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What is the value of [tex]\frac{2}{5} \div \frac{-1}{10}[/tex]?

Sagot :

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].