A circle with the are 16pi has a sector with the central angel of 8/5 radians

3/2 units^2

Step-by-step explanation:

The area of the entire circle is 16π.  What is the area of a sector of this circle if the central angle (not angel) is 8/5 radians?

Formula:   (fraction of circle represented by the sector)(area of the circle

Area of the sector described above is

  8/5 radians                                         8*16π square units

* 16π square units = = 3/2 units^2

    2π radians                                                      10π

If you want to reduce a fraction to lowest terms, you don't cancel
prime factors.  You cancel common factors.

The factors of  13  are  1  and  13 .

The factors of  24  are  1,  2,  3,  4,  6,  8,  12, and  24 .

The only common factor of  13  and  24  is ' 1 '.

So the fraction  13/24  is already in lowest terms,
and can't be reduced further.