THE COMPOUND // FIELD NOTES // WEEK 09
Complex fractions and polygon angles
Field Book
Lessons 32 to 35
Due
Test 7 due · Supplement 9
Method
Paper first, every step
Rationalize before you reach for the LCD. That single order of operations saves the whole week.
What you have to be able to do
- Rationalize denominators before combining
- Simplify complex fractions
- Handle same-direction motion and interior angles of polygons
The procedures
Rationalize firstField Book Lesson 32
- If a denominator carries a radical, clear it before finding the LCD.
- Multiply top and bottom by the radical to move it out of the denominator.
Complex fractionsField Book Lesson 33
- Combine the top into one fraction and the bottom into one fraction.
- Then divide: invert the bottom and multiply.
Same direction, unequal distancesField Book Lesson 34
- When one traveler goes k miles farther: D1 = D2 + k.
- Write both distances as rate times time and solve.
Angles of a polygonField Book Lesson 35
- Interior angles of an N-gon sum to (N - 2) times 180.
- Fractional exponents follow the same product and power theorems as integers.
Worked: hexagon interior sum
- Sum the interior angles of a hexagon.
- (6 - 2) times 180 = 4 times 180.
- The sum is 720°.
Terms on the record
| Term | Meaning |
|---|
| complex fraction | a fraction that contains fractions in its top or bottom |
| regular polygon | a polygon with all sides and all angles equal |
| fractional exponent | an exponent written as a fraction, naming a root and a power |