# Finding Reciprocals

Here, you will practice finding reciprocals (multiplicative inverses) of whole numbers and fractions.

For $\,x\ne 0\,,$ the reciprocal of $\,x\,$ is $\displaystyle\,\frac{1}{x}\,.$

In particular, the reciprocal of $\displaystyle\,\,\frac{a}{b}\,\,$ is $\displaystyle\,\,\frac{b}{a}\,\,.$

The number $\,0\,$ does not have a reciprocal, For all other numbers, a number multiplied by its reciprocal equals $\,1\,$:   $x\cdot \frac1x = 1$

## Examples

The reciprocal of $\,\,5\,\,$ is $\displaystyle\,\,\frac{1}{5}\,\,.$
The reciprocal of $\displaystyle\,\,\frac{2}{3}\,\,$ is $\displaystyle\,\,\frac{3}{2}\,\,.$
The reciprocal of $\quad-6\quad$ is $\quad\displaystyle-\frac{1}{6}\quad$.
The reciprocal of $\displaystyle\quad-\frac{5}{7}\quad$ is $\displaystyle\quad-\frac{7}{5}\quad$.
The reciprocal of $\,0\,$ is not defined. Zero is the only real number which does not have a reciprocal.

## Practice

Type in   nd   (uppercase or lowercase) if the reciprocal is not defined. Type fractions using a diagonal slash:   for example,  1/3 .
{"ft_lang_label":"__label__en","ft_lang_prob":0.82229704,"math_prob":0.9999989,"size":637,"snap":"2023-40-2023-50","text_gpt3_token_len":183,"char_repetition_ratio":0.15481833,"word_repetition_ratio":0.0,"special_character_ratio":0.29356357,"punctuation_ratio":0.24806201,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99964404,"pos_list":[0,1,2],"im_url_duplicate_count":[null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-09-29T23:58:33Z\",\"WARC-Record-ID\":\"<urn:uuid:a815cd22-95bb-42bc-9bd0-368017e0a077>\",\"Content-Length\":\"24504\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:f6ce5154-222b-4ff1-8fc0-0094791a5e44>\",\"WARC-Concurrent-To\":\"<urn:uuid:b652d71a-4aa4-4c42-876d-c905cf6e5512>\",\"WARC-IP-Address\":\"74.208.236.130\",\"WARC-Target-URI\":\"https://onemathematicalcat.org/algebra_book/online_problems/reciprocals.htm\",\"WARC-Payload-Digest\":\"sha1:D5PXJ6ZN4A5YBFU3SOFNBRHHQ3TNA3IS\",\"WARC-Block-Digest\":\"sha1:7CBER5ZYEIUHQBGOZWMED2ZP4ZYKFQF5\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-40/CC-MAIN-2023-40_segments_1695233510529.8_warc_CC-MAIN-20230929222230-20230930012230-00739.warc.gz\"}"}