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True or False? 5 1/7

is a rational number between 5 and 5 1/4
.(1 point)
Responses

3 answers

True.

The number \( 5 \frac{1}{7} \) can be converted to an improper fraction:

\[ 5 \frac{1}{7} = \frac{36}{7} \]

Now, let's compare \( 5 \frac{1}{4} \) (which is \( \frac{21}{4} \)) to see if \( 5 \frac{1}{7} \) lies between \( 5 \) and \( 5 \frac{1}{4} \).

We can convert the whole numbers to improper fractions:

  • \( 5 = \frac{35}{7} \)
  • \( 5 \frac{1}{4} = \frac{21}{4} = \frac{42}{8} \) (to have a common denominator of 28)
  • \( 5 \frac{1}{7} = \frac{36}{7} = \frac{144}{28} \)
  • Also, \( \frac{35}{7} = \frac{140}{28} \) and \( \frac{21}{4} = \frac{42}{8} = \frac{84}{16} = \frac{168}{32}\)

It’s clear that \( 5 \frac{1}{7} \) lies between \( 5 \) and \( 5 \frac{1}{4} \):

So, the final answer is True.

try agian\

Let's re-evaluate the statement more carefully.

  1. Convert all numbers to improper fractions:

    • \( 5 = \frac{35}{7} \)
    • \( 5 \frac{1}{4} = 5 + \frac{1}{4} = \frac{20}{4} + \frac{1}{4} = \frac{21}{4} \)
    • \( 5 \frac{1}{7} = 5 + \frac{1}{7} = \frac{35}{7} + \frac{1}{7} = \frac{36}{7} \)

  2. Convert \( 5 \frac{1}{4} \) to an equivalent fraction with a common denominator to compare with \( 5 \frac{1}{7} \):

    The denominators are \( 7 \) and \( 4 \). The least common multiple of \( 7 \) and \( 4 \) is \( 28 \).

    • Therefore, we convert:
      • \( 5 = \frac{35}{7} = \frac{140}{28} \)
      • \( 5 \frac{1}{4} = \frac{21}{4} = \frac{147}{28} \)
      • \( 5 \frac{1}{7} = \frac{36}{7} = \frac{144}{28} \)

  3. Now let's compare:

    • \( 5 = \frac{140}{28} \)
    • \( 5 \frac{1}{7} = \frac{144}{28} \)
    • \( 5 \frac{1}{4} = \frac{147}{28} \)

  4. Conclusion:

    • \( \frac{140}{28} < \frac{144}{28} < \frac{147}{28} \)

Thus, \( 5 \frac{1}{7} \) is indeed between \( 5 \) and \( 5 \frac{1}{4} \).

The statement is True. Thank you for your patience.