To solve the problem of adding the fractions [tex]\(\frac{7}{5}\)[/tex] and [tex]\(\frac{1}{4}\)[/tex], follow these steps:
1. Find the common denominator: The common denominator for the fractions with denominators 5 and 4 is found by multiplying these denominators together. Therefore, the common denominator is:
[tex]\[
5 \times 4 = 20
\][/tex]
2. Convert each fraction to an equivalent fraction with the common denominator:
- For [tex]\(\frac{7}{5}\)[/tex]: Multiply both the numerator and the denominator by 4:
[tex]\[
\frac{7 \times 4}{5 \times 4} = \frac{28}{20}
\][/tex]
- For [tex]\(\frac{1}{4}\)[/tex]: Multiply both the numerator and the denominator by 5:
[tex]\[
\frac{1 \times 5}{4 \times 5} = \frac{5}{20}
\][/tex]
3. Add the numerators of the two equivalent fractions, keeping the common denominator:
[tex]\[
\frac{28}{20} + \frac{5}{20} = \frac{28 + 5}{20} = \frac{33}{20}
\][/tex]
4. Simplify the resulting fraction: To simplify [tex]\(\frac{33}{20}\)[/tex], find the greatest common divisor (GCD) of the numerator (33) and the denominator (20). Since 33 and 20 are coprime (i.e., their GCD is 1), the fraction is already in its simplest form:
[tex]\[
\frac{33}{20}
\][/tex]
5. Conclusion: The result of adding [tex]\(\frac{7}{5}\)[/tex] and [tex]\(\frac{1}{4}\)[/tex] is:
[tex]\[
\frac{33}{20}
\][/tex]
Thus, [tex]\(\frac{7}{5} + \frac{1}{4} = \frac{33}{20}\)[/tex].
