Ray's New Higher Arithmetic · Arts. 178–181 · Unit 11: Compound Denominate Numbers
46. Measures, value and United States money
Goal: Your student explains what a measure and a compound number are, the kinds of value, and reads and writes U. S. money in dollars, cents and mills.
You'll need
- The book
- A slate, small whiteboard or scrap paper
- A notebook and pencil
What's in the book
Compound denominate numbers defined; measures of value (intrinsic, commercial, nominal; money and currency); United States money with its table (mills, cents, dimes, dollars, eagles), history notes, a table of the coins of 1880 and their metals and weights, and how to read sums of money.
The lesson, step by step
Warm-up
Ask: How many cents in $3.07? How many dimes in a dollar?
Measures
Read:
A Measure is a standard unit used in estimating quantity.
A quantity is measured by finding how many times it contains the unit.
A Compound Denominate Number is one expression of a quantity by different denominations under one kind of measure
Example: 3 ft. 7 in. is a compound number; 43 in. is not.
Value and money
Read:
Value is the worth of one thing as compared with another.
Money is a standard of value, and is the medium of exchange.
Ask: What's the difference between what a thing cost to make and what it would sell for? (The book's intrinsic and commercial value.)
U. S. money
Read:
United States Money is the legal currency of the United States.
The table: 10 mills = 1 cent, 10 cents = 1 dime, 10 dimes = 1 dollar, 10 dollars = 1 eagle.
The mill is not coined.
It is used only in calculations.
Old coins
Look at the coin table together: in 1880 there were 3-cent pieces, gold dollars, quarter eagles ($2.50), three-dollar pieces, half eagles, eagles and double eagles. Gold and silver coins were 9 parts precious metal to 1 part copper.
Practice
The book reads $9.124 as "9 dollars 12 ct. 4 mills". Your student reads $14.065, $0.375 and $100.009 the same way, and writes 6 eagles 3 dollars 4 dimes 5 cents as dollars.
Wrap-up
Ask: Why is U. S. money easy to calculate with? (It is decimal: every step is ten.)
Answers to the book's problems
Practice: $14.065 = 14 dollars 6 ct. 5 mills; $0.375 = 37 ct. 5 mills; $100.009 = 100 dollars 9 mills. 6 eagles 3 dollars 4 dimes 5 cents = $63.45.
Worked out for this site from the scan. If a number in your copy differs, trust the book.