Answer :
To simplify the fractions step-by-step, we will find the greatest common divisor (GCD) for each fraction and divide both the numerator and the denominator by this GCD to get the simplified form.
1. Simplifying [tex]\( \frac{24}{30} \)[/tex]:
- First, we find the GCD of 24 and 30.
- The GCD of 24 and 30 is 6.
- Divide both the numerator and the denominator by 6:
[tex]\[
\frac{24}{30} = \frac{24 \div 6}{30 \div 6} = \frac{4}{5}
\][/tex]
2. Simplifying [tex]\( \frac{8}{12} \)[/tex]:
- First, we find the GCD of 8 and 12.
- The GCD of 8 and 12 is 4.
- Divide both the numerator and the denominator by 4:
[tex]\[
\frac{8}{12} = \frac{8 \div 4}{12 \div 4} = \frac{2}{3}
\][/tex]
3. Simplifying [tex]\( \frac{98}{108} \)[/tex]:
- First, we find the GCD of 98 and 108.
- The GCD of 98 and 108 is 2.
- Divide both the numerator and the denominator by 2:
[tex]\[
\frac{98}{108} = \frac{98 \div 2}{108 \div 2} = \frac{49}{54}
\][/tex]
Thus, the simplified forms of the fractions are [tex]\( \frac{4}{5} \)[/tex], [tex]\( \frac{2}{3} \)[/tex], and [tex]\( \frac{49}{54} \)[/tex].
1. Simplifying [tex]\( \frac{24}{30} \)[/tex]:
- First, we find the GCD of 24 and 30.
- The GCD of 24 and 30 is 6.
- Divide both the numerator and the denominator by 6:
[tex]\[
\frac{24}{30} = \frac{24 \div 6}{30 \div 6} = \frac{4}{5}
\][/tex]
2. Simplifying [tex]\( \frac{8}{12} \)[/tex]:
- First, we find the GCD of 8 and 12.
- The GCD of 8 and 12 is 4.
- Divide both the numerator and the denominator by 4:
[tex]\[
\frac{8}{12} = \frac{8 \div 4}{12 \div 4} = \frac{2}{3}
\][/tex]
3. Simplifying [tex]\( \frac{98}{108} \)[/tex]:
- First, we find the GCD of 98 and 108.
- The GCD of 98 and 108 is 2.
- Divide both the numerator and the denominator by 2:
[tex]\[
\frac{98}{108} = \frac{98 \div 2}{108 \div 2} = \frac{49}{54}
\][/tex]
Thus, the simplified forms of the fractions are [tex]\( \frac{4}{5} \)[/tex], [tex]\( \frac{2}{3} \)[/tex], and [tex]\( \frac{49}{54} \)[/tex].
