To divide the fractions [tex]\(\frac{4}{5} \div \frac{12}{25}\)[/tex], follow these steps:
1. Invert the second fraction and multiply:
Changing division into multiplication involves inverting the second fraction:
[tex]\[
\frac{4}{5} \times \frac{25}{12}
\][/tex]
2. Multiply the numerators:
Multiply the numerator of the first fraction by the numerator of the inverted second fraction:
[tex]\[
4 \times 25 = 100
\][/tex]
3. Multiply the denominators:
Multiply the denominator of the first fraction by the denominator of the inverted second fraction:
[tex]\[
5 \times 12 = 60
\][/tex]
4. Form the new fraction:
The result from the multiplication step gives the new fraction:
[tex]\[
\frac{100}{60}
\][/tex]
5. Simplify the fraction:
To simplify [tex]\(\frac{100}{60}\)[/tex], find the greatest common divisor (GCD) of 100 and 60. The GCD of 100 and 60 is 20.
Now, divide both the numerator and the denominator by 20:
[tex]\[
\frac{100 \div 20}{60 \div 20} = \frac{5}{3}
\][/tex]
Hence, the simplified form of [tex]\(\frac{4}{5} \div \frac{12}{25}\)[/tex] is:
[tex]\[
\frac{5}{3}
\][/tex]
