Ray's New Practical Arithmetic · Arts. 148–150 · Unit 12: Decimal Fractions (continued)
70. Dividing decimals
Goal: Your child divides decimals, placing the point in the quotient by subtracting decimal places, and annexes ciphers when needed.
You'll need
- Paper and pencil, or a slate or small whiteboard
What's in the book
Page 183 defines Division of Decimals (Art. 148), gives the principle (Art. 149) and starts the worked examples (Art. 150). Page 184 finishes six worked examples and the rule; page 185 has four remarks and problems 7–29, and page 186 problems 30–33. Answers are printed.
The lesson, step by step
Warm-up
Ask: How many quarters are in $2? (8.) Write 2 ÷ .25 = 8. Dividing by a number less than 1 gives a bigger answer.
The idea
Division of Decimals is the process of finding the quotient of two numbers involving decimals.
The number of decimal orders in the quotient is equal to the number of decimal orders in the dividend, less the number in the divisor.
So: places in dividend − places in divisor = places in quotient.
Work the book's examples
Divide 2.125 by .5.
2125 ÷ 5 = 425. Three places − one place = two places: 4.25.
Then the book's Ex. 3, .3 ÷ .004. The dividend has fewer places, so annex ciphers: .300 ÷ .004 = 75.
And Ex. 5, 2.11 ÷ 3, which does not come out even: .703+.
The rule and remarks
1. Divide the numerator of the dividend by the numerator of the divisor as in simple numbers. 2. Point off as many decimal orders in the quotient as the number of orders in the dividend exceeds the number in the divisor.
And for 10, 100, 1000:
To divide a decimal by 10, 100, 1000, etc., remove the decimal point as many places to the left as there are ciphers in the divisor.
Guided practice
Do these two from page 185 together:
Divide 1.125 by .03.
Divide 1 by 1 tenth.
For the first, annex a cipher so the dividend has more places: 1.125 ÷ .030.
Independent practice and check
Your child works a selection of problems 8–33 (about 12). 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: .96 ÷ .24; 2 ÷ .5; 872.6 ÷ 100; 4.5 ÷ 1000; 1 ÷ .1.
Tip
Many families today teach "move both points until the divisor is a whole number". That gives the same answers. Ray counts places instead. Either is fine, but stick to one at a time.