Ray's New Practical Arithmetic · Art. 91 · Unit 9: Factoring
51. Cancellation
Goal: Your child shortens a division by striking out factors common to the dividend and divisor.
You'll need
- The book
- A slate, small whiteboard or scrap paper
- A notebook and pencil
What's in the book
The principle of cancellation, a worked oranges-for-pears problem solved two ways, the rule, and problems 2 to 20 with answers.
The lesson, step by step
Warm-up
Mental: (5 × 3) ÷ 3? (8 × 7) ÷ 7? What do you notice?
The principle
Read:
A number is not changed by multiplying it and then dividing the product by the multiplier.
Work:
I bought 3 oranges at 5 cents each, and paid for them with pears at 3 cents each: how many pears did it take?
3 × 5 ÷ 3: the 3s cancel, leaving 5 pears.
The rule
Read:
Cancellation is a process of abbreviation by omitting the common factors of the dividend and divisor.
Cancel the factors common to both the dividend and divisor.
Divide the product of the factors remaining in the dividend by the product of the factors remaining in the divisor.
Guided practice
Together:
How many barrels of molasses, at $13 a barrel, will pay for 13 barrels of flour, at $4 a barrel?
Write 13 × 4 over 13; cancel the 13s: 4 barrels.
Independent practice
Your child does problems 5 to 16, writing dividend factors above a line and divisor factors below.
Check and wrap-up
Answers are printed. Mental: (12 × 10) ÷ (4 × 5)? (6.)
Tip
Cancellation is the same idea your child will use constantly with fractions in the next unit.