Ray's New Practical Arithmetic · Arts. 46–48 · Unit 5: Division
24. Principles of division
Goal: Your child predicts how a quotient changes when the dividend or divisor is multiplied or divided.
You'll need
- The book
- A slate, small whiteboard or scrap paper
- A notebook and pencil
What's in the book
Three general principles of division, each shown with 24 divided by 6.
The lesson, step by step
Warm-up
Mental: 24 ÷ 6? 48 ÷ 6? 24 ÷ 3? 24 ÷ 12?
Principle I
Read:
If the dividend be multiplied, or the divisor be divided, the quotient will be multiplied.
Show: 24 ÷ 6 = 4. Double the dividend: 48 ÷ 6 = 8. Halve the divisor: 24 ÷ 3 = 8. Both doubled the quotient.
Principle II
Read:
If the dividend be divided, or the divisor be multiplied, the quotient will be divided.
Show: 12 ÷ 6 = 2, and 24 ÷ 12 = 2. Both halved the quotient.
Principle III
Read:
If both dividend and divisor be multiplied or divided by the same number, the quotient will not be changed.
Show: 48 ÷ 12 = 4 and 12 ÷ 3 = 4, same as 24 ÷ 6.
Try your own
Your child picks a division fact, changes the dividend or divisor, and predicts the new quotient before working it.
Wrap-up
Ask: How does Principle III help with 3600 ÷ 400? (Divide both by 100: 36 ÷ 4 = 9.)
Tip
These principles come back later in fractions. A few minutes making sure they make sense now pays off then.