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Which of the following is a rational number between 5 and 5 1/4

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5 answers

To find a rational number between \(5\) and \(5 \frac{1}{4}\), we first convert \(5 \frac{1}{4}\) to an improper fraction.

\[ 5 \frac{1}{4} = \frac{5 \times 4 + 1}{4} = \frac{20 + 1}{4} = \frac{21}{4} \]

Now, we need to consider the range between \(5\) (which can be expressed as \(\frac{20}{4}\)) and \(\frac{21}{4}\).

A rational number between \(5\) and \(5 \frac{1}{4}\) could be \(\frac{20 + 21}{2 \times 4} = \frac{41}{8}\), which is approximately \(5.125\).

Alternatively, you can also choose other simple fractions. For example, \(\frac{21}{5}\) or \(\frac{21}{10}\) are also valid rational numbers in that range.

So, some examples of rational numbers between \(5\) and \(5 \frac{1}{4}\) are \(\frac{41}{8}\), \(\frac{21}{5}\), and \(\frac{21}{10}\).

thats not fight

I apologize for any confusion. Let's clarify and find a rational number between \(5\) and \(5 \frac{1}{4}\) step by step.

  1. Convert mixed number to improper fraction:
    \(5 \frac{1}{4} = \frac{21}{4}\)

  2. Find a rational number between \(5\) and \(5 \frac{1}{4}\):

    • The decimal equivalent of \(5\) is \(5.0\) and the decimal equivalent of \(5 \frac{1}{4}\) is \(5.25\).
    • A simple way to find a number between them would be to choose a number like \(5.1\), \(5.2\), or \(5.15\).

  3. Convert to a rational number:

    • For example, \(5.1\) can be expressed as \(\frac{51}{10}\).
    • Similarly, \(5.2\) can be expressed as \(\frac{26}{5}\).

So, valid rational numbers between \(5\) and \(5 \frac{1}{4}\) include:

  • \( \frac{51}{10} \) (which is \(5.1\))
  • \( \frac{26}{5} \) (which is \(5.2\))
  • \( \frac{21}{4} > 5.2\) and less than \(5.25\)

If you are looking for one specific rational number, \(5.1\) or \(\frac{51}{10}\) is a valid choice, as it falls between \(5\) and \(5 \frac{1}{4}\).

Please let me know if you need further clarification!

Which of the following is a rational number between 5 and 51/4

A.26
B. 5 2/5
C. 5 1/3
D . 5 1/7

To find a rational number between \(5\) and \(5 \frac{1}{4}\) (which is the same as \(\frac{21}{4} = 5.25\)), we can evaluate each of the options provided.

Convert all options to improper fractions or decimals for easier comparison:

  1. Option A: 26

    • This is a whole number and is greater than \(5.25\).

  2. Option B: \(5 \frac{2}{5}\)

    • Convert to an improper fraction:
      \[ 5 \frac{2}{5} = \frac{5 \times 5 + 2}{5} = \frac{25 + 2}{5} = \frac{27}{5} = 5.4 \]
    • \(5.4\) is greater than \(5.25\).

  3. Option C: \(5 \frac{1}{3}\)

    • Convert to an improper fraction:
      \[ 5 \frac{1}{3} = \frac{5 \times 3 + 1}{3} = \frac{15 + 1}{3} = \frac{16}{3} \approx 5.3333 \]
    • \(5.3333\) is greater than \(5.25\).

  4. Option D: \(5 \frac{1}{7}\)

    • Convert to an improper fraction:
      \[ 5 \frac{1}{7} = \frac{5 \times 7 + 1}{7} = \frac{35 + 1}{7} = \frac{36}{7} \approx 5.142857 \]
    • \(5.142857\) is less than \(5.25\).

After evaluating these options, the only rational number that is between \(5\) and \(5 \frac{1}{4}\) is:

Option D: \(5 \frac{1}{7}\).