Certainly! To divide fractions, we need to multiply the first fraction by the reciprocal of the second fraction. Here are the steps to solve the given problem:
Given fractions:
[tex]\[
\frac{3}{10} \div \frac{5}{12}
\][/tex]
1. Find the reciprocal of the second fraction:
The reciprocal of [tex]\(\frac{5}{12}\)[/tex] is [tex]\(\frac{12}{5}\)[/tex]. This is because the reciprocal of a fraction is obtained by swapping its numerator and denominator.
2. Replace the division with multiplication by the reciprocal:
Instead of dividing [tex]\(\frac{3}{10}\)[/tex] by [tex]\(\frac{5}{12}\)[/tex], we multiply [tex]\(\frac{3}{10}\)[/tex] by [tex]\(\frac{12}{5}\)[/tex].
[tex]\[
\frac{3}{10} \times \frac{12}{5}
\][/tex]
3. Multiply the numerators together:
Multiply the numerators (the top numbers) of the two fractions:
[tex]\[
3 \times 12 = 36
\][/tex]
4. Multiply the denominators together:
Multiply the denominators (the bottom numbers) of the two fractions:
[tex]\[
10 \times 5 = 50
\][/tex]
5. Write the resulting fraction:
The result of the multiplication is:
[tex]\[
\frac{36}{50}
\][/tex]
Thus, [tex]\[
\frac{3}{10} \div \frac{5}{12} = \frac{36}{50}.
\][/tex]
And that is the final answer.
