Certainly, Ayoni! Let's break down this problem step-by-step:
We have the expression:
[tex]\[
-\frac{4}{5} \div \left(-\frac{8}{25}\right)
\][/tex]
### Step-by-Step Solution:
1. Understanding Division of Fractions:
Dividing by a fraction is equivalent to multiplying by its reciprocal. The reciprocal of a fraction is obtained by swapping the numerator and the denominator.
2. Find the Reciprocal of [tex]\(-\frac{8}{25}\)[/tex]:
The reciprocal of [tex]\(-\frac{8}{25}\)[/tex] is [tex]\(\frac{25}{-8}\)[/tex].
3. Set up the Multiplication:
We then multiply [tex]\(-\frac{4}{5}\)[/tex] by the reciprocal [tex]\(\frac{25}{-8}\)[/tex]:
[tex]\[
-\frac{4}{5} \times \frac{25}{-8}
\][/tex]
4. Multiply the Numerators:
Multiply the numerators [tex]\(-4\)[/tex] and [tex]\(25\)[/tex]:
[tex]\[
-4 \times 25 = -100
\][/tex]
5. Multiply the Denominators:
Multiply the denominators [tex]\(5\)[/tex] and [tex]\(-8\)[/tex]:
[tex]\[
5 \times -8 = -40
\][/tex]
6. Combine the Results:
Now we have the fraction:
[tex]\[
\frac{-100}{-40}
\][/tex]
7. Simplify the Fraction:
When you divide a negative number by another negative number, the result is positive. Simplify the fraction [tex]\(\frac{-100}{-40}\)[/tex] by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is [tex]\(20\)[/tex]:
[tex]\[
\frac{100}{40} = \frac{100 \div 20}{40 \div 20} = \frac{5}{2}
\][/tex]
So, the final result is:
[tex]\[
2.5
\][/tex]
To summarize, [tex]\(-\frac{4}{5} \div \left(-\frac{8}{25}\right) = 2.5\)[/tex].
Feel free to ask if you have any questions about these steps, Ayoni!
