To solve the problem [tex]$\frac{25}{12} - \frac{300}{60}$[/tex] step-by-step, let's follow the necessary procedures:
1. Simplify the fractions:
- The first fraction is [tex]$\frac{25}{12}$[/tex]. It is already in its simplest form.
- The second fraction is [tex]$\frac{300}{60}$[/tex]. We simplify it by dividing the numerator and the denominator by their greatest common divisor, which is 60:
[tex]\[
\frac{300}{60} = \frac{300 \div 60}{60 \div 60} = \frac{5}{1} = 5
\][/tex]
2. Convert fractions to a common denominator (if necessary):
- In this case, the fractions have different denominators (12 and 1). To perform the subtraction easily, we convert both fractions to have a common denominator. The least common denominator (LCD) between 12 and 1 is 12.
3. Rewrite each fraction with the common denominator:
- The first fraction is already [tex]$\frac{25}{12}$[/tex].
- Convert the second fraction, [tex]$5$[/tex], to have a denominator of 12:
[tex]\[
5 = \frac{5 \cdot 12}{1 \cdot 12} = \frac{60}{12}
\][/tex]
4. Subtract the fractions:
[tex]\[
\frac{25}{12} - \frac{60}{12} = \frac{25 - 60}{12} = \frac{-35}{12}
\][/tex]
5. Convert the result to a decimal (if needed for interpretation):
- The fraction [tex]$\frac{-35}{12}$[/tex] results in:
[tex]\[
\frac{-35}{12} \approx -2.9166666666666665
\][/tex]
So, the original problem [tex]$\frac{25}{12} - \frac{300}{60}$[/tex] simplifies and evaluates to approximately [tex]$-2.9166666666666665$[/tex].
