Ray's New Practical Arithmetic · Art. 31 (22–48) · Unit 4: Multiplication
16. Multiplying by large numbers
Goal: Your child multiplies by a number of two or three figures, using partial products, and proves the result.
You'll need
- The book
- A slate, small whiteboard or scrap paper
- A notebook and pencil
What's in the book
The rule for a multiplier larger than 12, a worked example with partial products, the proof, and numbered problems with answers.
The lesson, step by step
Warm-up
Mental: 25 × 10? 25 × 4? 43 × 20?
The rule
Read:
Write the multiplier under the multiplicand, placing figures of the same order in a column.
Multiply the multiplicand by each figure of the multiplier in succession, beginning with units,
Add the partial products together: their sum will be the product sought.
Work the book example
Read:
Multiply 2345 by 123.
Partial products: 2345 × 3 = 7035; 2345 × 2 tens = 4690 tens (write it one place left); 2345 × 1 hundred = 2345 hundreds (two places left). Add: 288435.
The proof
Read:
Multiply the multiplier by the multiplicand: the product thus obtained should be the same as the first product.
Prove: 123 × 2345 also gives 288435.
Guided practice
Do this one together:
What is the product of 43 X 25?
(Answer 1075.) Then problem 24 (327 by 203): show that the 0 in 203 means a partial product of zeros, which can be skipped as long as the next one moves two places.
Independent practice
Your child does about eight problems from 25 to 48.
Check and wrap-up
Compare with the printed answers. Mental finish: 11 × 25? 12 × 25?
Answers to the book's problems
Problem 24: 327 × 203 = 66381.
Worked out for this site from the scan. If a number in your copy differs, trust the book.