To solve the division of the fractions \(-\frac{3}{7} \div \frac{3}{8}\), follow these steps:
1. Rewrite the Division as Multiplication by the Reciprocal:
When dividing by a fraction, you can convert the operation to multiplication by the reciprocal of the second fraction. The reciprocal of \(\frac{3}{8}\) is \(\frac{8}{3}\). Therefore, the expression becomes:
[tex]\[
-\frac{3}{7} \div \frac{3}{8} = -\frac{3}{7} \times \frac{8}{3}
\][/tex]
2. Multiply the Numerators and the Denominators:
Multiply the numerators of the fractions together and the denominators together:
[tex]\[
\left( -\frac{3 \times 8}{7 \times 3} \right)
\][/tex]
This simplifies to:
[tex]\[
-\frac{24}{21}
\][/tex]
3. Simplify the Fraction:
The fraction \(-\frac{24}{21}\) can be simplified by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 3:
[tex]\[
-\frac{24 \div 3}{21 \div 3} = -\frac{8}{7}
\][/tex]
4. Convert to Decimal (If Needed):
To express \(-\frac{8}{7}\) as a decimal:
[tex]\[
-\frac{8}{7} \approx -1.1428571428571428
\][/tex]
Thus, the result of the division [tex]\(-\frac{3}{7} \div \frac{3}{8}\)[/tex] is [tex]\(-1.1428571428571428\)[/tex].
