THE TRANSITION LINE // FIELD NOTES // STOP 17
Mixed multiply and divide, and the parallelogram
Field Book
Lessons 65 to 68
Method
Pencil and paper. Calculators never.
The midterm sidequest posts this stop. The Line pauses next week for inspection. Mixed numbers multiply and divide through improper form, subtraction with unlike bottoms runs the full ladder of moves, and the parallelogram takes base times height with the height standing square.
What you have to be able to do
- Multiply mixed numbers
- Subtract mixed numbers with unlike denominators
- Divide mixed numbers
- Find the area of a parallelogram
The procedures
Multiplying mixed numbersField Book Lesson 65
- Change every mixed number to improper form.
- Multiply, reduce, and change back to mixed form.
Subtracting, unlike bottomsField Book Lesson 66
- Put the fraction parts over the LCD.
- Regroup if the top fraction runs short, then subtract wholes from wholes.
Dividing mixed numbersField Book Lesson 67
- Rewrite as a division of improper fractions.
- Invert the second fraction, multiply, reduce, and return to mixed form.
Area of a parallelogramField Book Lesson 68
- A_par = b · h, with the height measured square to the base.
Worked: improper and invert
- 3 12 ÷ 1 34 = 72 ÷ 74
- = 72 · 47 = 2
Worked: slanted floor
- A_par = b · h
- = 9 · 6
- = 54 yd2
Terms on the record
| Term | Meaning |
|---|
| parallelogram | a four-sided shape with two pairs of parallel sides |