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Miscellaneous Elementary Junior High Sum Of Positive Integral Divisors High School Manipulating Polygonal Numbers
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Percents:A. There are many ways of working with percents. Some of the ways are basic and can be solved just by knowing the information here. B. Most percents are in the form of small word problems, so just knowing what the words mean can be a HUGE help: Of: Of means multiply. Is: Is means equals. What: What is the value you are looking for (i.e. the variable). From: From means subtract. Less Than: Less than means subtract More Than: More than means addition As: As means a ratio. Into: Into means divide. C. Using the words above, we can set up an equation that should be simple enough to solve. Ex [1] 20% of 54 is 9% of _________. a. Substituting we get - (.20 x 54) = .09 x n b. Simplifying we get - (20 x 54)/9 = n. (Notice we can ignore the decimal places since there are the same number of decimal places in the denominator as in the numerator.) c. (20 x 54) / 9 = 20 x 6 = 120. d. The answer is 120. Ex [2] If x% of 140 is 16.8, then x = __________. a. Substituting we get - 140x = 16.8. (Ignore the percent for the time being. Just know that we will have to change the decimal to a percent in the end.) b. Solving we get x = 16.8/140 or x = 168/1400 which simplifies to 24/200 or 12/100 which is .12. Changing this to a percent we get 12. (Notice that I first divided by 7, then divided by 2. Also, there is no need, since we are dealing with percents, to simplify it to its most basic form.) c. The answer is 12. Ex [3] 18% of 6 2/3 = __________. a. Substituting we get - .18 x 20/3. b. Notice you need to change the mixed number to an improper fraction. c. Simplifying we get - .06 x 20 or 1.2. d. The answer is 1.2. Ex [4] 5 more than 12% of 15 is __________. a. Substituting from above we get 5 + .12 x 15 = ____. b. Solving we get 5 + 1.8 = 6.8. c. The answer is 6.8. D. The following example is how to work percents in a different type of form. This problem is a little harder than just following the definitions above. Ex [5] 14 is what percent more than 10? __________. a. In this problem we have to find out what times 10 and added back to 10 = 14. In other words, 10n + 10 = 14. b. Solving 10n + 10 = 14 we get 10n = 4 or n = .4 or 40%. c. The answer is 40.
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