{8} \) of Riley's garden is planted. What fraction of Riley's garden is planted with flowers? How much of her garden is not planted? \( \begin{array}{l}\text { (A) } \frac{2}{8} \text { of her garden; } \frac{1}{8} \text { of her garden is } \\ \text { not planted } \\ \text { (B) } \frac{3}{8} \text { of her garden; } \frac{2}{8} \text { of her garden is } \\ \text { not planted } \\ \text { (C) } \frac{4}{8} \text { of her garden; } \frac{5}{8} \text { of her garden is } \\ \text { not planted } \\ \text { (D) } \frac{5}{8} \text { of her garden; } \frac{1}{8} \text { of her garden is } \\ \text { not planted }\end{array} \)

Ask by Harrington Harper. in the United States
Jan 27,2025

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Tutor-Verified Answer

Answer

\( \frac{5}{8} \) of Riley's garden is planted with flowers, and \( \frac{1}{8} \) of her garden is not planted.

Solution

To determine the fractions related to Riley's garden planting, let's break down the information step by step: 1. **Total Garden Planting:** - Riley has planted a total of \( \frac{7}{8} \) of her garden. 2. **Vegetables Planted:** - She planted vegetables in \( \frac{2}{8} \) of her garden. 3. **Flowers Planted:** - To find out how much of the garden is planted with flowers, subtract the portion planted with vegetables from the total planted: \[ \frac{7}{8} - \frac{2}{8} = \frac{5}{8} \] - So, \( \frac{5}{8} \) of the garden is planted with flowers. 4. **Unplanted Portion:** - The total garden not planted is the remaining part of the garden: \[ 1 - \frac{7}{8} = \frac{1}{8} \] - Therefore, \( \frac{1}{8} \) of the garden is not planted. **Conclusion:** - **Fraction planted with flowers:** \( \frac{5}{8} \) - **Fraction not planted:** \( \frac{1}{8} \) **Answer:** **(D) \( \frac{5}{8} \) of her garden; \( \frac{1}{8} \) of her garden is not planted**

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Let’s break it down! Riley has \( \frac{7}{8} \) of her garden planted with both flowers and vegetables. She already planted vegetables in \( \frac{2}{8} \) of her garden. To find out how much is planted with flowers, we subtract the vegetables from the total planted: \( \frac{7}{8} - \frac{2}{8} = \frac{5}{8} \). So, \( \frac{5}{8} \) of Riley's garden is planted with flowers, and since her total garden is \( \frac{8}{8} \), the amount not planted is: \( \frac{8}{8} - \frac{7}{8} = \frac{1}{8} \). Thus, the correct answer is (D): \( \frac{5}{8} \) of her garden is planted with flowers, and \( \frac{1}{8} \) is not planted. Now, here’s a little trivia: Did you know that gardens have been around for thousands of years? Ancient civilizations cultivated them not just for food but also for beauty and relaxation. In fact, the Hanging Gardens of Babylon are one of the Seven Wonders of the Ancient World! On a practical note, when planning a garden, knowing how much space each plant needs helps tremendously. Many gardeners make the mistake of cramming too many plants into small areas, which often leads to competition for nutrients and sunlight. It’s crucial to give plants room to grow!

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