Ray's New Higher Arithmetic · Art. 78, Short Division · Unit 6: Division

18. Short division

Goal: Your student divides by small numbers in one line, carrying remainders in the head.

⏱ About 30 minutes · 7 steps

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You'll need

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

What's in the book

Short division explained with 652 ÷ 2, the rule, and examples with answers, including sheep and flour problems.

The lesson, step by step

  1. Warm-up

    Mental: half of 652; a third of 963.

  2. Work the book's example

    How often is 2 cents contained in 652 cents? Divide from the left: 6 hundreds ÷ 2 = 3 hundreds, 5 tens ÷ 2 = 2 tens and 1 over, 12 units ÷ 2 = 6. Quotient 326.

  3. The rule

    Read:

    Begin at the left, divide successively each figure or figures of the dividend by the divisor, and set the quotient beneath.

    Whenever a remainder occurs, prefix it to the figure in the next lower order, and divide as before.

  4. Guided practice

    Together:

    Divide 512653 by 5

    At $6 a head, how many sheep can be bought for $222?

    (102530 with 3 over, written 102530 3/5; 37 sheep.)

  5. Independent practice

    Your student works the rest of the short division examples.

  6. Check

    Answers are printed. Prove one by multiplying back and adding the remainder.

  7. Wrap-up

    Ask: When would you use short division instead of long? (Divisors up to about 12.)

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