To subtract the fractions [tex]\(\frac{4}{5}\)[/tex] and [tex]\(\frac{7}{12}\)[/tex], follow these steps:
1. Find the Least Common Denominator (LCD):
- The denominators of the fractions are 5 and 12.
- The least common denominator (LCD) is the smallest number that both 5 and 12 can divide into without leaving a remainder. The LCD of 5 and 12 is 60.
2. Convert the fractions to have the common denominator:
- For [tex]\(\frac{4}{5}\)[/tex]:
[tex]\[
\frac{4}{5} = \frac{4 \times 12}{5 \times 12} = \frac{48}{60}
\][/tex]
- For [tex]\(\frac{7}{12}\)[/tex]:
[tex]\[
\frac{7}{12} = \frac{7 \times 5}{12 \times 5} = \frac{35}{60}
\][/tex]
3. Subtract the fractions with the common denominator:
- Now that both fractions have the denominator 60, subtract the numerators:
[tex]\[
\frac{48}{60} - \frac{35}{60} = \frac{48 - 35}{60} = \frac{13}{60}
\][/tex]
4. Simplify the result (if possible):
- In this case, [tex]\(\frac{13}{60}\)[/tex] is already in its simplest form because 13 and 60 have no common factors other than 1.
Therefore, the result of [tex]\(\frac{4}{5} - \frac{7}{12}\)[/tex] is:
[tex]\[
\frac{13}{60}
\][/tex]
