Certainly! Let's reduce each of the given fractions to their simplest form step by step.
### (a) [tex]\(\frac{48}{60}\)[/tex]
To reduce [tex]\(\frac{48}{60}\)[/tex]:
1. Find the greatest common divisor (GCD) of 48 and 60.
2. The GCD of 48 and 60 is 12.
3. Divide both the numerator and the denominator by their GCD:
[tex]\[
\frac{48 \div 12}{60 \div 12} = \frac{4}{5}
\][/tex]
So, [tex]\(\frac{48}{60}\)[/tex] simplifies to [tex]\(\frac{4}{5}\)[/tex].
### (b) [tex]\(\frac{150}{60}\)[/tex]
To reduce [tex]\(\frac{150}{60}\)[/tex]:
1. Find the greatest common divisor (GCD) of 150 and 60.
2. The GCD of 150 and 60 is 30.
3. Divide both the numerator and the denominator by their GCD:
[tex]\[
\frac{150 \div 30}{60 \div 30} = \frac{5}{2}
\][/tex]
So, [tex]\(\frac{150}{60}\)[/tex] simplifies to [tex]\(\frac{5}{2}\)[/tex].
### (c) [tex]\(\frac{84}{98}\)[/tex]
To reduce [tex]\(\frac{84}{98}\)[/tex]:
1. Find the greatest common divisor (GCD) of 84 and 98.
2. The GCD of 84 and 98 is 14.
3. Divide both the numerator and the denominator by their GCD:
[tex]\[
\frac{84 \div 14}{98 \div 14} = \frac{6}{7}
\][/tex]
So, [tex]\(\frac{84}{98}\)[/tex] simplifies to [tex]\(\frac{6}{7}\)[/tex].
### (d) [tex]\(\frac{12}{52}\)[/tex]
To reduce [tex]\(\frac{12}{52}\)[/tex]:
1. Find the greatest common divisor (GCD) of 12 and 52.
2. The GCD of 12 and 52 is 4.
3. Divide both the numerator and the denominator by their GCD:
[tex]\[
\frac{12 \div 4}{52 \div 4} = \frac{3}{13}
\][/tex]
So, [tex]\(\frac{12}{52}\)[/tex] simplifies to [tex]\(\frac{3}{13}\)[/tex].
### (e) [tex]\(\frac{7}{28}\)[/tex]
To reduce [tex]\(\frac{7}{28}\)[/tex]:
1. Find the greatest common divisor (GCD) of 7 and 28.
2. The GCD of 7 and 28 is 7.
3. Divide both the numerator and the denominator by their GCD:
[tex]\[
\frac{7 \div 7}{28 \div 7} = \frac{1}{4}
\][/tex]
So, [tex]\(\frac{7}{28}\)[/tex] simplifies to [tex]\(\frac{1}{4}\)[/tex].
To summarize, the simplified forms of the given fractions are:
- [tex]\(\frac{48}{60} = \frac{4}{5}\)[/tex]
- [tex]\(\frac{150}{60} = \frac{5}{2}\)[/tex]
- [tex]\(\frac{84}{98} = \frac{6}{7}\)[/tex]
- [tex]\(\frac{12}{52} = \frac{3}{13}\)[/tex]
- [tex]\(\frac{7}{28} = \frac{1}{4}\)[/tex]
