Ray's New Practical Arithmetic · Arts. 162–163 · Unit 14: Percentage
76. Per cent, and the words of percentage
Goal: Your child knows that per cent means hundredths, writes any per cent as a fraction and a decimal, and can name the base, rate and percentage.
You'll need
- Paper and pencil, or a slate or small whiteboard
What's in the book
Page 197 opens Percentage (Art. 162) with a table of 1% to 6% as fractions and decimals. Page 198 has exercises turning per cents into fractions and decimals and back, then the definitions of Art. 163.
The lesson, step by step
Warm-up
Ask: If you got 50 out of 100 on a test, what per cent is that? 25 out of 100? Then 1 out of 2? Talk about why both are 50%.
The idea
Any per cent of a number is so many hundredths of it.
The book says per cent comes from the Latin per centum, "by the hundred". It can be written as a common fraction or as a decimal: 5% = 5/100 = 1/20 = .05.
The three words
Read Art. 163 together:
The Base is the number upon which the per cent is estimated.
The Rate is the per cent when expressed as a common fraction or as a decimal.
The Percentage is the result of taking the per cent of the base.
And the key promise:
Any two of these quantities being given, the third may be found. There are four cases.
Guided practice
Using the exercise "Express the following as common fractions and as decimals" on page 198, do 6¼% and 12½% together (1/16 and .0625; 1/8 and .125).
Independent practice and check
Your child works the rest of that exercise, then "How many per cent are equivalent to the following fractions?" The book prints the answers beside each one; cover them while working.
Mental-math wrap-up
Learn these by heart: 50% = 1/2, 25% = 1/4, 75% = 3/4, 20% = 1/5, 10% = 1/10, 12½% = 1/8, 33⅓% = 1/3.
Tip
The book writes the rate as a fraction or decimal ("the rate is .06"). Today we often call the per cent itself the rate. Keep the book's words for these lessons.