To solve [tex]\(\frac{2}{-3} \div 2 \frac{3}{4}\)[/tex], we will follow these steps:
1. Understand and Simplify the Fractions:
- The first fraction given is [tex]\(\frac{2}{-3}\)[/tex].
- The second term is a mixed number, [tex]\(2 \frac{3}{4}\)[/tex], which can be converted into an improper fraction.
2. Convert the Mixed Number to an Improper Fraction:
- [tex]\(2 \frac{3}{4}\)[/tex] means [tex]\(2\)[/tex] whole parts and [tex]\(\frac{3}{4}\)[/tex].
- Convert [tex]\(2\)[/tex] whole parts: [tex]\(2\)[/tex] is equal to [tex]\(8\)[/tex] quarters (since [tex]\(2 \times 4 = 8\)[/tex]).
- Add the [tex]\(\frac{3}{4}\)[/tex]: [tex]\(8/4 + 3/4 = 11/4\)[/tex].
3. Set up the Division Problem:
- Now we have [tex]\(\frac{2}{-3} \div \frac{11}{4}\)[/tex].
4. Convert Division to Multiplication by the Reciprocal:
- Dividing by a fraction is the same as multiplying by its reciprocal.
- The reciprocal of [tex]\(\frac{11}{4}\)[/tex] is [tex]\(\frac{4}{11}\)[/tex].
5. Perform the Multiplication:
- Multiply [tex]\(\frac{2}{-3}\)[/tex] by [tex]\(\frac{4}{11}\)[/tex]:
[tex]\[
\frac{2}{-3} \times \frac{4}{11} = \frac{2 \times 4}{-3 \times 11} = \frac{8}{-33}.
\][/tex]
6. Simplify if Possible:
- The fraction [tex]\(\frac{8}{-33}\)[/tex] cannot be simplified further.
- The negative sign is usually written in the numerator for convention, resulting in [tex]\(-\frac{8}{33}\)[/tex].
Hence, the solution to [tex]\(\frac{2}{-3} \div 2 \frac{3}{4}\)[/tex] is:
[tex]\[
\frac{2}{-3} \div 2 \frac{3}{4} = -\frac{8}{33}.
\][/tex]
For the purposes of clarity and precision, in terms of decimal values:
- Converting [tex]\(\frac{2}{-3}\)[/tex] into a decimal gives approximately [tex]\(-0.67\)[/tex].
- Converting [tex]\(\frac{11}{4}\)[/tex] into a decimal gives [tex]\(2.75\)[/tex].
- Now, dividing [tex]\(-0.67\)[/tex] by [tex]\(2.75\)[/tex] yields approximately [tex]\(-0.242424\)[/tex].
Therefore, [tex]\(\frac{2}{-3} \div 2 \frac{3}{4}\)[/tex] equals roughly [tex]\(-0.242424\)[/tex].
