To divide the fractions [tex]\(\frac{4}{44}\)[/tex] by [tex]\(\frac{8}{-20}\)[/tex], follow these steps:
1. Understand the operation: Dividing by a fraction is equivalent to multiplying by its reciprocal. So, we can rewrite the division as a multiplication:
[tex]\[
\frac{4}{44} \div \frac{8}{-20} = \frac{4}{44} \times \frac{-20}{8}
\][/tex]
2. Multiply the numerators and multiply the denominators:
- Numerators: [tex]\(4 \times (-20)\)[/tex]
- Denominators: [tex]\(44 \times 8\)[/tex]
3. Calculate the numerator of the result:
[tex]\[
4 \times (-20) = -80
\][/tex]
4. Calculate the denominator of the result:
[tex]\[
44 \times 8 = 352
\][/tex]
5. Form the resulting fraction:
[tex]\[
\frac{-80}{352}
\][/tex]
6. Simplify the fraction if possible: To simplify, find the greatest common divisor (GCD) of 80 and 352 and divide both the numerator and the denominator by this GCD. However, if simplification is not required, you can leave it as is.
7. Express the fraction as a decimal: To provide a decimal form, divide the numerator by the denominator:
[tex]\[
\frac{-80}{352} \approx -0.22727272727272727
\][/tex]
So, the result of [tex]\(\frac{4}{44} \div \frac{8}{-20}\)[/tex] is:
[tex]\[
\boxed{\frac{-80}{352}} \quad \text{or approximately} \quad \boxed{-0.22727272727272727}
\][/tex]
