03.22.2018: One Chapter of Math

Today's soundtrack is Monotheist: Scourge.

I'm now on Chapter 12 of Basic Math & Pre-Algebra For Dummies, "Playing With Percents."

"Percent" means, in practice, "out of 100" (p. 171). The symbol "%" means "percent." Percentage, fractions, and decimals are all ways of talking about parts of a whole.

Any percentage under 100 is less than one whole. Any percentage over 100 is more than one whole.

To convert a percent to a decimal, take away the percent symbol and move the decimal point two places to the left, adding any leading 0s as necessary. 42% = 0.42. Inversely, converting a decimal to a percent simply requires moving the decimal two places to the right and adding a percent symbol. 0.53 = 53%.

To convert a percent to a fraction, remove the percent symbol, then use the percent number as the numerator and the number 100 as the denominator. 64% = 64/100. Reduce as necessary. If there is a decimal in the percentage, move the decimal to the right and add as many 0s to the denominator as you moved the decimal places to the right. 75.75% = 7,575/10,000.

To convert a fraction into a percent, first convert the faction to a decimal by dividing the numerator by the denominator, then move the decimal point two places to the right and add a percent symbol.

To simplify complicated problems, remember that a percent can also be read as a decimal, and when we are finding the percentage of something, we are multiplying the decimal times the number (e.g. to find 50% of 200, we are multiplying 200 by 0.5). By this logic, we can flip around percentage problems to make them easier to read: finding 90% of 50 is hard, but finding 50% of 90 is 45. It is easy to use decimal multiplication as well: 50x0.90 is easy!

There are three main types of percent problems: We try to find the ending number, the percentage, or the starting number. Examples given for each are listed in the book as follows: "50% of 2 is what? What percent of 2 is 1? 50% of what is 1?" (p. 179).

To solve percent problems where a number is missing, we convert the percentage to a decimal, change the word "of" to "x," change "what" to "n," change the word "percent" to "x 0.01," and change "is" to "="; thus, "25% of what is 100?" becomes "0.25 x n = 100." Once we have the rephrased equation, we divide the known numbers on both sides of the equals sign by the decimal: "0.25 x n / 0.25 = 100 / 0.25"; therefore in this equation n = 400. For another example, if we were to look at the question "What percent of 400 is 100?" we would rephrase it as "n x 0.01 x 400 = 100," then we would perform the known part of the equation (0.01 x 400), giving us "n x 4 = 100," then we would solve for "n": "n x 4 / 4 = 100 / 4," therefore, in this equation, n = 25.