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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 answer

To compare the fractions and mixed numbers, it's helpful to convert all of them to either improper fractions or decimal form. Let's convert each one:

  1. \( \frac{4}{6} = \frac{2}{3} \) (which is approximately 0.6667)
  2. \( 2 \frac{5}{6} = 2 + \frac{5}{6} = \frac{12}{6} + \frac{5}{6} = \frac{17}{6} \) (which is approximately 2.8333)
  3. \( 2 \frac{1}{2} = 2 + \frac{1}{2} = \frac{4}{2} + \frac{1}{2} = \frac{5}{2} \) (which is 2.5)
  4. \( 2 \frac{3}{4} = 2 + \frac{3}{4} = \frac{8}{4} + \frac{3}{4} = \frac{11}{4} \) (which is 2.75)

Now, let's summarize the decimal approximations:

  • \( \frac{2}{3} \) is approximately 0.6667
  • \( 2 \frac{1}{2} \) is 2.5
  • \( 2 \frac{3}{4} \) is 2.75
  • \( 2 \frac{5}{6} \) is approximately 2.8333

Now we can arrange these from smallest to largest:

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

So, the numeric order from smallest to largest is: \[ \frac{4}{6}, , 2 \frac{1}{2}, , 2 \frac{3}{4}, , 2 \frac{5}{6} \]