To reduce the fraction [tex]\(\frac{21}{72}\)[/tex] to its lowest terms, follow these steps:
1. Identify the Greatest Common Divisor (GCD):
To reduce a fraction to its lowest terms, you first need to find the greatest common divisor (GCD) of the numerator and the denominator. The GCD is the largest integer that can divide both numbers without leaving a remainder.
- The GCD of 21 and 72 is 3.
2. Divide Both the Numerator and Denominator by the GCD:
Once we have the GCD, we divide both the numerator and the denominator by this number to simplify the fraction.
- [tex]\( \frac{21 \div 3}{72 \div 3} \)[/tex]
3. Perform the Division:
- [tex]\( 21 \div 3 = 7 \)[/tex]
- [tex]\( 72 \div 3 = 24 \)[/tex]
Therefore, [tex]\( \frac{21}{72} \)[/tex] simplifies to [tex]\( \frac{7}{24} \)[/tex].
Upon examining the given choices:
a. [tex]\(\frac{7}{18}\)[/tex]
b. [tex]\(\frac{21}{72}\)[/tex]
c. [tex]\(\frac{14}{48}\)[/tex]
d. [tex]\(\frac{7}{24}\)[/tex]
We see that the simplified form of [tex]\(\frac{21}{72}\)[/tex] is:
d. [tex]\(\frac{7}{24}\)[/tex]
Thus, the correct answer is [tex]\(\frac{7}{24}\)[/tex].
