Video Transcript
What is the reciprocal of one and
one eleventh? Give your answer in simplest
form.
We have this value one and one
eleventh. And we want to know what we could
multiply by one and one eleventh to equal one. Whatever that value is will be the
reciprocal or the multiplicative inverse. If we remember that, for fractions
𝑎 over 𝑏, the multiplicative inverse is 𝑏 over 𝑎. The reciprocal of 𝑎 over 𝑏 is 𝑏
over 𝑎. And that means our goal will be to
write this mixed number one and one eleventh as a fraction in the form 𝑎 over
𝑏. We need to convert this mixed
number to an improper fraction as our first step.
To convert a mixed number to a
fraction, you first multiply the whole number portion by the denominator. For us, that’s one times 11. And then, you add whatever is in
the numerator. We have one in the numerator. And the denominator of the improper
fraction is the same denominator as the mixed number we started with. One times 11 equals 11. And 11 plus one equals 12. And now, we can say twelve
elevenths times what is equal to one. Well, when we have a fraction 𝑎
over 𝑏, its reciprocal is 𝑏 over 𝑎. We flip the numerator and the
denominator. And we get eleven twelfths. 12 over 11 times 11 over 12 is
equal to one. And that means eleven twelfths is
the reciprocal of one and one eleventh. Eleven twelfths is already in its
most simplified form. And so that’s our final answer.
