Ray's New Higher Arithmetic · Arts. 67–69 · Unit 5: Multiplication
14. Short cuts: composite multipliers and ciphers
Goal: Your student multiplies by splitting the multiplier into factors, and multiplies quickly by 10, 100, 1000 and by numbers ending in ciphers.
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, a composite multiplier (multiply by its factors); Case II, a multiplier of 1 with ciphers; Case III, ciphers at the right of one or both factors. Each has a rule and a few examples with answers.
The lesson, step by step
Warm-up
Mental: 36 × 10, 36 × 100, 36 × 20.
Composite numbers
Read:
A Composite Number is the product of two or more whole numbers, each greater than 1, called its factors.
Separate the multiplier into two or more factors.
Work the book's example: At 7 cents a piece, what will 6 melons cost? 7 × 2 = 14, then 14 × 3 = 42 cents.
Guided practice
Together, using factors of the multiplier:
At the rate of 37 miles a day, how far will a man walk in 28 days?
Sound moves about 1130 feet per second: how far will it move in 54 seconds?
(1036 miles; 61020 feet.)
Ciphers
Read the rules:
Annex to the multiplicand as many ciphers as there are in the multiplier
Multiply as if there were no ciphers on the right in the numbers;
then annex to the product as many ciphers as there are on the right in both the factors.
Work: Find the product of 5400 by 130. (54 × 13 = 702, then add three ciphers: 702000.)
Independent practice
Your student works the remaining examples of Cases I, II and III.
Check
All answers are printed.
Wrap-up
Ask: What is 250 × 400 in your head? (25 × 4 = 100, then three ciphers: 100000.)