To divide the fractions [tex]\(\frac{4}{15}\)[/tex] by [tex]\(-\frac{4}{5}\)[/tex], follow these steps:
### Step 1: Understand Division of Fractions
Dividing by a fraction is equivalent to multiplying by its reciprocal. Thus, dividing by [tex]\(-\frac{4}{5}\)[/tex] is the same as multiplying by [tex]\(-\frac{5}{4}\)[/tex].
### Step 2: Write the Multiplication
[tex]\[
\frac{4}{15} \div -\frac{4}{5} = \frac{4}{15} \times -\frac{5}{4}
\][/tex]
### Step 3: Multiply the Numerators and the Denominators
Multiply the numerators together:
[tex]\[
4 \times -5 = -20
\][/tex]
Multiply the denominators together:
[tex]\[
15 \times 4 = 60
\][/tex]
So, we have:
[tex]\[
\frac{4}{15} \times -\frac{5}{4} = -\frac{20}{60}
\][/tex]
### Step 4: Simplify the Fraction
To simplify [tex]\(-\frac{20}{60}\)[/tex], find the greatest common divisor (GCD) of 20 and 60. The GCD of 20 and 60 is 20.
Now, divide both the numerator and the denominator by their GCD:
[tex]\[
-\frac{20 \div 20}{60 \div 20} = -\frac{1}{3}
\][/tex]
### Conclusion
Thus, the simplified result of [tex]\(\frac{4}{15} \div -\frac{4}{5}\)[/tex] in its lowest terms is:
[tex]\[
-\frac{1}{3}
\][/tex]
