To solve the subtraction of the fractions [tex]\(\frac{7}{9} - \frac{1}{2}\)[/tex], follow these steps:
1. Identify the Least Common Denominator (LCD):
The denominators of the two fractions are 9 and 2. The LCD of these two numbers is the smallest number that both denominators divide evenly into. The least common multiple of 9 and 2 is 18. Thus, the common denominator is 18.
2. Convert the fractions to have the common denominator:
- For [tex]\(\frac{7}{9}\)[/tex], to convert it to have a denominator of 18, multiply the numerator and the denominator by 2:
[tex]\[
\frac{7}{9} = \frac{7 \times 2}{9 \times 2} = \frac{14}{18}
\][/tex]
- For [tex]\(\frac{1}{2}\)[/tex], to convert it to have a denominator of 18, multiply the numerator and the denominator by 9:
[tex]\[
\frac{1}{2} = \frac{1 \times 9}{2 \times 9} = \frac{9}{18}
\][/tex]
3. Subtract the numerators:
Now that both fractions have the same denominator, subtract the numerators while keeping the common denominator:
[tex]\[
\frac{14}{18} - \frac{9}{18} = \frac{14 - 9}{18} = \frac{5}{18}
\][/tex]
4. Simplify the result (if needed):
In this case, [tex]\(\frac{5}{18}\)[/tex] is already in its simplest form since the greatest common divisor (GCD) of 5 and 18 is 1.
Therefore, the result of the subtraction [tex]\(\frac{7}{9} - \frac{1}{2}\)[/tex] is:
[tex]\[
\frac{5}{18}
\][/tex]
