PATTERNS IN PLACE – 25%
In many instances the Torah provides an additional requirement when one wishes make amends, which is to add חומשיו (a “fifth”). For example, if one steals, and swears falsely, or if one eats Terumah.
Usually, in our common usage, when we refer to adding a fifth, we mean adding 20% more. Thus, if we usually receive 5 in a package, and the package now offers a fifth more, then 1/5 of the original total (1/5 of 5 = 1) additional item is added, making a total of 6. In simple algebra the formula is (1)X + (1/5)X = (6/5)X. Thus, in the above example, X = 5, thus 5 + (1/5*5) = (6/5)5 = 6. Therefore, the added amount in a “fifth” of the original value (or 20% from the inside of the original amount or מלגב)
However, the Rabbis explain that when the Torah uses the concept of a “fifth”, they mean a different concept, מלבר (from the outside of the principal amount), meaning a “fifth” from the final result. Thus, one takes the original amount, divides it into 4 parts, and then, adds a “fifth” part. Thus, if one has 4 items, and needs to add a “fifth”, one would add an additional one item, making a total of 5.
Thus, the added “fifth” is actually one-fifth of the final total (and not of the original amount). In simple algebra the formula would be (1)X + (1/4)X = (5/4)X. Thus, in the above example, X =4, thus 4 + (1/4*4) = 5/4(4) = 5. Therefore, the added amount is a “fifth” of the result (or 25% of the original amount).
Example: Original amount is 100
Must pay an additional “fifth”
100+25=125 25 is 1/5 of 125 or 25 = 25% of 100
Please complete the following based on above example of a “fifth”
I. If original amount is 160, adding a fifth:
Amount of total to be paid = __________
Amount of the additional fifth =
II. If original amount is 40, adding a fifth:
Amount of total to be paid =
Amount of the additional fifth =
