### Video Transcript

Simplify the following expression:
negative six and two-ninths minus negative six and four-ninths plus 12 and
eight-ninths.

In this question, we are asked to
simplify an expression involving the sum and difference of rational numbers all
given as mixed numbers. We can start by recalling that
subtracting a negative is the same as adding the positive value. This allows us to rewrite the
expression as negative six and two-ninths plus six and four-ninths plus 12 and
eight-ninths.

We could now convert all of the
numbers into fractions. However, it is easier to directly
add the mixed numbers together. We do this by adding the integer
and fractional parts separately.

First, we evaluate the integer
parts. We have negative six plus six plus
12. Then, we want to evaluate the
fractional parts. It’s very important to include the
signs of each term in this calculation. We get negative two-ninths plus
four-ninths plus eight ninths. We can now evaluate each part
separately. We have that negative six plus six
plus 12 is equal to 12. We can add the fractions together
by recalling that we can add fractions together with the same denominator by adding
their numerators.

In general, we have that 𝑎 over 𝑐
plus 𝑏 over 𝑐 is equal to 𝑎 plus 𝑏 all over 𝑐. This holds true for any number of
fractions with the same denominator. So we get negative two plus four
plus eight all over nine. If we evaluate the numerator, then
we see that our expression is equal to 12 plus 10 over nine.

Since the original expression is
given in terms of mixed numbers, we will give our answer as a mixed number. We can calculate that 10 over nine
is equal to one and one-ninth. So our expression simplifies to
give 13 and one-ninth.