To divide the fractions [tex]\(\frac{3}{5}\)[/tex] by [tex]\(\frac{6}{7}\)[/tex], follow these steps:
1. Understand the operation:
Dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of a fraction is simply switching its numerator and denominator. So, the reciprocal of [tex]\(\frac{6}{7}\)[/tex] is [tex]\(\frac{7}{6}\)[/tex].
2. Rewrite the division as a multiplication:
[tex]\[
\frac{3}{5} \div \frac{6}{7} = \frac{3}{5} \times \frac{7}{6}
\][/tex]
3. Multiply the fractions:
To multiply two fractions, multiply the numerators together and the denominators together.
[tex]\[
\frac{3 \times 7}{5 \times 6} = \frac{21}{30}
\][/tex]
4. Simplify if possible:
Check if the resulting fraction [tex]\(\frac{21}{30}\)[/tex] can be simplified. Both the numerator (21) and the denominator (30) are divisible by 3.
[tex]\[
\frac{21 \div 3}{30 \div 3} = \frac{7}{10}
\][/tex]
So, the answer to the division [tex]\(\frac{3}{5} \div \frac{6}{7}\)[/tex] is [tex]\(\frac{7}{10}\)[/tex].
