Ray's New Practical Arithmetic · Arts. 98–101 · Unit 10: Fractions
53. Kinds of fractions and their principles
Goal: Your child sorts fractions into proper, improper, mixed, compound and complex, and knows how changing a numerator or denominator changes a fraction.
You'll need
- The book
- A slate, small whiteboard or scrap paper
- A notebook and pencil
What's in the book
Whole numbers written as fractions, proper and improper fractions, mixed numbers, compound and complex fractions, then six principles about multiplying and dividing a fraction.
The lesson, step by step
Warm-up
Ask: Is 3/4 more or less than 1? 4/4? 5/4?
Kinds of fractions
Read:
A proper fraction is one whose value is less than 1.
An improper fraction is one whose value is equal to or greater than 1.
A mixed number is a whole number and a fraction.
A compound fraction is a fraction of a fraction.
Sort them
Write 2/3, 7/4, 3 1/2, 5/5, 1/2 of 3/4 on cards. Your child sorts them by kind.
Four principles
Read:
A fraction is multiplied by multiplying the numerator.
A fraction is divided by dividing the numerator.
A fraction is divided by multiplying the denominator.
A fraction is multiplied by dividing the denominator.
Show each with a drawing: 2/8 to 4/8 (doubled), 2/8 to 2/16 (halved).
Value unchanged
Read:
Multiplying both terms of a fraction by the same number does not change its value.
Dividing both terms of a fraction by the same number does not change its value.
Show 1/2 = 2/4 = 4/8 with folded paper.
Wrap-up
Ask: What happens to 3/5 if you double the denominator? (It is halved.) If you double both terms? (No change.)
Tip
These principles are the reason every later rule for fractions works. Return to them whenever a rule seems like magic.