To solve the expression [tex]\(\frac{y}{4} - \frac{3}{5}\)[/tex], we need to find a common denominator for the fractions involved. The denominators are 4 and 5. The least common multiple (LCM) of 4 and 5 is 20.
1. Rewrite the fractions with the common denominator 20:
[tex]\[
\frac{y}{4} = \frac{y \cdot 5}{4 \cdot 5} = \frac{5y}{20}
\][/tex]
[tex]\[
\frac{3}{5} = \frac{3 \cdot 4}{5 \cdot 4} = \frac{12}{20}
\][/tex]
2. Subtract the second fraction from the first:
[tex]\[
\frac{5y}{20} - \frac{12}{20} = \frac{5y - 12}{20}
\][/tex]
3. Express the result as a proper fraction:
[tex]\[
\frac{5y - 12}{20}
\][/tex]
Thus, the simplified form of the expression [tex]\(\frac{y}{4} - \frac{3}{5}\)[/tex] is:
[tex]\[
\frac{5y - 12}{20}
\][/tex]
However, for verification, continuing the problem mathematically, one could approach it piecewise, examining how this fraction simplifies and considering any secondary reductions to confirm:
- The form [tex]\(\frac{y - 2.4}{4}\)[/tex] indicates [tex]\(2.4\)[/tex] in numerator balances to determine if numerical constants align with initial reduction factor calculations.
- Rewriting back, translates:
\[
(y - 2.4) \quad \text{in the numerator maps initial coefficients}, \quad (5y - 12)/resulting \quad 20 - confirming given formatted respective calculation form equivalences.
Thus [tex]\(\frac{y - 2.4}{4}\)[/tex] summarized alternative reduction, alongside fractional consistent formatting result and final propositionally balanced response.
