To write the fraction [tex]\(\frac{75}{60}\)[/tex] as a simplified mixed number, follow these steps:
1. Divide the numerator by the denominator to obtain the whole number part of the mixed number:
[tex]\[
75 \div 60 = 1 \text{ with a remainder of } 15.
\][/tex]
This means the whole number part is 1.
2. Write the remainder as a fraction with the original denominator:
[tex]\[
\frac{15}{60}.
\][/tex]
3. Simplify the fraction [tex]\(\frac{15}{60}\)[/tex]:
- Find the greatest common divisor (GCD) of 15 and 60. The GCD of 15 and 60 is 15.
- Divide both the numerator and the denominator by their GCD:
[tex]\[
\frac{15 \div 15}{60 \div 15} = \frac{1}{4}.
\][/tex]
So, [tex]\(\frac{15}{60}\)[/tex] simplifies to [tex]\(\frac{1}{4}\)[/tex].
Combining the whole number part and the simplified fraction, the mixed number is:
[tex]\[
1 \frac{1}{4}.
\][/tex]
Thus, [tex]\(\frac{75}{60}\)[/tex] written as a simplified mixed number is [tex]\(1 \frac{1}{4}\)[/tex].
