### Video Transcript

Evaluate two-fifths minus
one-eighth plus 0.4 minus 0.025, giving the answer as a fraction in its simplest
form.

In this question, we are asked to
evaluate the sum and difference of four rational numbers, giving our answer as a
fraction in its simplest form.

To answer this question, we can
first recall that we can evaluate the addition and subtraction in any order. So, we can start by evaluating 0.4
minus 0.025. Evaluating this difference gives us
two-fifths minus one-eighth plus 0.375. To add and subtract the remaining
rational numbers, we will rewrite all of the numbers to be fractions. One way of doing this is to note
that 0.375 is equal to 375 over 1,000. However, this is not the simplest
form of this fraction.

By factoring or otherwise, we can
note that 375 is equal to 125 times three and 1,000 is equal to 125 times eight. So they share a factor of 125. Canceling the shared factor of 125
in the numerator and denominator leaves us with three-eighths. So, we have two-fifths minus
one-eighth plus three-eighths. To add or subtract fractions, we
need their denominators to be equal. We can see in our expression that
one-eighth and three-eighths have the same denominator. Therefore, we can add these
fractions by adding their numerators.

We note that subtracting one-eighth
is the same as adding negative one over eight. So we have two-fifths plus negative
one plus three over eight. We can then evaluate this sum to
obtain two-fifths plus two over eight. We can then simplify two-eighths by
canceling the shared factor of two in the numerator and denominator to obtain
one-quarter.

We now need to evaluate two-fifths
plus one-quarter. To add these fractions together, we
need them to have the same denominator. To rewrite the fractions so that
they have the same denominator, we first find that the lowest common multiple of
five and four is 20. So, we want to rewrite both
fractions to have a denominator of 20. We can rewrite the fractions to
have the same denominator by multiplying the numerator and denominator of the first
fraction by four and the numerator and denominator of the second fraction by
five. We can then evaluate each of the
products to see that two-fifths is equal to eight over 20 and one-quarter is equal
to five over 20.

Now that the fractions have the
same denominator, we can add them together by adding their numerators. We have eight plus five over 20 is
equal to 13 over 20. Finally, we see that 13 and 20
share no nontrivial common factors. So we cannot simplify any
further. Hence, our answer is 13 over
20.