What is the reciprocal of nine elevenths divided by five-halves? Give your answer in its simplest form.
The reciprocal of any number is one divided by the number. Before we can work this out in this question, we need to divide nine elevenths by five-halves or nine over 11 divided by five over two. When we’re dividing two fractions, we need to follow three simple steps.
Firstly, we need to turn the division sign into a multiplication sign. Secondly, we need to flip the second fraction or turn it upside down. The numerator becomes the denominator and vice versa. In this case, five over two becomes two over five or two-fifths. Finally, we need to multiply the numerators and multiply the denominators.
In this case, we need to multiply nine by two and 11 by five. Nine multiplied by two is equal to 18. And 11 multiplied by five equals 55. Therefore, nine over 11 multiplied by two over five equals 18 over 55. This also means that nine over 11 divided by five over two is equal to 18 over 55.
We now need to work out the reciprocal of this fraction. As mentioned earlier, to calculate the reciprocal, we divide one by the number. In this case, we need to divide one by eighteen fifty-fifths or 18 over 55. Following the same steps as the left-hand side, we can rewrite this as one multiplied by 55 over 18. Multiplying any number by one gives the number itself. In this case, one multiplied by 55 over 18 is equal to 55 over 18 or fifty-five eighteenths.
The reciprocal of nine elevenths divided by five-halves is fifty-five eighteenths or 55 over 18. We also notice here that, to find the reciprocal of a fraction, you just turn it upside down. You swap the numerator and the denominator.
The reciprocal of 18 over 55 is 55 over 18.