To subtract the fractions [tex]\(\frac{9}{20}\)[/tex] and [tex]\(\frac{2}{15}\)[/tex], follow these steps:
1. Find the Least Common Multiple (LCM) of the denominators:
The first step is to determine the LCM of 20 and 15, which will be the common denominator of the two fractions. The LCM of 20 and 15 is 60.
2. Convert each fraction to the common denominator:
For [tex]\(\frac{9}{20}\)[/tex]:
- Multiply both the numerator and the denominator by 3 (since [tex]\( \frac{60}{20} = 3 \)[/tex]):
[tex]\[
\frac{9 \times 3}{20 \times 3} = \frac{27}{60}
\][/tex]
For [tex]\(\frac{2}{15}\)[/tex]:
- Multiply both the numerator and the denominator by 4 (since [tex]\( \frac{60}{15} = 4 \)[/tex]):
[tex]\[
\frac{2 \times 4}{15 \times 4} = \frac{8}{60}
\][/tex]
3. Subtract the numerators:
With the common denominator now at 60, subtract the numerators of the adjusted fractions:
[tex]\[
\frac{27}{60} - \frac{8}{60} = \frac{27 - 8}{60} = \frac{19}{60}
\][/tex]
4. Simplify the fraction:
The fraction [tex]\(\frac{19}{60}\)[/tex] is already in its simplest form because 19 and 60 have no common factors other than 1.
Therefore, the answer to the expression [tex]\(\frac{9}{20} - \frac{2}{15}\)[/tex] as a fraction in lowest terms is:
[tex]\[
\frac{19}{60}
\][/tex]
