To solve the problem [tex]\(\left(-\frac{35}{4}\right) \div \left(-\frac{28}{9}\right)\)[/tex], we need to follow the rules of fraction division. Dividing by a fraction is equivalent to multiplying by its reciprocal. Here are the steps to solve this:
1. Expression Review:
[tex]\[
\left(-\frac{35}{4}\right) \div \left(-\frac{28}{9}\right)
\][/tex]
2. Reciprocal of the Divisor:
Find the reciprocal of [tex]\(-\frac{28}{9}\)[/tex]:
[tex]\[
\left( -\frac{28}{9} \right)^{-1} = -\frac{9}{28}
\][/tex]
3. Multiplication by the Reciprocal:
Multiply [tex]\(-\frac{35}{4}\)[/tex] by [tex]\(-\frac{9}{28}\)[/tex]:
[tex]\[
\left(-\frac{35}{4}\right) \times \left(-\frac{9}{28}\right)
\][/tex]
4. Multiply the Numerators and the Denominators:
Multiply the numerators:
[tex]\[
-35 \times -9 = 315
\][/tex]
Multiply the denominators:
[tex]\[
4 \times 28 = 112
\][/tex]
5. Form the Fraction:
Place the product of the numerators over the product of the denominators:
[tex]\[
\frac{315}{112}
\][/tex]
6. Simplifying the Fraction:
[tex]\[
\frac{315}{112} \approx 2.8125
\][/tex]
Therefore, the simplified result of [tex]\(\left(-\frac{35}{4}\right) \div \left(-\frac{28}{9}\right)\)[/tex] is [tex]\(\frac{315}{112}\)[/tex], which is approximately [tex]\(2.8125\)[/tex].
