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Simplify the following expression:
[tex]\[ \frac{-4}{5 \div \frac{2}{5}} = \][/tex]

A. [tex]\(1 \frac{7}{20}\)[/tex]

B. [tex]\(-21 \frac{3}{5}\)[/tex]

C. [tex]\(-\frac{20}{27}\)[/tex]

D. [tex]\(-1 \frac{7}{20}\)[/tex]


Sagot :

Let's solve the given fraction step by step.

Given:
[tex]\[ \frac{-4}{5 \frac{2}{5}} \][/tex]

Firstly, let's simplify the denominator [tex]\(5 \frac{2}{5}\)[/tex].

1. Convert the mixed number [tex]\(5 \frac{2}{5}\)[/tex] into an improper fraction:
[tex]\[ 5 \frac{2}{5} = 5 + \frac{2}{5} \][/tex]

2. Rewrite [tex]\(5\)[/tex] as a fraction:
[tex]\[ 5 = \frac{5 \times 5}{5} = \frac{25}{5} \][/tex]

3. Add [tex]\(\frac{25}{5}\)[/tex] and [tex]\(\frac{2}{5}\)[/tex]:
[tex]\[ 5 \frac{2}{5} = \frac{25}{5} + \frac{2}{5} = \frac{27}{5} \][/tex]

So now, the original expression becomes:
[tex]\[ \frac{-4}{\frac{27}{5}} \][/tex]

When dividing by a fraction, we multiply by its reciprocal:
[tex]\[ \frac{-4}{\frac{27}{5}} = -4 \times \frac{5}{27} \][/tex]

Multiply the fractions:
[tex]\[ -4 \times \frac{5}{27} = -\frac{4 \times 5}{27} = -\frac{20}{27} \][/tex]

So, the simplified value of the given expression is:
[tex]\[ -\frac{20}{27} \][/tex]

Therefore, the correct answer from the provided options is:
[tex]\(-\frac{20}{27}\)[/tex].