Answer :
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.
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.
