To find the difference between the two fractions [tex]\(\frac{5}{7}\)[/tex] and [tex]\(\frac{2}{5}\)[/tex] and express the result in simplest terms, follow these steps:
1. Identify the fractions to subtract:
[tex]\[
\frac{5}{7} \quad \text{and} \quad \frac{2}{5}
\][/tex]
2. Find a common denominator for the fractions. The denominators are 7 and 5. The common denominator can be found by multiplying the two denominators:
[tex]\[
\text{Common denominator} = 7 \times 5 = 35
\][/tex]
3. Convert each fraction to have the common denominator of 35:
- For [tex]\(\frac{5}{7}\)[/tex], we multiply both the numerator and the denominator by 5:
[tex]\[
\frac{5}{7} = \frac{5 \times 5}{7 \times 5} = \frac{25}{35}
\][/tex]
- For [tex]\(\frac{2}{5}\)[/tex], we multiply both the numerator and the denominator by 7:
[tex]\[
\frac{2}{5} = \frac{2 \times 7}{5 \times 7} = \frac{14}{35}
\][/tex]
4. Subtract the two fractions with the common denominator:
[tex]\[
\frac{25}{35} - \frac{14}{35} = \frac{25 - 14}{35} = \frac{11}{35}
\][/tex]
5. Simplify the result if possible. In this case, 11 and 35 have no common factors other than 1, so the fraction is already in its simplest form.
Thus, the difference between the fractions [tex]\(\frac{5}{7}\)[/tex] and [tex]\(\frac{2}{5}\)[/tex] is:
[tex]\[
\frac{11}{35}
\][/tex]
