Question

How do you find the reciprocal of 3 3/4?

Answer 1

See a solution process below:

Explanation:

First, we need to convert the mixed number into an improper fraction:

`3 3/4 = 3 + 3/4 = (4/4 xx 3) + 3/4 = 12/4 + 3/4 = (12 + 3)/4 = 15/4`

The reciprocal of a number when multiplied by itself is equal to `1`

So we can write and solve for `r`:

`15/4 xx r = 1`

`(15/4 xx r)/color(red)(15/4) = 1/color(red)(15/4)`

`(color(red)(cancel(color(black)(15/4))) xx r)/cancel(color(red)(15/4)) = 4/15`

`r = 4/15`

`15/4 xx 4/15 = (15 xx 4)/(4 xx 15) = 60/60 = 1`

Any easy way to remember this is to just flip the fraction to get the reciprocal:

`color(red)(15)/color(blue)(4) -> color(blue)(4)/color(red)(15)`

If the number is an integer and not a fraction, say `7`, we can write `7` as `7/1` to turn it into a fraction and apply the same rule:

`color(red)(7)/color(blue)(1) -> color(blue)(1)/color(red)(7)`

Answer 2

`4/15`

Explanation:

`"first express "3 3/4" as an improper fraction"`

`3 3/4=(4xx3+3)/4=15/4`

`"the reciprocal of any number "n" is "1/n`

`"the reciprocal of "15/4" is "1/(15/4)=4/15`