### Video Transcript

Find the value of the product of
negative one and one-third and negative 0.4 in its simplest fraction form.

In this question, we are asked to
find the product of two rational numbers given in different forms. We need to give our answer as a
fraction in its simplest form.

To answer this question, we can
note that we can multiply rational numbers together in many ways. However, it is usually easiest to
multiply rational numbers written as fractions. Therefore, we will start by
converting both rational numbers into fractions.

First, we can convert the mixed
number negative one and one-third into the fraction negative four-thirds. Next, we can recall that 0.2 is
one-fifth. So negative 0.4 will be negative
two times one-fifth, which is negative two-fifths. We can now use these fractions to
rewrite the product of negative one and one-third and negative 0.4 as negative
four-thirds multiplied by negative two-fifths. We can now multiply the two
fractions together by recalling that the product of two negatives is a positive and
that we can multiply fractions by multiplying their numerators and denominators
separately. In general, we have that 𝑎 over 𝑏
times 𝑐 over 𝑑 is equal to 𝑎𝑐 over 𝑏𝑑.

Therefore, since a negative times a
negative is a positive, we can multiply the numerators and denominators separately
to obtain four times two over three times five. We can then evaluate the products
in the numerator and denominator to get eight over 15. We note that the greatest common
factor of these values is one. So we cannot simplify any
further. Hence, we leave our answer as eight
over 15.