To solve the problem of dividing the fraction [tex]\(-\frac{35}{4}\)[/tex] by the fraction [tex]\(-\frac{28}{9}\)[/tex], we can follow these detailed steps:
1. Understand the division of fractions:
- Dividing one fraction by another is equivalent to multiplying the first fraction by the reciprocal of the second fraction.
- The reciprocal of a fraction is obtained by swapping its numerator and denominator.
2. Find the reciprocal:
- The second fraction is [tex]\(-\frac{28}{9}\)[/tex].
- The reciprocal of [tex]\(-\frac{28}{9}\)[/tex] is [tex]\(-\frac{9}{28}\)[/tex].
3. Convert the division into multiplication:
- Now our problem becomes:
[tex]\[
-\frac{35}{4} \times -\frac{9}{28}
\][/tex]
4. Multiply the numerators and denominators:
- Multiply the numerators:
[tex]\[
-35 \times -9 = 315
\][/tex]
- Multiply the denominators:
[tex]\[
4 \times 28 = 112
\][/tex]
- So, [tex]\(-\frac{35}{4} \times -\frac{9}{28}\)[/tex] results in:
[tex]\[
\frac{315}{112}
\][/tex]
5. Simplify the resulting fraction:
- To simplify [tex]\(\frac{315}{112}\)[/tex], we need to find the greatest common divisor (GCD) of 315 and 112.
- The GCD of 315 and 112 is 7.
- Divide both the numerator and the denominator by the GCD:
[tex]\[
\frac{315 \div 7}{112 \div 7} = \frac{45}{16}
\][/tex]
6. Conclusion:
- The fraction [tex]\(\frac{315}{112}\)[/tex] simplifies to [tex]\(\frac{45}{16}\)[/tex].
Therefore, the result of the division [tex]\(-\frac{35}{4}\)[/tex] by [tex]\(-\frac{28}{9}\)[/tex] is [tex]\(\frac{45}{16}\)[/tex]. The simplified fraction is [tex]\(-\frac{45}{16}\)[/tex] as a final step if considering the sign correction for mathematical standard reasons.
