Ray's New Higher Arithmetic · Arts. 70–71 · Unit 5: Multiplication
15. More short cuts in multiplication
Goal: Your student multiplies by numbers near 10, 100 or 1000, and uses a part of the multiplier that is a factor of another part.
You'll need
- The book
- A slate, small whiteboard or scrap paper
- A notebook and pencil
What's in the book
Case IV, when the multiplier is a little less or more than 10, 100, 1000 (example: 3046 × 997), and Case V, when one part of the multiplier is a factor of another part (example: 387295 × 216324). Examples with answers follow each. A topical outline of multiplication closes the chapter.
The lesson, step by step
Warm-up
Mental: 45 × 99 (think 4500 − 45). 12 × 101.
Near a round number
Read:
When the multiplier is a little less or a little greater than 10, 100, 1000, etc.
Work the book's example: Multiply 3046 by 997. 3046 × 1000 = 3046000; 3046 × 3 = 9138; subtract: 3036862.
Guided practice
Together:
3. 7023 X 99.
4. 16642 X 996.
(695277 and 16575432.)
Using a factor inside the multiplier
Read the heading:
When one part taken as units, in the multiplier, is a factor of another part so taken.
In 216324 the 3 is a factor of 24, and 24 of 216. Follow the book's working: multiply by 3, multiply that line by 8 (that gives × 24), then by 9 (that gives × 216), placing each line correctly, and add. This one is a puzzle; take it slowly.
Independent practice
Your student tries two or three of the Case V examples (all answers printed), for instance 38057 × 48618, checking against the printed answer 1850255226.
Wrap-up
Ask your student which short cut they'd actually use in daily life. (Usually Case IV.)
Tip
Case V is a clever trick, not a skill to master. If it frustrates, do one example and move on.