Ray's New Higher Arithmetic · Arts. 160–161 · Unit 9: Decimal Fractions

41. Adding and subtracting decimals

Goal: Your student adds and subtracts decimals, lining up the points and annexing ciphers where needed.

⏱ About 40 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

Addition of decimals (definition, a worked example with complex decimals, the rule, and 14 examples) and subtraction of decimals (definition, the example 6.8 − 2.057, the rule, notes, and 16 examples). Answers are printed.

The lesson, step by step

  1. Warm-up

    Mental: $2.50 + $1.75; $5 − $1.35.

  2. Adding

    Read:

    Addition of Decimals is finding the sum of two or more decimals.

    Write the numbers so that figures of the same order shall stand in the same column.

    The point in the sum goes right under the other points. Try one of the book's:

    Of 4 units, 4 tenths, 4 hundredths.

    (4.44.)

  3. Subtracting

    Read:

    Subtraction of Decimals is finding the difference between two decimals.

    If the minuend has not as many decimal places as the subtrahend, annex decimal ciphers to it.

    Work the book's example: From 6.8 subtract 2.057. Write 6.800 − 2.057 = 4.743.

  4. Guided practice

    Together:

    Subtract 8.00717 from 19.54

    3 thousandths from 3000.

    (11.53283; 2999.997.)

  5. Independent practice

    Your student works a selection of both sets of examples.

  6. Check

    Read:

    The proof of each fundamental operation in decimals is the same as in simple numbers.

    Check subtraction by adding back. Answers are printed.

  7. Wrap-up

    Ask: Why line up the points instead of the right-hand figures? (So tenths stand under tenths, the same rule as for whole numbers.)

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