THE TRANSITION LINE // FIELD NOTES // STOP 16
Mixed sums over the LCD, and volume
Field Book
Lessons 61 to 64
Method
Pencil and paper. Calculators never.
Room 4 opens this stop. Three crates stack only on a common footing. Mixed numbers with unlike bottoms add over the LCD and regroup when top-heavy, three fractions share one LCD, the box takes length times width times height, and canceling trims fractions before they multiply.
What you have to be able to do
- Add mixed numbers with unlike denominators
- Combine three fractions over one LCD
- Find the volume of a box and a cube
- Cancel before multiplying fractions
The procedures
Mixed sums, unlike bottomsField Book Lesson 61
- Put the fraction parts over the LCD and add them.
- Regroup a top-heavy result, then add the whole numbers.
Three at onceField Book Lesson 62
- Find one LCD for all three bottoms.
- Expand each fraction to it, then combine.
Volume of a boxField Book Lesson 63
- V_box = l · w · h, on three lines.
- A cube is a box with three equal edges.
CancelingField Book Lesson 64
- Before multiplying, divide any factor on top and any factor on bottom by the same number.
Worked: cancel first
- 512 · 815: divide 8 and 12 by 4, divide 5 and 15 by 5.
- 13 · 23 = 29
Worked: crate volume
- V_box = l · w · h
- = 6 · 4 · 9
- = 216 ft3
Terms on the record
| Term | Meaning |
|---|
| volume | the amount of space a solid shape occupies |
| capacity | another name for the space a three-dimensional shape holds |
| cube | a box whose three edges are equal |
| canceling | dividing a top factor and a bottom factor by the same number before multiplying |