### Video Transcript

Calculate three and two-thirds
multiplied by one and two-thirds.

In order to answer this question,
we will begin by converting both of our mixed numbers into improper fractions. We know that one whole one is equal
to three-thirds. This means that three whole ones is
equal to nine-thirds. From the diagram, we can see that
three and two-thirds can be written as the improper fraction eleven-thirds. A quick way of calculating the 11
is to multiply the whole number by the denominator and then adding the
numerator. Three multiplied by three is nine,
and adding two gives us 11. In the same way, we can see that
the mixed number one and two-thirds is equal to the improper fraction
five-thirds. We need to multiply eleven-thirds
by five-thirds.

In order to multiply two fractions,
we simply multiply the numerators and separately the denominators. 11 multiplied by five is 55, and
three multiplied by three is nine. Eleven-thirds multiplied by
five-thirds is equal to fifty-five ninths or 55 over nine. As the line in a fraction means
divide, we can now convert this back to a mixed number by dividing 55 by nine. Nine multiplied by six is equal to
54. Therefore, 55 divided by nine is
equal to six remainder one. The improper fraction fifty-five
ninths is the same as the mixed number six and one-ninth. Therefore, three and two-thirds
multiplied by one and two-thirds is also equal to six and one-ninth.