THE TRANSITION LINE // FIELD NOTES // STOP 26
Signed products and unit multipliers
Field Book
Lessons 97 to 100
Method
Pencil and paper. Calculators never.
A term walk posts this stop. Count the negative signs before you move a wheel. Products and quotients of signed numbers answer to one count of negative signs, unit multipliers convert by multiplying by a fraction worth one, complex perimeter recovers its missing sides first, and the missing-number rules now run on every number type.
What you have to be able to do
- Multiply and divide signed numbers
- Convert units with unit multipliers
- Find the perimeter of a complex shape
- Solve missing-number statements with fractions and decimals
The procedures
Signed multiply and divideField Book Lesson 97
- Count the negative signs in the whole product or quotient.
- An even count comes out positive. An odd count comes out negative.
Unit multipliersField Book Lesson 98
- A unit multiplier is a fraction worth 1 built from a conversion fact.
- Write the disappearing unit on the bottom, then multiply.
Complex perimeterField Book Lesson 99
- Use the given sides to find every missing side first.
- Then add all the outside edges once.
Missing numbers, all typesField Book Lesson 100
- The same largest-number rules apply unchanged.
- Fractions and decimals ride the rules exactly as whole numbers did.
Worked: a mile in feet
- 6.5 mi · 5280 ft/1 mi: the mile unit cancels.
- 6.5 · 5280 = 34,320 ft
Worked: odd count
- (-3) · (-4) · (-5): three negative signs, an odd count.
- 3 · 4 · 5 = 60, so the answer is -60.
Terms on the record
| Term | Meaning |
|---|
| unit multiplier | a fraction worth 1 built from a conversion fact |
| conversion fact | an equality linking two units, like 1 mile = 5280 feet |