To solve [tex]\(\frac{3}{5} \div \frac{12}{25}\)[/tex], let's follow these steps in detail:
1. Understand the Division of Fractions:
Dividing by a fraction is equivalent to multiplying by its reciprocal. The reciprocal of [tex]\(\frac{12}{25}\)[/tex] is [tex]\(\frac{25}{12}\)[/tex].
2. Find the Reciprocal:
[tex]\( \frac{12}{25} \)[/tex] changes to [tex]\( \frac{25}{12} \)[/tex].
3. Rewrite the Division as Multiplication:
Now the problem [tex]\(\frac{3}{5} \div \frac{12}{25}\)[/tex] can be rewritten as:
[tex]\[
\frac{3}{5} \times \frac{25}{12}
\][/tex]
4. Multiply the Numerators:
To multiply two fractions, multiply the numerators together:
[tex]\[
3 \times 25 = 75
\][/tex]
5. Multiply the Denominators:
Next, multiply the denominators together:
[tex]\[
5 \times 12 = 60
\][/tex]
6. Form the Resulting Fraction:
Combine the results from the numerators and denominators:
[tex]\[
\frac{3}{5} \times \frac{25}{12} = \frac{75}{60}
\][/tex]
Thus, the result of [tex]\(\frac{3}{5} \div \frac{12}{25} \)[/tex] is [tex]\(\frac{75}{60}\)[/tex].
This fraction can be further simplified, but the result as obtained is [tex]\(\frac{75}{60}\)[/tex].
