Vayigash- Percentages

"And it will be at the ingatherings that you will give a fifth to Pharaoh; the [other] four parts shall be yours, as seed for the field, and for feeding yourselves and for those who are in your household, and to feed your young ones." ~Bereishit 47;24

Back in Parshat Vayishlach, we looked at how to create ratios and fractions with a set of numbers that represent portions of a whole group. In this week's parsha, we actually have fractions given to us straight out. Working as an agent of Pharoah, throughout the course of the years of famine, Joseph purchased land from all of the landowners across Egypt in exchange for giving them food from his food storage. We are then told that the Priests were given food, and the landowners- who now all lived on land belonging to Pharoah and Joseph- were given seeds to plant for crops. They were instructed to work the fields, grow crops from the seeds that they received, and when they harvested their crops, 1/5 would be given to Pharoah, and the other 4/5 was to be kept for feeding themselves, their families, and their servants.

Percentage:
A rate or proportion per one hundred (dictionary.com)

While fractions are great for comparing parts of a group, there are times when you want to be able to compare across different groups, which can become messy and difficult if you're trying to compare fractions with different denominators. One way to create a standardization for comparison of information is to use percentages. Percentages readjust all the different groups so that for each group, the whole amount is represented by 100. Any portion of the group is then a percentage from 0-100%. All the total percentages within a group, when added together, should equal 100%.

How do we convert our information from fractions to percentages?
There are two basic ways to convert a fraction into a percentage.
1) Just as we could simplify fractions by dividing both numerator and denominator by the same divisor, we can make equivalent larger fractions by multiplying both numerator and denominator by the same factor. Since a percentage is a fraction out of 100 (per cent), then if you can easily identify how to multiply or divide your original denominator to make it 100, then you do the same to your numerator to find your percent.
Two basic examples:
--To find the percentage of 1/2, we know that 2x50=100, and then we can calculate 1x50=50. So, the percentage for 1/2 is 50/100 or 50%.
--To find the percentage of 350/500, we know that 500÷5=100, and then we can calculate 350÷5=70, so the percentage for 350/500 is 70/100 or 70%.
2) Some numbers just don't calculate nicely using the first method- try 1/8 or 1/3, for example. For these cases, you can divide the numerator divided by the denominator (eg. 1÷8 or 1÷3). This calculation will result in a decimal number. (1/8=.125 and 1/3=.33333...). These numbers multiplied times 100 (so the decimal moves 2 places to the right) are your percentages (1/8=12.5% and 1/3=33.3% -rounded off).
Intuitive connection- the first two decimal places, from left to right are tenths and hundredths; the fractions over 100 are read as "fifty hundredths" or "seventy hundredths"; when we multiply the decimal times 100, we are just changing it into the number that we would use in the fraction over 100

Using our method for calculating percentages, we can now look back to see what percentage of crops Joseph was collecting as taxes on Pharoah's behalf, and what percentage the previous landowners were allowed to keep for themselves and their families.

We are told that 1/5 was to be for Pharoah and the other 4/5 would be for the families. We lucked out here, since fifths are a fairly easy denominator to work with- 5x20=100. So, the percentages were:
Taxes for Pharoah: 1x20=20; 20/100 or 20%
Remaining crops for families: 4x20=80; 80/100 or 80%

To check our work, let's test our 100%. 20% taxes for Pharoah + 80% remaining for families should equal 100%. 20+80=100, so our math works and our calculated numbers are correct.