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

Answer 1

To compare the fractions and mixed numbers, it's helpful to convert them into decimal form or improper fractions. Here are each of them converted:

1. 4/6 can be simplified to 2/3, which is approximately 0.67.
2. 2 5/6 can be converted into an improper fraction: \(2 \times 6 + 5 = 12 + 5 = 17/6\), which is approximately 2.83.
3. 2 1/2 can be converted similarly: \(2 \times 2 + 1 = 4 + 1 = 5/2\), which is 2.5.
4. 2 3/4 converts to: \(2 \times 4 + 3 = 8 + 3 = 11/4\), which is approximately 2.75.

Now, let's order them based on their decimal values:

• 4/6 (2/3) ≈ 0.67
• 2 1/2 (5/2) = 2.5
• 2 3/4 (11/4) = 2.75
• 2 5/6 (17/6) ≈ 2.83

Arranging from smallest to largest gives us:

1. \(4/6\) (or \(2/3\))
2. \(2 \frac{1}{2}\) (or \(5/2\))
3. \(2 \frac{3}{4}\) (or \(11/4\))
4. \(2 \frac{5}{6}\) (or \(17/6\))

So, the numeric order from smallest to largest is:

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