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Who knows a fifth?

?חמישית - מי יודע

In the spirit of the song "Echad - mi yodeya", please post interesting and significant Jewish facts about the number 0.2.

Lazy gematria may be worthy of discission, but perhaps not of a full-fledged answer. [This may not apply in the conventional sense, but, e.g., saying x is a quarter of y is just not keeping in the spirit. However, there maybe be examples that the Arizal, Baal Haturim, etc., mention and they are perfect for comments.]

Check out for the previous three hundred fifty entries in this ongoing series.

Please include sources for your information wherever possible, as with all other answers on this site.

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10 Answers 10

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Rashi on "וַחֲמֻשִׁ֛ים עָל֥וּ בְנֵי־יִשְׂרָאֵ֖ל מֵאֶ֥רֶץ מִצְרָֽיִם" famously quotes the Mechilta in saying that only one-fifth of Bnei Yisrael left Egypt.

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The sinner shall make full restitution for his guilt, and add to it a fifth part to it and give it to the claimant in respect to whom he had been guilty. [Numbers 5:7]

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One-fifth of one's salary is the ideal amount one should give to maaser as the Shulchan Aruch YD (249:1) writes

שיעור נתינתה אם ידו משגת יתן כפי צורך העניים ואם אין ידו משגת כל כך יתן עד חומש נכסיו - The amount of charity one should give is as follows: if one can but afford, let him give as much as is needed. Under ordinary circumstances, a fifth of one's property is most laudable.

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Famous mishna in Bava Metziah 55b:

MISHNAH: In this mishnah, as in the previous one, the tanna enumerates several halakhot that share a common element. There are five halakhic situations where one-fifth is added to the value of the principal, and these are they: (1) A non-priest who eats either terumah, or terumah of the tithe, which the Levite separates from the first tithe and gives to a priest, or terumah of the tithe of demai, or cḥalla, or first fruits; in each of these cases, he adds one-fifth when paying restitution to the priest who owned the produce. (2) And one who redeems his own fruit of a fourth-year sapling or second-tithe produce adds one-fifth. (3) One who redeems his own consecrated property adds one-fifth. (4) One who derives benefit worth one peruta from consecrated property adds one-fifth. (5) And one who robs the value of one peruta from another and takes a false oath in response to his claim adds one-fifth when paying restitution.

(Sefaria translation and notation)

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In Bereishis 47:24:

וְהָיָה֙ בַּתְּבוּאֹ֔ת וּנְתַתֶּ֥ם חֲמִישִׁ֖ית לְפַרְעֹ֑ה וְאַרְבַּ֣ע הַיָּדֹ֡ת יִהְיֶ֣ה לָכֶם֩ לְזֶ֨רַע הַשָּׂדֶ֧ה וּֽלְאָכְלְכֶ֛ם וְלַאֲשֶׁ֥ר בְּבָתֵּיכֶ֖ם וְלֶאֱכֹ֥ל לְטַפְּכֶֽם׃

And when harvest comes, you shall give one-fifth to Pharaoh, and four-fifths shall be yours as seed for the fields and as food for you and those in your households, and as nourishment for your children.”

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Kesubos 17a:

כי סמכו רבנן לרבי אמי ולרבי אסי שרו להו הכי כל מן דין וכל מן דין סמוכו לנא לא תסמכו לנא לא מן סרמיסין ולא מן סרמיטין ואמרי לה לא מן חמיסין ולא מן טורמיסין

When the Sages ordained Rabbi Ami and Rabbi Asi, this is what they sang to them: Anyone from people of this kind and anyone from people of that kind, ordain them for us. Do not ordain for us others, neither from those who corrupt [sarmisin] halakhot, nor from those who are worthless [sarmitin]. And some say: Not from those who provide only one-fifth [ḥamisin] of the reason for a halakha, and not from those whose knowledge is incomplete [turmisin]. (Sefaria translation & annotation)

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Bottom of Kesubos 66b at the end of the Mishnah which discusses pledges over the amount brought for a dowry, the Mishnah concludes:

מה שחתן פוסק הוא פוסק פחות חומש

What the son-in-law pledges according to the amount of the dowry that the bride brings, he pledges one-fifth less in the marriage contract, which is the actual value of the property.

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Vayikra 27:15

וְאִ֨ם־הַמַּקְדִּ֔ישׁ יִגְאַ֖ל אֶת־בֵּית֑וֹ וְ֠יָסַף חֲמִישִׁ֧ית כֶּֽסֶף־עֶרְכְּךָ֛ עָלָ֖יו וְהָ֥יָה לֽוֹ׃

and if he who has consecrated his house wishes to redeem it, he must add one-fifth to the sum at which it was assessed, and it shall be his.

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One who eats terumah unwittingly must repay its value plus a fifth, whether he eats it or drinks it, or anoints himself with it, or whether the terumah is clean or unclean. [If he eats the added fifth] he must pay its fifth, and a fifth of that fifth. He may not repay with terumah, but rather with tithed hullin, which becomes terumah. And whatever may be repaid in its place also becomes terumah and if the priest wishes to forego [the fine], he cannot do so. [Terumah 6:1]

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Pesachim 109a:

אָמַר רַב חִסְדָּא: רְבִיעִית שֶׁל תּוֹרָה אֶצְבָּעַיִם עַל אֶצְבָּעַיִם בְּרוּם אֶצְבָּעַיִם וַחֲצִי אֶצְבַּע וְחוֹמֶשׁ אֶצְבַּע.

Rav Ḥisda said: The quarter-log measurement of the Torah is two fingerbreadths by two fingerbreadths in volume, by the height of two fingerbreadths and one half fingerbreadth and one-fifth of a fingerbreadth.

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  • Why the downvote?
    – Dov
    Feb 8 at 21:40
  • 2
    I didn't downvote, but maybe it's because this isn't really a fact about 1/5 per se, but about 7/10 (or 2 7/10). After all, the same fraction could also have been expressed as 2/3 + 1/30, for example.
    – Meir
    Feb 9 at 0:00
  • Also not a downvoter, but this seems to be a cubic measure of 2x2x2.7 (or 10.8 cubic fingerbreadths). How accurate were finger measurements that they could be measured to 10%? Feb 9 at 15:36

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