Ray's New Practical Arithmetic · Art. 142 · Unit 12: Decimal Fractions (continued)
66. Changing a common fraction to a decimal
Goal: Your child changes a common fraction to a decimal by annexing ciphers and dividing, and knows how to place the decimal point.
You'll need
- Paper and pencil, or a slate or small whiteboard
What's in the book
Page 177 gives Case IV with the worked example 3/4 = .75 and a three-part rule, then problems 2–4. Page 178 continues with problems 5–12, all with printed answers.
The lesson, step by step
Warm-up
Ask: How much is 3 divided by 4? Let your child say "three fourths" and then try to say it as money ($0.75).
The idea
Read the rule together:
1. Annex decimal ciphers to the numerator. 2. Divide by the denominator. 3. Point off as many decimal orders in the quotient as there are decimal ciphers annexed to the numerator.
SayA fraction is a division waiting to happen. We write zeros after the numerator so the division can keep going.
Work the book's example
Reduce 3/4 to a decimal.
Write 3.00 and divide by 4. 30 tenths ÷ 4 = 7 tenths with 2 tenths left; 20 hundredths ÷ 4 = 5 hundredths. Answer .75.
Point out that the book explains why annexing the zeros is allowed: it does not change the value (the last guide).
Guided practice
Do problems 2 and 3 on page 177 together: 4/5 and 5/8. Count the ciphers you annexed so you know how many decimal places to point off.
Independent practice
Your child works problems 4–12 on pages 177–178.
Check
The book prints each answer at the end of the problem line (for example .8 and .625). Cover the answers with a strip of paper, work, then check.
Mental-math wrap-up
Quick fire: 1/2, 1/4, 3/4, 1/5, 2/5, 1/8, 3/8, 1/10, 1/20 as decimals. Your child says each one aloud.
Tip
Some fractions never come out even (1/3, 1/6). If one turns up, stop at three or four places and write "+" after the answer, the way Ray does.