To determine the value of [tex]\(\frac{2}{5} \div \frac{-1}{10}\)[/tex], we follow the steps used for division of fractions, which involves multiplying by the reciprocal.
1. Identify the fractions:
The fractions given are [tex]\(\frac{2}{5}\)[/tex] and [tex]\(\frac{-1}{10}\)[/tex].
2. Find the reciprocal of the second fraction:
The reciprocal of [tex]\(\frac{-1}{10}\)[/tex] is [tex]\(\frac{10}{-1}\)[/tex].
3. Set up the multiplication:
Dividing by a fraction is the same as multiplying by its reciprocal.
[tex]\[
\frac{2}{5} \div \frac{-1}{10} = \frac{2}{5} \times \frac{10}{-1}
\][/tex]
4. Multiply the numerators:
The numerators of the fractions are 2 and 10. Multiply them together:
[tex]\[
2 \times 10 = 20
\][/tex]
5. Multiply the denominators:
The denominators of the fractions are 5 and -1. Multiply them together:
[tex]\[
5 \times -1 = -5
\][/tex]
6. Form the new fraction and simplify:
The new fraction is:
[tex]\[
\frac{20}{-5}
\][/tex]
Simplifying this fraction, we get:
[tex]\[
\frac{20}{-5} = -4
\][/tex]
Therefore, the value of [tex]\(\frac{2}{5} \div \frac{-1}{10}\)[/tex] is [tex]\(-4\)[/tex].
