Answer :

To solve the expression [tex]51 \frac{4}{25} - 3 \frac{13}{15}[/tex], we need to first convert the mixed numbers into improper fractions and then perform the subtraction.

  1. Convert the mixed numbers to improper fractions:

    • For [tex]51 \frac{4}{25}[/tex]:

      The whole number is 51 and the fractional part is [tex]\frac{4}{25}[/tex]. To express this as an improper fraction:

      [tex]51 = \frac{51 \times 25}{25} = \frac{1275}{25}[/tex]

      Adding the fractional part:

      [tex]\frac{1275}{25} + \frac{4}{25} = \frac{1279}{25}[/tex]

    • For [tex]3 \frac{13}{15}[/tex]:

      The whole number is 3 and the fractional part is [tex]\frac{13}{15}[/tex]. To express this as an improper fraction:

      [tex]3 = \frac{3 \times 15}{15} = \frac{45}{15}[/tex]

      Adding the fractional part:

      [tex]\frac{45}{15} + \frac{13}{15} = \frac{58}{15}[/tex]

  2. Find a common denominator:

    The denominators are 25 and 15, so we need to find the least common multiple (LCM) of these numbers. The LCM of 25 and 15 is 75.

  3. Convert the fractions to have the common denominator:

    • For [tex]\frac{1279}{25}[/tex]:

      Multiply both the numerator and denominator by 3:

      [tex]\frac{1279 \times 3}{25 \times 3} = \frac{3837}{75}[/tex]

    • For [tex]\frac{58}{15}[/tex]:

      Multiply both the numerator and denominator by 5:

      [tex]\frac{58 \times 5}{15 \times 5} = \frac{290}{75}[/tex]

  4. Subtract the fractions:

    Now that both fractions have the same denominator, subtract the numerators:

    [tex]\frac{3837}{75} - \frac{290}{75} = \frac{3547}{75}[/tex]

  5. Simplify the fraction if possible:

    Check if [tex]\frac{3547}{75}[/tex] can be simplified. Since 3547 and 75 have no common factors other than 1, the fraction is already in its simplest form.

Therefore, the result of [tex]51 \frac{4}{25} - 3 \frac{13}{15}[/tex] is [tex]\frac{3547}{75}[/tex].

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