the reciprocal of 4 plus the reciprocal of 5 is the reciprocal of what number?

Question

anonymous · Answer

9/20

killa · Answer

can you please show me how you came up with that answer step by step?

anonymous · Answer

Don't you have a math book or something to teach you how to add fractions? 1/4+1/5, their lowest common denominator is 20, so you multiple 1/4 by 5/5 and 1/5 by 4/4 to get 5/20+4/20

anonymous · Answer

The answer should actually be 20/9.
The way the question is worded, you want the reciprocal of 9/20.

In general, these word problems require a bit of set up.

Let x be the number you’re looking for.
Then the reciprocal of the number is 1/x.

The reciprocal of 4 is 1/4 and the reciprocal of 5 is 1/5.

So the problem says that 1/4 + 1/5 = 1/x.
Adding the fractions as flyingpigg showed above,
we see that 9/20 = 1/x, which is the reciprocal of x.
But if 9/20 is the reciprocal of x, then x itself must be 20/9.