### Video Transcript

Mia is designing a flag. She colors four-sixths of the flag
yellow and two-ninths of the flag blue. She leaves the rest of the flag
white. What fraction of the flag does Mia
color altogether?

Let’s quickly sketch what is
happening. Mia is designing a flag. She colors four-sixths yellow and
two-ninths blue. We need to find the fraction of the
flag that is colored altogether. This means we need to add the
fractions.

We know that to add two fractions,
we count the number of equal parts. However, in this case, we do not
have equal parts. Fractions with equal parts have the
same denominator, but these fractions have different denominators: six and nine. So we need to find a common
denominator, which is a common multiple of six and nine.

The product of six and nine in this
case is certainly a multiple of six and a multiple of nine. But this method does not always
lead to the least common denominator. 54 is quite a large number. And because six and nine both have
three as a factor, it is likely not the least common denominator.

To find the least common
denominator, we will begin by listing the multiples of both six and nine then select
the smallest multiple they have in common. The first six multiples of six are
six, 12, 18, 24, 30, and 36. The smallest multiple of six that
is also a multiple of nine will be our least common denominator. The first four multiples of nine
are nine, 18, 27, and 36. Which multiples do they have in
common? 18 and 36. Since we want the least common
denominator, we select 18.

Now we are ready to create
equivalent fractions with our new common denominator. To find the fraction equivalent to
four-sixths, we must think of the number we multiply by six to get 18. We know that six multiplied by
three equals 18. So we multiply the numerator by
three as well. The result is the equivalent
fraction twelve eighteenths. Then we do the same for
two-ninths. But in this case, we multiply the
denominator nine by two to get 18. So we also multiply the numerator
by two to find our equivalent fraction. And we find that two-ninths equals
four-eighteenths.

Now that we have rewritten our
fractions with a common denominator, we can add the parts of equal size
together. Twelve eighteenths plus
four-eighteenths equals sixteen eighteenths altogether. This means four-sixths plus
two-ninths is equivalent to twelve eighteenths plus four-eighteenths, which equals
sixteen eighteenths, which is the fraction of the flag Mia colored.

We should check whether our answer
can be simplified. In this case, it can, as the
numerator and denominator are both divisible by two. So the simplified answer is
eight-ninths.