Answer :

To solve the expression [tex]64 \frac{13}{15} - 5 \frac{15}{16}[/tex], we need to work with mixed numbers. Here's a step-by-step breakdown:

  1. Convert Mixed Numbers to Improper Fractions

    • For [tex]64 \frac{13}{15}[/tex]:

      Convert [tex]64[/tex] whole to a fraction:
      [tex]64 = \frac{64 \times 15}{15} = \frac{960}{15}[/tex]

      Add [tex]\frac{13}{15}[/tex] to this:
      [tex]64 \frac{13}{15} = \frac{960}{15} + \frac{13}{15} = \frac{973}{15}[/tex]

    • For [tex]5 \frac{15}{16}[/tex]:

      Convert [tex]5[/tex] whole to a fraction:
      [tex]5 = \frac{5 \times 16}{16} = \frac{80}{16}[/tex]

      Add [tex]\frac{15}{16}[/tex] to this:
      [tex]5 \frac{15}{16} = \frac{80}{16} + \frac{15}{16} = \frac{95}{16}[/tex]

  2. Subtract the Improper Fractions

    To subtract [tex]\frac{973}{15}[/tex] from [tex]\frac{95}{16}[/tex], we need a common denominator. The least common multiple of 15 and 16 is 240.

    • Convert [tex]\frac{973}{15}[/tex] to a denominator of 240:
      [tex]\frac{973}{15} = \frac{973 \times 16}{15 \times 16} = \frac{15568}{240}[/tex]

    • Convert [tex]\frac{95}{16}[/tex] to a denominator of 240:
      [tex]\frac{95}{16} = \frac{95 \times 15}{16 \times 15} = \frac{1425}{240}[/tex]

    • Now subtract:
      [tex]\frac{15568}{240} - \frac{1425}{240} = \frac{14143}{240}[/tex]

  3. Convert the Result Back to a Mixed Number

    Divide 14143 by 240 to find the whole number part:

    • [tex]14143 \div 240 \approx 58.930[/tex] which gives a whole number of 58.

    • The remainder is [tex]14143 - (58 \times 240) = 223[/tex].

    Therefore, [tex]\frac{14143}{240}[/tex] is equivalent to [tex]58 \frac{223}{240}[/tex].

In conclusion, [tex]64 \frac{13}{15} - 5 \frac{15}{16} = 58 \frac{223}{240}[/tex]. This includes converting mixed numbers to improper fractions, finding a common denominator, and simplifying the result back to a mixed number.

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