Reciprocal problem

[PJones]

This question says reciprocal and I don't know what this means.

Find 2 consecutive integers whose reciprocals add up to 9/20

[DaveD]

This question says reciprocal and I don't know what this means.

Find 2 consecutive integers whose reciprocals add up to 9/20

Reciprocal means to divide into 1
so the reciprocal of 3 is 1/3 etc.

[Mr Moo]

and what do you get if you find the reciprocal of a reciprocal? the original number...

When answering questions involving reciprocals, i imagine there are two groups of numbers:

1) those that are more than zero but less than one
2) those that are more than one
(note, whilst imagining this it is irrelivant whether a number is positive or negative, ie -100 would be in group 2)

In my mind, every number can be expressed equally in both groups. It's like there's a number line with a mirror placed bang in the middle at number 1... as the numbers approach infinity to the right of the mirror, their reflections approach zero to the left of the mirror. "finding the reciprocal" simply means switching from one group to the other.

Another way of thinking about it is that every number is actually a fraction, even the ones that are presented as integers! (ie 3 becomes 3/1 and 5 becomes 5/1 etc.) the difference now between groups 1 and 2 is that group two are top heavy fractions (which is why they are more than one). To find the reciprocal of a number, just flip the nominator and denominator (ie 3 becomes 1/3 and 365/52 becomes 52/365 etc.)

but this is just what i find helpful. Everyones mind works differently. find your own analogies...

- Mr Moo

[PJones]

Wow, thats some answer Mr. Moo