What is the reciprocal of six and a half?
Before we can find the reciprocal, we need to turn six and a half into a top heavy or improper fraction. If we consider the six and a half rectangles that are shaded, we have 13 halves.
There are 12 halves in six whole ones. And we have the extra half. Therefore, six and a half is equal to 13 over two or 13 halves.
A quicker way of doing this without drawing the diagrams is to multiply the whole number, in this case six, by the denominator two and add the numerator one. Six multiplied by two equals 12. 12 plus one equals 13.
Therefore, our new numerator will be 13. We can use this method to turn any mixed fraction into a top heavy or improper fraction. The reciprocal of any number is found by dividing one by the number.
However, when dealing with a fraction, it is much easier just to swap the numerator and denominator. The reciprocal of any fraction is just a fraction upside down. This means that the reciprocal of 13 over two is two over 13.
We can therefore say that the reciprocal of six and a half is also two-13ths or two over 13.