THE TRANSITION LINE // FIELD NOTES // STOP 07
Mixed numbers, reciprocals, and the LCM
Field Book
Lessons 25 to 28
Method
Pencil and paper. Calculators never.
The switch yard: every improper fraction finds its siding. Improper fractions change into mixed numbers by dividing, mixed numbers change back by the bottom-times-whole-plus-top move, reciprocals flip a fraction so division becomes multiplication, and the least common multiple falls out of two lists.
What you have to be able to do
- Change improper fractions to mixed numbers and back
- Write a reciprocal
- Multiply and divide fractions
- Find the LCM of two numbers
The procedures
Improper to mixedField Book Lesson 25
- Divide the top by the bottom.
- Write the remainder over the original bottom.
Mixed to improperField Book Lesson 26
- Multiply the bottom by the whole number and add the top.
- Keep the original bottom, with that sum on top.
Reciprocals, multiply and divideField Book Lesson 27
- A reciprocal trades the top and bottom.
- Multiply straight across. To divide, multiply by the reciprocal of the second fraction.
Least common multipleField Book Lesson 28
- List multiples of each number until one number shows up in every list.
Worked: divide by flipping
- 34 ÷ 25 = 34 · 52
- = 158 = 1 78
Worked: two lists meet
- 6: 6, 12, 18, 24, 30. 8: 8, 16, 24, 32.
- The LCM of 6 and 8 is 24.
Terms on the record
| Term | Meaning |
|---|
| improper fraction | a fraction whose top is at least as large as its bottom |
| mixed number | a whole number joined with a fraction part |
| reciprocal | the fraction made when top and bottom trade places |
| least common multiple | the smallest number that two or more numbers multiply into evenly |