THE TRANSITION LINE // FIELD NOTES // STOP 13
Unlike denominators and dividing by decimals
Field Book
Lessons 49 to 52
Method
Pencil and paper. Calculators never.
Two gauges, one track: the LCD lays the common rail. Mixed-number subtraction learns to borrow a fraction worth one, the least common denominator puts unlike fractions on one bottom, the decimal point slides for tens and hundreds, and a decimal divisor gets shifted whole before the division starts.
What you have to be able to do
- Subtract mixed numbers with regrouping
- Add and subtract unlike fractions over an LCD
- Multiply and divide by 10, 100, 1000 by moving the point
- Divide by a decimal number
The procedures
Subtracting mixed numbersField Book Lesson 49
- Subtract fractions from fractions and wholes from wholes.
- If the top fraction is too small, exchange 1 from the whole for a fraction worth 1.
The least common denominatorField Book Lesson 50
- The LCD is the least common multiple of the bottoms.
- Expand every fraction to the LCD, then combine over it.
Point moves for tensField Book Lesson 51
- Multiplying by 10, 100, 1000 moves the point right one place per zero.
- Dividing moves it left the same way.
Dividing by a decimalField Book Lesson 52
- Shift both decimal points right until the divisor is a whole number.
- Then divide, riding the point straight up.
Worked: LCD twenty-four
- 58 + 16: the LCD of 8 and 6 is 24.
- 1524 + 424 = 1924
Worked: shift both points
- 7.56 ÷ 1.2: shift both one place.
- 75.6 ÷ 12 = 6.3
Terms on the record
| Term | Meaning |
|---|
| least common denominator | the least common multiple of the bottoms in play |
| divisor | the number doing the dividing |