"50% out of 100%" is not the right way to word it. Let me explain....
100% = 100÷100 = 1.00, this is the same as moving the decimal place over by two digits.
- Just saying "of" by itself in a word problem will multiply (×) those two things together, whether they are percent numbers or value numbers (not percents)
- Saying "out of" in a word problem will divide (÷) the two things, but we can only use it for value numbers (not percents); we cannot use it with percent numbers
So to emphasize what another tutor told you the last time you asked this question:
50% of 100% = (50÷100) × (100÷100) = 0.50 × 1.00 = 0.50 = 50%
75% of 100% = (75÷100) × (100÷100) = 0.75 × 1.00 = 0.75 = 75%
65% of 100% = (65÷100) × (100÷100) = 0.65 × 1.00 = 0.65 = 65%
The number pattern you're given should not be using "out of" or "of."
What you're doing is taking the Average between the two percents. For example, say you got a 50% on your first test and a 100% on your second test, your current Major Grade in the class would have to be the Average between the two. The formula looks like this
Let me apply it here:
(50% + 100%)/2 = (0.50 + 1.00)/2 = (1.50)/2 = 0.75 = 75%
(75% + 100%)/2 = (0.75 + 1.00)/2 = (1.75)/2 = 0.875 = 87.5%
(65% + 100%)/2 = (0.65 + 1.00)/2 = (1.65)/2 = 0.825 = 82.5%
**Remember: (1) before doing any math with percents, turn it into a value by moving the decimal place to the left 2 digits. (2) Certain english words mean specific things in math talk. Remembering these "translations" and using them correctly will make understanding word problems and equations easier.**
