Parsha Math 25%

MATH IN THE PARSHA PATTERNS IN PLACE – 25%

In many instances the Torah provides an additional requirement when one wishes make amends, which is to add ‫( חומשיו‬a “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% 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, ‫( מלבר‬from the outside), 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. Original amount is 160 Amount of total to be paid = Amount of the additional fifth = II. Original amount is 40 Amount of total to be paid = Amount of the additional fifth =

[email protected]

__________

MATH IN THE PARSHA NOTES FOR TEACHER OR PARENT Age group – 12 years and up Objective of this lesson: Appreciate math in the Parsha Introduction to concepts within Judaism of 25% and adding a “fifth”

ANSWERS

Original amount is 160 Amount of total to be paid = Amount of additional fifth =

200 40

Original amount is 40 Amount of total to be paid = Amount of additional fifth =

50 10

[email protected]