Video: Applying the Multiplicative Inverse Property after Adding Two Fractions with Unlike Denominators

Find the multiplicative inverse of (8/3 + 9/2).

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Video Transcript

Find the multiplicative inverse of eight over three plus nine over two.

Weโ€™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 doesnโ€™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 ๐‘Ž over ๐‘, its multiplicative inverse is ๐‘ over ๐‘Ž. 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.

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