I'm looking for a source. I heard that if you add 2 coins that are פחות משוה פרוטה nothing happens (they don't equal a פרוטה. But if you add a פחות משוה פרוטה coin with a פרוטה it does add together. Doesn't necessarily have to be a coin I'm just using it as the example. Does anyone know where this is mentioned?

I believe I heard it in regards to Bava Metzia Perek Hazahav 54-55 somewhere but it was a shiur and it's possible it was referenced from somewhere else.

Edit: the main idea here is that less then a prutah cannot be added to less then a prutah.9 + .9 = nothing it terms of money. Please also cite sources

Thanks!

• I'm not sure what coin(s) the first expression means, or if it just means something generic worth less than a prutah, but there were coins called leptons minted by the Hasmoneans and Herodians that were officially valued at half a prutah.
– Gary
Nov 22, 2016 at 0:27

Mishna BM 4, 8:

חֲמִשָּׁה חֻמְשִׁין הֵן . הָאוֹכֵל תְּרוּמָה, וּתְרוּמַת מַעֲשֵׂר, וּתְרוּמַת מַעֲשֵׂר שֶׁל דְּמַאי , וְהַחַלָּה, וְהַבִּכּוּרִים מוֹסִיף חֹמֶשׁ. וְהַפּוֹדֶה נֶטַע רְבָעִי וּמַעֲשֵׂר שֵׁנִי שֶׁלּוֹ, מוֹסִיף חֹמֶשׁ. הַפּוֹדֶה אֶת הֶקְדֵּשׁוֹ, מוֹסִיף חֹמֶשׁ. הַנֶּהֱנֶה בְשָׁוֶה פְרוּטָה מִן הַהֶקְדֵּשׁ, מוֹסִיף חֹמֶשׁ. וְהַגּוֹזֵל אֶת חֲבֵרוֹ שָׁוֶה פְרוּטָה וְנִשְׁבַּע לוֹ, מוֹסִיף חֹמֶשׁ:

[The addition of] a fifth [to the principal] is prescribed in five cases: [I] one who eats terumah, the terumah of the tithe, the terumah of the tithe of demai, hallah, and the first fruits, must add a fifth; [II] he who redeems the fourth year planting and his own second tithe adds a fifth; [III] he who redeems his sacred objects adds a fifth; [IV] he who benefits from hekdesh to the value of a perutah adds a fifth; and [V] he who robs his neighbour of a perutah's worth and swears [falsely] to him [concerning it] must add a fifth.

The following may be an answer. See in the 9th chapter of Baba Kama (Mishna 7):

נָתַן לוֹ אֶת הַקֶּרֶן וְנִשְׁבַּע לוֹ עַל הַחֹמֶשׁ, הֲרֵי זֶה מְשַׁלֵּם חֹמֶשׁ עַל חֹמֶשׁ, עַד שֶׁיִּתְמַעֵט הַקֶּרֶן פָּחוֹת מִשָּׁוֶה פְרוּטָה. וְכֵן בְּפִקָּדוֹן, שֶׁנֶּאֱמַר (ויקרא ה) בְּפִקָּדוֹן אוֹ בִתְשׂוּמֶת יָד אוֹ בְגָזֵל אוֹ עָשַׁק אֶת עֲמִיתוֹ אוֹ מָצָא אֲבֵדָה וְכִחֶשׁ בָּהּ וְנִשְׁבַּע עַל שָׁקֶר, הֲרֵי זֶה מְשַׁלֵּם קֶרֶן וָחֹמֶשׁ וְאָשָׁם: ‏

If he refunded to him the principal and took an oath regarding the fifth, he would have to pay him a fifth on top of the fifth and so on until the principal becomes reduced to less than the value of a perutah.

For the calculation of Chomesh, Bartenura Trumot 6, 1: (thanks to @msh210)

וְהַחֹמֶשׁ הוּא רְבִיעִית מַה שֶּׁאָכַל, כְּגוֹן אִם אָכַל תְּרוּמָה שֶׁשָּׁוָה דִּינָר מְשַׁלֵּם דִּינָר וּרְבִיעַ, שֶׁהֵם בֵּין הַכֹּל חֲמִשָּׁה רְבִיעִיּוֹת דִּינָר, נִמְצָא הַקֶּרֶן עִם חֻמְשׁוֹ חֲמִשָּׁה. וְכָל חֳמָשִׁים הָאֲמוּרִים בַּתּוֹרָה כָּךְ הֵם:

All fifths of the Tora are 1/5(1 + 1/4)

`if you add 2 coins that are פחות משוה פרוטה nothing happens (they don't equal a פרוטה.`

-->

I can imagine a case in which the keren is 0.9 pruta, he sweared, so the sum is:

```0.9 // < pruta + 0.9/4 // < pruta == 1.225```

`But if you add a פחות משוה פרוטה coin with a פרוטה it does add together`

-->

But if the keren is 1 pruta, the chomesh is 0,25, the sum is 1.25 pruta and has an importance.

### Thus less than pruta + less than pruta are not added. But pruta + less than pruta are added. (pseudo paradox)

`I believe I heard it in regards to Bava Metzia Perek Hazahav 54-55 somewhere but it was a shiur and it's possible it was referenced from somewhere else.`

הכי אתמר אמר רב קטינא אם הוזקקו בית דין לשוה פרוטה גומרין אפילו לפחות משוה פרוטה תחילת הדין בעינן פרוטה גמר דין לא בעינן פרוטה:‏

But if stated, it was stated thus: R`Kattina said, if the court met for [a claim of] the equivalent of a perutah, they conclude [the hearing] even for less, [ubecause] at the beginning of a trial a perutah must be involved, but at the end a [claim of a] perutah is unnecessary.

• Not like usual from you, This is a tight answer. please explain how the last source is connected with the question. Nov 23, 2016 at 3:07
• The way I understand your sources is that, if something IN TOTAL is worth less then a pruta then it = to 0 => 0 + less then a pruta = 0. But, it seems (not sposificly from your sources) that if it will be 2 things less-the-a-pruta (.9) TOGETHER it will be looked at as 1.8 and not 0. (The last source to you bring says that if the judgement started with more then a pruta it can end with less then a pruta. meaning less then a pruta in such a case is not = 0, but something that needs to be paid Nov 23, 2016 at 3:18
• When you have a basis of one pruta you can add to the basis a less than pruta. But if you have not a first step with a pruta, e. g. 0.9 keren, even to add 0.24 from the chomesh would not help to begin with the din @hazoriz Nov 23, 2016 at 3:25
• is that not becouse .9 by ITSELF is look on as 0, (unless it is in the end of a din Torah)? Nov 23, 2016 at 3:32
• @hazoriz yes I think that this is the explanation Nov 23, 2016 at 3:34

From my understanding less then a pruta coins do get added together, with exceptions when they looked at as separate (then we look at the first one as equal to 0 when you add the second one it is still less then a pruta to = 0) by law, see answer above,

Maybe the teacher was talking about the gemoro in kedushin 7b were there is a question of adding 2 half prutos

(h)Question #1 (Rava): If one told a woman 'half of you is Mekudeshes to me with half a Perutah, and half of you with half a Perutah', what is the law?
1.Since he said 'half of you', that shows that he was Mekadesh only half of her (and then tried again to be Mekadesh half of her. She is not Mekudeshes);.
2.Or, perhaps he just tallies how much he is being Mekadesh (and in total, he is Mekadesh all of her)!
(i)Question #2: If you will say that he just tallies, if he said 'I am Mekadesh half of you with a Perutah, and half of you with a Perutah', what is the law?
1.Since he gave a Perutah (the amount required for Kidushin) for half, this shows that he is Mekadesh only half each time;.
2.Or, perhaps the entire day he tallies how much he is Mekadesh!
(j)Question #3: If you will say that the entire day he just tallies, if he said 'I am Mekadesh half of you today with a Perutah, and half of you tomorrow with a Perutah', what is the law?
1.Since he said 'tomorrow', this shows that he is Mekadesh half each time;.
2.Or, perhaps he just tells her that the Kidushin should start today and finish tomorrow!
(k)Question: If he said 'I am Mekadesh both halves of you with a Perutah' what is the law?
1.Here, surely he is Mekadesh her at once;.
2.Or, perhaps one cannot be Mekadesh a woman in halves at all!
(l)These questions are not resolved.