THE TRANSITION LINE // FIELD NOTES // STOP 06
Ratios, like denominators, and equivalent fractions
Field Book
Lessons 21 to 24
Method
Pencil and paper. Calculators never.
A term walk posts this stop. Ten reps, one slip, on the record. Zeros ride along when tens multiply, ratios get their three costumes, fractions with matching bottoms add cleanly, and equivalent fractions reduce by one shared divide.
What you have to be able to do
- Multiply whole numbers by 10, 100, and 1000
- Write and reduce a ratio three ways
- Add like fractions and mixed numbers
- Reduce a fraction to an equivalent form
The procedures
Times 10, 100, 1000Field Book Lesson 21
- Times 10 appends one zero, times 100 two, times 1000 three.
RatiosField Book Lesson 22
- Write a ratio three ways: 5 to 8, 5:8, or as the fraction 58.
- Reduce by dividing top and bottom by the same number.
Adding like fractions and mixed numbersField Book Lesson 23
- Same bottoms: add the tops, keep the bottom.
- Mixed numbers: add the fraction parts, then add the whole numbers.
Equivalent fractionsField Book Lesson 24
- Two fractions are equivalent when they name the same portion with different numbers.
- Divide top and bottom by the same number to reduce.
Worked: like denominators
- 3 29 + 5 49: fraction parts give 69, wholes give 8.
- 8 69 reduces to 8 23.
Worked: reduce the ratio
- 24 boxcars to 36 flatcars is 24:36.
- Divide both by 12: the ratio is 2:3.
Terms on the record
| Term | Meaning |
|---|
| ratio | a comparison of two amounts, written three ways |
| equivalent fractions | two fractions naming the same portion with different numbers |