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Simplify. Express your answer as a single fraction in simplest form. \newline25−y3\frac{2}{5} - \frac{y}{3}

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Full solution

Q. Simplify. Express your answer as a single fraction in simplest form. \newline25−y3\frac{2}{5} - \frac{y}{3}
  1. Identify LCD: 25−y3\frac{2}{5} - \frac{y}{3}\newlineIdentify the least common denominator (LCD) for the fractions.\newlineThe LCD for 55 and 33 is 1515 because 1515 is the smallest number that both 55 and 33 can divide into without leaving a remainder.
  2. Rewrite fractions: 25−y3\frac{2}{5} - \frac{y}{3}\newlineRewrite each fraction with the common denominator of 1515.\newline25=(2×35×3)=615\frac{2}{5} = \left(\frac{2\times3}{5\times3}\right) = \frac{6}{15}\newliney3=(y×53×5)=5y15\frac{y}{3} = \left(\frac{y\times5}{3\times5}\right) = \frac{5y}{15}
  3. Combine fractions: 615−5y15\frac{6}{15} - \frac{5y}{15}\newlineCombine the fractions now that they have a common denominator.\newline6−5y15\frac{6 - 5y}{15}
  4. Check simplification: (6−5y)/15(6 - 5y)/15\newlineCheck if the numerator can be simplified further. Since 66 and 5y5y do not have any common factors other than 11, the fraction is already in its simplest form.

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