Percentage

College and School of Mathematics
Math::Arithmetic::Grade V::Percentage

Percentages are special kind of numbers. They are special because when you write them in a fraction, their denominator is always 100.

The word "percent" itself gives you a clue as to what it is. Per means you have to divide it with something. And cent means one hundred.

So when you say 50%, you mean 50/100. After simplification, 50/100 becomes 1/2.

Now let's do some word problems.
1. What is 50% of 100?
2. What is 50% of 50?
3. What is 1% of 100?
4. If you cut a pizza in 8 slices, what is the percentage of each slice?
5. If you got 90% correct in a 20 questions test, how many answers did you got correct?

John Sindayen

Precalculus::Composite Function

Composite function or composition of functions is when you are working on two functions and one of them is the input of the other.

Let's say you have a function f(x) = 2x and another function g(x) = 3x.

Let's say you want to find the composite function (f * g)(x). Well (f * g)(x) = f(g(x)), which simply means that the input of the function f(x) is the output of the function g(x). In short, the input of function f(x) is the function g(x).

So now we have f(3x). Now, applying the input of function f(x), we now have f(3x) = 2(3x) = (2)(3)(x) = 6x.

Composite functions are used when something depend on another. Say, your monthly salary depends on the number of days of the month. So you have the composite function (monthlysalary * month)(days) = (monthlysalary(month(days)).

Now find the composite function of the following.
1. f(x) = 5x and g(x) = x + 1, what is (f * g)(x)?
2. f(x) = x + 1 and g(x) = 5x, what is (f * g)(x)?
3. f(x) = 5x and g(x) = x + 1, what is (g * f)(x)?

It's only math!

John Sindayen