Ray's New Practical Arithmetic · Art. 42 (rule) · Unit 5: Division
21. Long division
Goal: Your child divides by divisors larger than 12, writing every step: divide, multiply, subtract, bring down.
You'll need
- The book
- A slate, small whiteboard or scrap paper
- A notebook and pencil
What's in the book
Long division: when it is used, the rule, a worked example sharing $3465 among 15 men, remarks to avoid common mistakes, and the first problems.
The lesson, step by step
Warm-up
Mental: 15 × 2? 15 × 3? 45 ÷ 15? 30 ÷ 15?
What long division is
Read:
When the entire work of the division is written down, it is termed Long Division.
SayThe steps are always the same: divide, multiply, subtract, bring down.
Work the book example
Read:
Divide 3465 dollars equally among 15 men.
15 into 34: 2 times. 2 × 15 = 30. 34 − 30 = 4. Bring down 6: 46. 15 into 46: 3 times, 45, remainder 1. Bring down 5: 15. 15 into 15: 1 time. Each man gets $231.
Avoiding mistakes
Read two of the remarks:
The product must never be greater than the partial dividend from which it is to be subtracted;
After subtracting, the remainder must always be less than the divisor;
SayIf either one happens, the quotient figure was too big or too small.
Guided practice
Do the next worked example together, writing each step:
Divide 78994 by 319.
Prove it by multiplying back.
Independent practice
Your child does about five of the next problems.
Wrap-up
Mental: 60 ÷ 15? 75 ÷ 25? 96 ÷ 16?
Tip
Long division is usually where children get stuck. Do only a few problems at a time, all steps neat and in columns, rather than many messy ones.
Answers to the book's problems
Divide 78994 by 319: 247, remainder 201 (319 × 247 = 78793, and 78793 + 201 = 78994).
Worked out for this site from the scan. If a number in your copy differs, trust the book.