Ray's New Practical Arithmetic · Arts. 145–147 · Unit 12: Decimal Fractions (continued)
69. Multiplying decimals
Goal: Your child multiplies decimals and places the point by counting the decimal places in both factors, and multiplies by 10, 100, 1000 by moving the point.
You'll need
- Paper and pencil, or a slate or small whiteboard
What's in the book
Page 180 begins Multiplication of Decimals (Art. 145). Page 181 gives the principle of decimal places and three worked examples (Art. 147). Page 182 has the rule, three remarks and problems 4–22; page 183 finishes with problems 23–28. All answers are printed.
The lesson, step by step
Warm-up
Ask: What is half of a half? (A fourth.) Now write .5 × .5. Ask how the answer can be smaller than either number. Multiplying by a decimal less than 1 means "take part of".
The idea
Read the definition and the principle:
Multiplication of Decimals is the process of finding the product of numbers involving decimals.
The number of decimal orders in the product is equal to the number of decimal orders in both the factors.
The book proves it with .2 × .03 = .006: two tenths times three hundredths is six thousandths.
Work the book's examples
Multiply 2.149 by 6.34.
Multiply 2149 × 634 as whole numbers, then count: 3 places + 2 places = 5 places. Answer 13.62466.
Multiply .0276 by .035.
276 × 35 = 9660. You need 7 places but have only 4 digits, so prefix three ciphers: .0009660, which is .000966.
The shortcut for 10, 100, 1000
Read Remark 3:
To multiply a decimal by 10, 100, 1000, etc., remove the decimal point as many places to the right as there are ciphers in the multiplier.
Try 2.075 × 100 = 207.5 (the book's Ex. 3).
Guided practice
Do problems 4 and 12 on page 182 together: 33.21 × 4.41 and .135 × .005. In the second, count places carefully and prefix ciphers.
Independent practice and check
Your child works problems 5–28 (choose about 12 if that is too many). The book prints the answer at the end of each problem line. Have your child cover the answers with a strip of paper, work the problem, then slide the strip down to check.
Mental-math wrap-up
Aloud: .2 × .8; .02 × .4; 4.87 × 10; 5.3 × 100; .125 × 8.
Tip
Before multiplying, have your child estimate. 33 × 4 is about 130, so 146.4561 is sensible and 14.64561 is not.