Ray's New Practical Arithmetic · Arts. 32–34 · Unit 4: Multiplication
18. Short cuts in multiplication
Goal: Your child multiplies by splitting the multiplier into factors, by 10, 100 and 1000, and by numbers ending in zeros.
You'll need
- The book
- A slate, small whiteboard or scrap paper
- A notebook and pencil
What's in the book
Contractions in multiplication: Case I (multiplier split into factors), Case II (multiplier 1 with ciphers), Case III (ciphers on the right of the factors), each with a rule and problems.
The lesson, step by step
Warm-up
Mental: 15 × 2? 30 × 4? 8 × 10? 8 × 100?
Case I: factors
Read:
When the multiplier can be separated into factors.
Work the example: What will 15 oranges cost, at 8 cents each? 15 = 3 × 5. 8 × 3 = 24, then 24 × 5 = 120 cents.
Read the warning:
Do not confound the factors of a number with the parts into which it may be separated.
Case II: 10, 100, 1000
Read:
Annex as many ciphers to the multiplicand as there are ciphers in the multiplier
Examples: 245 × 100 = 24500; 138 × 1000 = 138000.
Case III: zeros on the end
Read:
When there are ciphers at the right of one or both of the factors.
Work: 625 × 500. Multiply 625 × 5 = 3125, then annex the two ciphers: 312500.
Guided practice
Do these together:
Multiply 2350 by 60.
Multiply 80300 by 450.
(Answers 141000 and 36135000.)
Independent practice
Your child does the remaining problems of all three cases.
Check and wrap-up
Answers are printed for most. Mental: 25 × 40? 120 × 30? 600 × 50?