THE TRANSITION LINE // FIELD NOTES // STOP 11
Expanding fractions and percent of a number
Field Book
Lessons 41 to 44
Method
Pencil and paper. Calculators never.
The gauge widens: same fraction, bigger bottom, no change in freight. Expanding pushes a fraction up to a chosen bottom without changing its worth, decimal multiplication counts its places before placing the point, and a percent of a number falls to one multiply once the percent changes costume.
What you have to be able to do
- Expand a fraction to a target denominator
- Multiply decimal numbers
- Change percents to decimals
- Take a percent of a number
The procedures
Expanding to a target bottomField Book Lesson 41
- Divide the target bottom by the current bottom to find the multiplier.
- Multiply top and bottom by that multiplier.
Multiplying decimalsField Book Lesson 42
- Count the total decimal digits in both numbers.
- Multiply as whole numbers, then place the point so the answer carries that count.
Percent to decimalField Book Lesson 43
- Move the decimal point two places to the left.
- A fraction over 100 works as the bridge when the move is unclear.
Percent of a numberField Book Lesson 44
- Change the percent to a decimal or a fraction.
- Multiply it by the given amount.
Worked: 35 percent of 80
- 35% = 0.35
- 0.35 · 80 = 28
Worked: expand to fortieths
- 38 to fortieths: 40 ÷ 8 = 5 is the multiplier.
- 38 · 55 = 1540
Terms on the record
| Term | Meaning |
|---|
| expanding a fraction | multiplying top and bottom by the same number to reach a chosen bottom |
| decimal digits | the digits sitting to the right of the decimal point |