Question

Identify the numeric order of these fractions and mixed numbers from smallest to largest: 4/6
, 2(5/6
, 2(1/2
, 2(3/4
.(1 point)
Responses

5/2
, 11/4
, 17/6
, 4/6
Start Fraction 5 over 2 End Fraction , Start Fraction 11 over 4 End Fraction , Start Fraction 17 over 6 End Fraction , Start Fraction 4 over 6 End Fraction

4/6
, 2(1/2
, 2(3/4
, 2(5/6
Start Fraction 4 over 6 End Fraction , 2 Start Fraction 1 over 2 End Fraction , 2 Start Fraction 3 over 4 End Fraction , 2 Start Fraction 5 over 6 End Fraction

2/5
, 4/11
, 6/17
, 4/6
Start Fraction 2 over 5 End Fraction , Start Fraction 4 over 11 End Fraction , Start Fraction 6 over 17 End Fraction , Start Fraction 4 over 6 End Fraction

2(5/6
, 2(3/4
, 2(1/2
, 4/6

Answer 1

To compare the fractions and mixed numbers \(4/6\), \(2(5/6)\), \(2(1/2)\), and \(2(3/4)\), we first convert the mixed numbers into improper fractions:

1. \(2(5/6) = 2 + \frac{5}{6} = \frac{12}{6} + \frac{5}{6} = \frac{17}{6}\)
2. \(2(1/2) = 2 + \frac{1}{2} = \frac{4}{2} + \frac{1}{2} = \frac{5}{2}\)
3. \(2(3/4) = 2 + \frac{3}{4} = \frac{8}{4} + \frac{3}{4} = \frac{11}{4}\)

Now we have the following fractions:

- \(4/6 = \frac{4}{6} = \frac{2}{3}\)
- \(2(5/6) = \frac{17}{6}\)
- \(2(1/2) = \frac{5}{2}\)
- \(2(3/4) = \frac{11}{4}\)

Next, let's convert all fractions to a common denominator to easily compare their sizes. The common denominator for \(6\), \(2\), and \(4\) could be \(12\):

1. \(4/6 = \frac{8}{12}\)
2. \(17/6 = \frac{34}{12}\)
3. \(5/2 = \frac{30}{12}\)
4. \(11/4 = \frac{33}{12}\)

Now we can list them in order from smallest to largest:

1. \(4/6 = \frac{8}{12}\)
2. \(2(1/2) = \frac{5}{2} = \frac{30}{12}\)
3. \(2(3/4) = \frac{11}{4} = \frac{33}{12}\)
4. \(2(5/6) = \frac{17}{6} = \frac{34}{12}\)

Thus, the order from smallest to largest is:

\[
\frac{4}{6}, \frac{5}{2}, \frac{11}{4}, \frac{17}{6}
\]

In proper notation, this can be summarized as:

**4/6, 5/2, 11/4, 17/6**.