College

Divide and write your answer as a fraction or mixed number in simplest form.

[tex]-\frac{8}{5} \div \frac{12}{25}[/tex]

Answer :

Sure! Let's go through the process of dividing the fractions step-by-step.

We start with the division problem:

[tex]\[
-\frac{8}{5} \div \frac{12}{25}
\][/tex]

To divide by a fraction, we multiply by its reciprocal. The reciprocal of [tex]\(\frac{12}{25}\)[/tex] is [tex]\(\frac{25}{12}\)[/tex]. So, we change the division to multiplication:

[tex]\[
-\frac{8}{5} \times \frac{25}{12}
\][/tex]

Now, we multiply the numerators and the denominators:

- For the numerators: [tex]\(-8 \times 25 = -200\)[/tex]
- For the denominators: [tex]\(5 \times 12 = 60\)[/tex]

This gives us the fraction:

[tex]\[
-\frac{200}{60}
\][/tex]

Next, we simplify [tex]\(-\frac{200}{60}\)[/tex]. We do this by finding the greatest common divisor (GCD) of 200 and 60, which is 20. We divide both the numerator and the denominator by this GCD:

- Numerator: [tex]\(-\frac{200}{20} = -10\)[/tex]
- Denominator: [tex]\(\frac{60}{20} = 3\)[/tex]

So, in its simplest form, the fraction is:

[tex]\[
-\frac{10}{3}
\][/tex]

Therefore, the answer to the division problem [tex]\(-\frac{8}{5} \div \frac{12}{25}\)[/tex] is [tex]\(-\frac{10}{3}\)[/tex].