Try This
You are tasked with designing a vegetable garden consisting of lettuce, tomatoes, peppers, cucumbers, zucchini, carrots, and cauliflower. Draw a grid like the following to make your design.
Table Grid
These are the specifications for your design:
Lettuce should be planted in 38
of the garden space.
Tomatoes and peppers together should take up 13
of the garden space.
Cucumbers, zucchini, and carrots together should take up 316
of the garden space.
Cauliflower should be planted in the rest of the garden space.
Based on your design, what fraction of the garden is planted with each vegetable? Record your answers in the following table.
Vegetable Fraction of the Garden Planted
Lettuce
Tomatoes
Peppers
Cucumbers
Zucchini
Carrots
Cauliflower
Fraction of Vegetables
How can you verify if the fraction of the garden each vegetable composes makes sense?
To verify if the fraction of the garden each vegetable composes makes sense, you can add up all the fractions of the vegetables and check if it equals 1.
For example, in this case, the sum of the fractions of lettuce, tomatoes, peppers, cucumbers, zucchini, carrots, and cauliflower should equal 1. If it does, it means that the entire garden space is covered by these vegetables, which makes sense.
tell me the answer
To determine the fraction of the garden planted with each vegetable, we can use the given specifications and calculate the fractions.
Let's calculate the fractions for each vegetable:
1. Lettuce: Given that lettuce should be planted in 3/8 of the garden space, the fraction of the garden planted with lettuce is 3/8.
2. Tomatoes and peppers together: Given that tomatoes and peppers should take up 1/3 of the garden space together, we divide it equally between them. So, the fraction of the garden planted with tomatoes is 1/6 and the fraction planted with peppers is also 1/6.
3. Cucumbers, zucchini, and carrots together: Given that these three vegetables should take up 3/16 of the garden space together, we divide it equally between them. So, the fraction of the garden planted with cucumbers is 1/16, the fraction planted with zucchini is 1/16, and the fraction planted with carrots is also 1/16.
4. Cauliflower: Since it's mentioned that cauliflower should be planted in the rest of the garden space, we can subtract the fractions of the other vegetables from 1 to find the fraction planted with cauliflower. Therefore, the fraction of the garden planted with cauliflower is (1 - 3/8 - 1/6 - 1/6 - 1/16 - 1/16 - 1/16) = 5/48.
To summarize, the fraction of the garden planted with each vegetable is as follows:
Lettuce: 3/8
Tomatoes: 1/6
Peppers: 1/6
Cucumbers: 1/16
Zucchini: 1/16
Carrots: 1/16
Cauliflower: 5/48
To verify if these fractions make sense, we can add them up:
3/8 + 1/6 + 1/6 + 1/16 + 1/16 + 1/16 + 5/48 = 1.
Since the sum of the fractions equals 1, it verifies that the entire garden space is covered by these vegetables, which confirms that the fractions make sense.