Question Video: Finding the Reciprocal of a Mixed Number Mathematics • 6th Grade

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.