THE TRANSITION LINE // FIELD NOTES // STOP 21
Powers of fractions, functions, and ratio problems
Field Book
Lessons 77 to 80
Method
Pencil and paper. Calculators never.
The signal box: one input, one rule, one output, every time. A fraction raised to a power sends top and bottom up separately, a function turns inputs into outputs through one fixed rule, surface area sums the faces of a solid, and ratio word problems settle on five short lines.
What you have to be able to do
- Raise fractions and mixed numbers to powers
- Fill a function table
- Find the surface area of a box
- Solve ratio problems on five lines
The procedures
Powers of fractionsField Book Lesson 77
- Raise the top and the bottom to the exponent separately.
- A mixed number goes improper before it takes a power.
FunctionsField Book Lesson 78
- Input goes in, the operation acts, the output comes out.
- Fill a table by running each input through the rule in turn.
Surface areaField Book Lesson 79
- Find the area of every external face.
- A box has three matching pairs of faces. Add them all.
Ratio problems on five linesField Book Lesson 80
- Write the units, the given ratio, and the actual amount.
- Find the multiplier from the pair you know, then multiply for the answer.
Worked: five lines at the yard
- Trucks to vans run 4:3, and 24 vans are on the lot.
- 24 ÷ 3 = 8 is the multiplier, so trucks = 4 · 8 = 32.
Worked: a squared fraction
- (25)2: square the top and square the bottom.
- 2 squared is 4, and 5 squared is 25, so the answer is 425.
Terms on the record
| Term | Meaning |
|---|
| function | a fixed rule that turns each input into one output |
| input | the number placed into a function |
| output | the number a function produces |
| surface area | the sum of the areas of all external faces of a solid |