Ray's New Practical Arithmetic · Arts. 43–45 · Unit 5: Division

23. Short cuts in division

Goal: Your child divides by splitting the divisor into factors, by 10, 100 and 1000, and by numbers ending in zeros, and finds the true remainder.

⏱ About 35 minutes · 7 steps

Open it at the Internet Archive ↗

You'll need

  • The book
  • A slate, small whiteboard or scrap paper
  • A notebook and pencil

What's in the book

Contractions in division: Case I (divisor separated into factors), Case II (divisor 1 with ciphers), Case III (ciphers at the right of the divisor), with rules and examples.

The lesson, step by step

  1. Warm-up

    Mental: 240 ÷ 2, then ÷ 3? (40.) 240 ÷ 6? (40.) Same answer: that is Case I.

  2. Case I: factors

    Read:

    Divide the dividend by one of the factors of the divisor; then divide the quotient thus obtained by the other factor.

    Work the example: A man paid $255 for 15 acres of land: how much was that per acre? 255 ÷ 3 = 85, 85 ÷ 5 = 17. $17 an acre.

  3. The true remainder

    Read:

    Multiply the last remainder by the first divisor; to the product add the first remainder

    Work 6145 ÷ 42 together using 6 and 7: 6145 ÷ 6 = 1024, remainder 1. 1024 ÷ 7 = 146, remainder 2. True remainder: 2 × 6 + 1 = 13. Check: 146 × 42 + 13 = 6145.

  4. Cases II and III

    Read:

    Cut off as many figures from the right of the dividend as there are ciphers in the divisor;

    Work: Divide 34872 by 100. Quotient 348, remainder 72.

    Then Case III: Divide 62700 by 2500. Cut off two ciphers from each: 627 ÷ 25 = 25, remainder 2. Annex the two figures cut off to the remainder: 200.

  5. Independent practice

    Your child does Case I problems 3 to 12 using factors, then the Case II and III examples.

  6. Check

    Check with the answers below, or by multiplying back.

  7. Wrap-up

    Mental: 4500 ÷ 100? 3600 ÷ 90? 800 ÷ 16 (by 4, then 4)?

Answers to the book's problems

Case I: 2583 ÷ 63 = 41. 6976 ÷ 32 = 218. 2744 ÷ 28 = 98. 6145 ÷ 42 = 146, remainder 13. 19008 ÷ 132 = 144. 7840 ÷ 64 = 122, remainder 32. 14771 ÷ 72 = 205, remainder 11. 10206 ÷ 81 = 126. 81344 ÷ 121 = 672, remainder 32. 98272 ÷ 108 = 909, remainder 100. Case II: 34872 ÷ 100 = 348, remainder 72. Case III: 62700 ÷ 2500 = 25, remainder 200. If a number on your page differs from these, work it from the page.

Worked out for this site from the scan. If a number in your copy differs, trust the book.

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