Ray's New Higher Arithmetic · Arts. 164–166 · Unit 9: Decimal Fractions

43. Dividing decimals

Goal: Your student divides decimals, places the point in the quotient, and annexes ciphers to carry the division further.

⏱ About 40 minutes · 8 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

Division of decimals: definition, two principles (the worked example .50312 ÷ .19), the rule and note on annexing ciphers (examples .36 ÷ .008 and .002475 ÷ .066), examples, then Oughtred's shortened division (84.27 ÷ 1.27395807 to four places) with more examples. Answers are printed.

The lesson, step by step

  1. Warm-up

    Mental: 6 ÷ .5; 1.2 ÷ 4; .36 ÷ .6.

  2. The idea

    Read:

    Division of Decimals is the process of finding the quotient when either or when each term is a decimal.

    The dividend must contain as many decimal places as the divisor.

    The quotient gets the difference: dividend places minus divisor places.

  3. Work the book's examples

    .50312 ÷ .19: 50312 ÷ 19 = 2648; 5 places − 2 places = 3, so 2.648. Next, .36 ÷ .008: annex a cipher so the dividend has three places, .360; 360 ÷ 8 = 45.

  4. Going on

    Read:

    When the division is not exact, annex ciphers to the dividend, and carry the work as far as may be necessary.

  5. Guided practice

    Together, the first two examples:

    63 ÷ 4000

    3.15 ÷ 375

    (.01575; .0084.)

  6. Independent practice

    Your student works a selection of the examples. Try one of the contracted division examples if there's time.

  7. Check

    Answers are printed. Check one by multiplying quotient × divisor.

  8. Wrap-up

    Ask: Why does dividing by .5 make a number bigger? (There are two halves in every unit.)

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