Ray's New Practical Arithmetic · Arts. 40–41 · Unit 5: Division
20. Short division
Goal: Your child divides large numbers by divisors up to 12, writing only the quotient, 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
Short division without and with remainders: the rule, the proof, worked examples and problems.
The lesson, step by step
Warm-up
Mental: 48 ÷ 4? 63 ÷ 7? 96 ÷ 8? 17 ÷ 5 (3 and 2 over)?
What short division is
Read:
When the division is performed mentally, and merely the result written, it is termed Short Division.
Short Division is used when the divisor does not exceed 12.
Work the book example
Read:
How many times is 2 contained in 468?
2 into 4 is 2, into 6 is 3, into 8 is 4: the quotient is 234.
With carrying remainders
Read:
How many times is 3 contained in 129?
3 into 1 won't go, so try 12: 4 times. 3 into 9: 3 times. Quotient 43.
Read the rule's first line:
Write the divisor at the left of the dividend, with a curved line between them, and draw a line beneath the dividend.
The proof
Read:
Multiply the quotient by the divisor, and add the remainder, if any, to the product.
Prove 129 ÷ 3: 43 × 3 = 129.
Guided and independent practice
Do these together:
How many times 3 in 462? 154.
How many times 5 in 1170? 234.
Then your child does the rest of the problems and proves two of them.
Wrap-up
Mental: 100 ÷ 4? 120 ÷ 8? 144 ÷ 12?
Answers to the book's problems
Worked examples on the page: 735 ÷ 3 = 245; 618 ÷ 3 = 206; 609 ÷ 3 = 203; 743 ÷ 3 = 247, remainder 2.
Worked out for this site from the scan. If a number in your copy differs, trust the book.