Looking for reliable answers? Westonci.ca is the ultimate Q&A platform where experts share their knowledge on various topics. Discover comprehensive answers to your questions from knowledgeable professionals on our user-friendly platform. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.
Sagot :
To solve this problem, we'll follow a step-by-step approach to determine the ratio of the area designated for decking to the area designated for grass.
1. Determine the fraction of the area that is grass:
We know that [tex]\(\frac{3}{7}\)[/tex] of the garden area is decking. Since the total area of the garden is 1 (or 100% of the garden), the fraction of the garden that is grass is given by:
[tex]\[ 1 - \frac{3}{7} \][/tex]
2. Calculate the fraction of the garden that is grass:
[tex]\[ 1 - \frac{3}{7} = \frac{7}{7} - \frac{3}{7} = \frac{4}{7} \][/tex]
So, [tex]\(\frac{4}{7}\)[/tex] of the garden is grass.
3. Express the ratio of decking to grass:
We now have the fractions for decking [tex]\(\left(\frac{3}{7}\right)\)[/tex] and for grass [tex]\(\left(\frac{4}{7}\right)\)[/tex]. The ratio of decking to grass is the fraction of the decking area divided by the fraction of the grass area:
[tex]\[ \frac{\frac{3}{7}}{\frac{4}{7}} \][/tex]
4. Simplify the ratio:
To simplify this, we divide the numerator by the denominator:
[tex]\[ \frac{\frac{3}{7}}{\frac{4}{7}} = \frac{3}{7} \times \frac{7}{4} = \frac{3}{4} \][/tex]
Therefore, the ratio of decking to grass in its simplest form is:
[tex]\[ \frac{3}{4} \][/tex]
Thus, the ratio of the decking area to the grass area is [tex]\(\frac{3}{4}\)[/tex].
1. Determine the fraction of the area that is grass:
We know that [tex]\(\frac{3}{7}\)[/tex] of the garden area is decking. Since the total area of the garden is 1 (or 100% of the garden), the fraction of the garden that is grass is given by:
[tex]\[ 1 - \frac{3}{7} \][/tex]
2. Calculate the fraction of the garden that is grass:
[tex]\[ 1 - \frac{3}{7} = \frac{7}{7} - \frac{3}{7} = \frac{4}{7} \][/tex]
So, [tex]\(\frac{4}{7}\)[/tex] of the garden is grass.
3. Express the ratio of decking to grass:
We now have the fractions for decking [tex]\(\left(\frac{3}{7}\right)\)[/tex] and for grass [tex]\(\left(\frac{4}{7}\right)\)[/tex]. The ratio of decking to grass is the fraction of the decking area divided by the fraction of the grass area:
[tex]\[ \frac{\frac{3}{7}}{\frac{4}{7}} \][/tex]
4. Simplify the ratio:
To simplify this, we divide the numerator by the denominator:
[tex]\[ \frac{\frac{3}{7}}{\frac{4}{7}} = \frac{3}{7} \times \frac{7}{4} = \frac{3}{4} \][/tex]
Therefore, the ratio of decking to grass in its simplest form is:
[tex]\[ \frac{3}{4} \][/tex]
Thus, the ratio of the decking area to the grass area is [tex]\(\frac{3}{4}\)[/tex].
Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. We're glad you visited Westonci.ca. Return anytime for updated answers from our knowledgeable team.