To solve the division of two fractions [tex]\(\frac{-3}{4} \div \frac{7}{6}\)[/tex], we follow these steps:
1. Understand the division of fractions:
Division of fractions is essentially multiplying the first fraction by the reciprocal (or inverse) of the second fraction. The reciprocal of a fraction is obtained by swapping its numerator and denominator.
2. Reciprocal of the second fraction:
The second fraction is [tex]\(\frac{7}{6}\)[/tex]. Its reciprocal is [tex]\(\frac{6}{7}\)[/tex].
3. Setup the multiplication:
Replace the division by multiplication with the reciprocal of the second fraction:
[tex]\[
\frac{-3}{4} \div \frac{7}{6} = \frac{-3}{4} \times \frac{6}{7}
\][/tex]
4. Multiply the numerators:
Multiply the numerator of the first fraction by the numerator of the second fraction:
[tex]\[
-3 \times 6 = -18
\][/tex]
5. Multiply the denominators:
Multiply the denominator of the first fraction by the denominator of the second fraction:
[tex]\[
4 \times 7 = 28
\][/tex]
6. Form the new fraction:
Combine the results of the numerator and denominator multiplications to form a new fraction:
[tex]\[
\frac{-18}{28}
\][/tex]
7. Simplify the fraction:
Simplify [tex]\(\frac{-18}{28}\)[/tex] by finding the greatest common divisor (GCD) of 18 and 28, which is 2:
[tex]\[
\frac{-18 \div 2}{28 \div 2} = \frac{-9}{14}
\][/tex]
Therefore, the result of [tex]\(\frac{-3}{4} \div \frac{7}{6}\)[/tex] is:
[tex]\[
\frac{-9}{14} \approx -0.6428571428571428
\][/tex]
