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Which set of fractions is ordered from least to greatest?

A. [tex]\(\frac{7}{8}, \frac{5}{11}, \frac{2}{3}\)[/tex]

B. [tex]\(\frac{5}{11}, \frac{7}{8}, \frac{2}{3}\)[/tex]

C. [tex]\(\frac{2}{3}, \frac{5}{11}, \frac{7}{8}\)[/tex]

D. [tex]\(\frac{5}{11}, \frac{2}{3}, \frac{7}{8}\)[/tex]


Sagot :

To determine which set of fractions is ordered from least to greatest, let's examine each choice and compare the fractions.

We start with the given fractions: [tex]\(\frac{7}{8}, \frac{5}{11}, \frac{2}{3}\)[/tex].

To compare the fractions, let's convert each one to its decimal equivalent:

1. [tex]\(\frac{7}{8}\)[/tex]:
- Decimal: [tex]\( \frac{7}{8} = 0.875 \)[/tex]

2. [tex]\(\frac{5}{11}\)[/tex]:
- Decimal: [tex]\( \frac{5}{11} \approx 0.4545 \)[/tex]

3. [tex]\(\frac{2}{3}\)[/tex]:
- Decimal: [tex]\( \frac{2}{3} \approx 0.6667 \)[/tex]

Now, we need to order these decimal values from least to greatest:
- [tex]\(0.4545\)[/tex]
- [tex]\(0.6667\)[/tex]
- [tex]\(0.875\)[/tex]

So, the fractions in ascending order are:
[tex]\[ \frac{5}{11}, \frac{2}{3}, \frac{7}{8} \][/tex]

Now, let's review the choices given:

A) [tex]$\frac{7}{8}, \frac{5}{11}, \frac{2}{3}$[/tex]

B) [tex]$\frac{5}{11}, \frac{7}{8}, \frac{2}{3}$[/tex]

C) [tex]$\frac{2}{3}, \frac{5}{11}, \frac{7}{8}$[/tex]

D) [tex]$\frac{5}{11}, \frac{2}{3}, \frac{7}{8}$[/tex]

Among these choices, the correct order from smallest to largest is in:

D) [tex]$\frac{5}{11}, \frac{2}{3}, \frac{7}{8}$[/tex]

Thus, the answer is:
D