### Video Transcript

Evaluate one-third minus five
twelfths plus three-eighths minus one-sixth, 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 all given as fractions. We need to give our answer as a
fraction in its simplest form. To answer this question, we can
begin by recalling that we can add and subtract fractions by first rewriting them to
have the same denominator. In general, we have that 𝑎 over 𝑐
plus 𝑏 over 𝑐 is equal to 𝑎 plus 𝑏 over 𝑐. And 𝑎 over 𝑐 minus 𝑏 over 𝑐 is
equal to 𝑎 minus 𝑏 over 𝑐. In other words, we can add and
subtract the numerators of fractions when they have the same denominator.

This result holds for the sum and
difference of any number of fractions, provided that they all have the same
denominator. Therefore, we can evaluate the
expression by first rewriting all four fractions to have the same denominator. To rewrite each of the fractions to
have the same denominator, we need to find the lowest common multiple of the four
denominators. We can start by noting that 12 is
the lowest common multiple of three and 12. We can then consider the lowest
common multiple of 12 and eight. We see that this is 24.

Finally, we can note that 24 is a
multiple of six, so the lowest common multiple of the four denominators is 24. We want to rewrite each fraction to
have a denominator of 24. To do this, we need to multiply the
numerator and denominator of each fraction by the same value. First, we multiply the numerator
and denominator of the first fraction by eight. Next, we multiply the numerator and
denominator of the second fraction by two. Then, we multiply the numerator and
denominator of the third fraction by three. Finally, we multiply the numerator
and denominator of the fourth fraction by four to obtain the following
expression.

We can now evaluate each of the
products. The denominators should all
evaluate to give 24. We have eight over 24 minus 10 over
24 plus nine over 24 minus four over 24. Now that the denominators are all
the same, we can add and subtract the numerators of the fractions to get eight minus
10 plus nine minus four all over 24. Evaluating the numerator then gives
us three over 24. Remember, we need to give our
answer in its simplest form. We can note that the numerator and
denominator are both divisible by three. Canceling this shared factor of
three gives us one-eighth, which is our final answer.