Find the multiplicative inverse of
eight over three plus nine over two.
We’re given this expression that is
the sum of two fractions. And we want to find the
multiplicative inverse. We first need to take this
expression and find its sum. To do that, we need to find a
common denominator for two and three. If we use the denominator of six,
three times two equals six. But if we multiply the denominator
by two, we need to multiply the numerator by two. Eight-thirds is equal to sixteen
sixths. We can follow the same process for
nine-halves. Two times three equals six. And nine times three equals 27.
When two fractions have a common
denominator, you can add them by adding their numerators. 16 plus 27 equals 43. And the denominator doesn’t
change. Eight-thirds plus nine-halves is
equal to forty-three sixths. And this is what we need to find
the multiplicative inverse of. We know that, for the fraction 𝑎
over 𝑏, its multiplicative inverse is 𝑏 over 𝑎. If we flip the numerator and
denominator, we get six over 43. And 43 times six over 43 times six
is the same thing as one. Our final answer for the inverse of
eight-thirds plus nine-halves is six over 43.