Ray's New Higher Arithmetic · Art. 106 · Unit 7: Properties of Numbers
29. Cancellation
Goal: Your student sets out a chain of multiplications and divisions and cancels equal factors before working it.
You'll need
- The book
- A slate, small whiteboard or scrap paper
- A notebook and pencil
What's in the book
Cancellation defined, two principles, the worked example (75 × 153 × 28 divided by 63 × 36), the rule, and four examples for practice with printed answers. A topical outline of the chapter follows.
The lesson, step by step
Warm-up
Mental: (12 × 5) ÷ 6. Can you do it without multiplying first?
The idea
Read:
Cancellation is the process of crossing out equal factors from dividend and divisor.
Canceling a factor in both dividend and divisor, does not change the quotient.
Work the book's example
Read:
Multiply 75, 153, and 28 together, and divide by the product of 63 and 36.
Write the dividend factors above a line and the divisor factors below. Cancel common factors one at a time, as the book does (4, then 7, then 9, then 3), until only 25 × 17 is left above and 3 below. Result: 425 ÷ 3 = 141⅔.
The rule
Read:
Cancel equal factors from dividend and divisor
then multiply what is left above and divide by what is left below.
Guided practice
Together:
How many cows, worth $24 each, can I get for 9 horses, worth $80 each?
Write 9 × 80 over 24, cancel 8 and 3: answer 30 cows.
Independent practice
Your student works the other three examples (molasses for tea, cotton for sugar, and the long chain in Example 4).
Check
Answers are printed: 30 cows, 44 cents, 9 bales, 34.
Wrap-up
Look over the topical outline for Properties of Numbers. Your student explains any two headings in their own words.