At Westonci.ca, we make it easy for you to get the answers you need from a community of knowledgeable individuals. Join our platform to connect with experts ready to provide precise answers to your questions in different areas. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.
Sagot :
To determine which set of fractions is ordered from greatest to least, we'll compare the given fractions: [tex]\(\frac{2}{3}\)[/tex], [tex]\(\frac{3}{8}\)[/tex], and [tex]\(\frac{5}{12}\)[/tex].
### Step-by-Step Solution:
1. Identify the fractions to be compared:
- [tex]\(\frac{2}{3}\)[/tex]
- [tex]\(\frac{3}{8}\)[/tex]
- [tex]\(\frac{5}{12}\)[/tex]
2. Order the fractions from greatest to least:
Comparing [tex]\(\frac{2}{3}\)[/tex] and [tex]\(\frac{5}{12}\)[/tex]:
- Convert them to have a common denominator (let's use 12):
[tex]\[\frac{2}{3} = \frac{2 \times 4}{3 \times 4} = \frac{8}{12}\][/tex]
[tex]\[\frac{5}{12} = \frac{5}{12}\][/tex]
- Compare the numerators: [tex]\(8 > 5\)[/tex]
- So, [tex]\(\frac{2}{3} > \frac{5}{12}\)[/tex]
Comparing [tex]\(\frac{5}{12}\)[/tex] and [tex]\(\frac{3}{8}\)[/tex]:
- Convert them to have a common denominator (let's use 24):
[tex]\[\frac{5}{12} = \frac{5 \times 2}{12 \times 2} = \frac{10}{24}\][/tex]
[tex]\[\frac{3}{8} = \frac{3 \times 3}{8 \times 3} = \frac{9}{24}\][/tex]
- Compare the numerators: [tex]\(10 > 9\)[/tex]
- So, [tex]\(\frac{5}{12} > \frac{3}{8}\)[/tex]
Comparing [tex]\(\frac{2}{3}\)[/tex] and [tex]\(\frac{3}{8}\)[/tex]:
- Convert them to have a common denominator (let's use 24):
[tex]\[\frac{2}{3} = \frac{2 \times 8}{3 \times 8} = \frac{16}{24}\][/tex]
[tex]\[\frac{3}{8} = \frac{3 \times 3}{8 \times 3} = \frac{9}{24}\][/tex]
- Compare the numerators: [tex]\(16 > 9\)[/tex]
- So, [tex]\(\frac{2}{3} > \frac{3}{8}\)[/tex]
3. Order the fractions:
- Based on the comparisons above:
- [tex]\(\frac{2}{3}\)[/tex] is the greatest.
- [tex]\(\frac{5}{12}\)[/tex] is the next largest.
- [tex]\(\frac{3}{8}\)[/tex] is the smallest.
So, the ordered set from greatest to least is: [tex]\(\frac{2}{3}, \frac{5}{12}, \frac{3}{8}\)[/tex]
4. Match this order with the given options:
- Option A: [tex]\(\frac{2}{3}, \frac{3}{8}, \frac{5}{12}\)[/tex]
- Option B: [tex]\(\frac{5}{12}, \frac{3}{8}, \frac{2}{3}\)[/tex]
- Option C: [tex]\(\frac{2}{3}, \frac{5}{12}, \frac{3}{8}\)[/tex]
- Option D: [tex]\(\frac{3}{8} \cdot \frac{2}{3}, \frac{5}{12}\)[/tex] (This involves a product, isn't relevant for comparison)
Therefore, the correct answer is option C: [tex]\(\frac{2}{3}, \frac{5}{12}, \frac{3}{8}\)[/tex].
### Step-by-Step Solution:
1. Identify the fractions to be compared:
- [tex]\(\frac{2}{3}\)[/tex]
- [tex]\(\frac{3}{8}\)[/tex]
- [tex]\(\frac{5}{12}\)[/tex]
2. Order the fractions from greatest to least:
Comparing [tex]\(\frac{2}{3}\)[/tex] and [tex]\(\frac{5}{12}\)[/tex]:
- Convert them to have a common denominator (let's use 12):
[tex]\[\frac{2}{3} = \frac{2 \times 4}{3 \times 4} = \frac{8}{12}\][/tex]
[tex]\[\frac{5}{12} = \frac{5}{12}\][/tex]
- Compare the numerators: [tex]\(8 > 5\)[/tex]
- So, [tex]\(\frac{2}{3} > \frac{5}{12}\)[/tex]
Comparing [tex]\(\frac{5}{12}\)[/tex] and [tex]\(\frac{3}{8}\)[/tex]:
- Convert them to have a common denominator (let's use 24):
[tex]\[\frac{5}{12} = \frac{5 \times 2}{12 \times 2} = \frac{10}{24}\][/tex]
[tex]\[\frac{3}{8} = \frac{3 \times 3}{8 \times 3} = \frac{9}{24}\][/tex]
- Compare the numerators: [tex]\(10 > 9\)[/tex]
- So, [tex]\(\frac{5}{12} > \frac{3}{8}\)[/tex]
Comparing [tex]\(\frac{2}{3}\)[/tex] and [tex]\(\frac{3}{8}\)[/tex]:
- Convert them to have a common denominator (let's use 24):
[tex]\[\frac{2}{3} = \frac{2 \times 8}{3 \times 8} = \frac{16}{24}\][/tex]
[tex]\[\frac{3}{8} = \frac{3 \times 3}{8 \times 3} = \frac{9}{24}\][/tex]
- Compare the numerators: [tex]\(16 > 9\)[/tex]
- So, [tex]\(\frac{2}{3} > \frac{3}{8}\)[/tex]
3. Order the fractions:
- Based on the comparisons above:
- [tex]\(\frac{2}{3}\)[/tex] is the greatest.
- [tex]\(\frac{5}{12}\)[/tex] is the next largest.
- [tex]\(\frac{3}{8}\)[/tex] is the smallest.
So, the ordered set from greatest to least is: [tex]\(\frac{2}{3}, \frac{5}{12}, \frac{3}{8}\)[/tex]
4. Match this order with the given options:
- Option A: [tex]\(\frac{2}{3}, \frac{3}{8}, \frac{5}{12}\)[/tex]
- Option B: [tex]\(\frac{5}{12}, \frac{3}{8}, \frac{2}{3}\)[/tex]
- Option C: [tex]\(\frac{2}{3}, \frac{5}{12}, \frac{3}{8}\)[/tex]
- Option D: [tex]\(\frac{3}{8} \cdot \frac{2}{3}, \frac{5}{12}\)[/tex] (This involves a product, isn't relevant for comparison)
Therefore, the correct answer is option C: [tex]\(\frac{2}{3}, \frac{5}{12}, \frac{3}{8}\)[/tex].
Visit us again for up-to-date and reliable answers. We're always ready to assist you with your informational needs. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Thank you for using Westonci.ca. Come back for more in-depth answers to all your queries.
