High School

Divide the fractions. Write your answer as a fraction or mixed number in simplest form.

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

Answer :

To divide fractions, you multiply by the reciprocal of the divisor. Let's break it down step by step:

1. Identify the fractions:
We have [tex]\(-\frac{8}{5}\)[/tex] that we want to divide by [tex]\(\frac{12}{25}\)[/tex].

2. Find the reciprocal of the divisor:
The divisor is [tex]\(\frac{12}{25}\)[/tex]. Its reciprocal is [tex]\(\frac{25}{12}\)[/tex].

3. Multiply by the reciprocal:
Now, instead of dividing, we can multiply [tex]\(-\frac{8}{5}\)[/tex] by [tex]\(\frac{25}{12}\)[/tex]:
[tex]\[
-\frac{8}{5} \times \frac{25}{12}
\][/tex]

4. Multiply the numerators and the denominators:
- Numerator: [tex]\(-8 \times 25 = -200\)[/tex]
- Denominator: [tex]\(5 \times 12 = 60\)[/tex]

5. Form the new fraction:
This gives us the fraction [tex]\(-\frac{200}{60}\)[/tex].

6. Simplify the fraction:
To simplify [tex]\(-\frac{200}{60}\)[/tex], we find the greatest common divisor (GCD) of 200 and 60, which is 20. Then, divide both the numerator and the denominator by 20:
[tex]\[
-\frac{200 \div 20}{60 \div 20} = -\frac{10}{3}
\][/tex]

7. Result:
The simplified result is [tex]\(-\frac{10}{3}\)[/tex].

So, [tex]\(-\frac{8}{5} \div \frac{12}{25}\)[/tex] simplifies to [tex]\(-\frac{10}{3}\)[/tex]. This is your final answer.