7. Dividing both numerator and denominator of a fraction by the same number does not change the value of the fraction.

Many practical problems should be given involving the four operations in fractions.

Don't give fool problems like some arithmetics. Make them practical.

These from arithmetics in use are not practical: —

1. A man who weighs 155 lbs. wishes to buy a bicycle that weighs of his weight. What will the bicycle weigh?

No sane man buys a bicycle in that way.

2. The thermometer showed 343 degrees at 10 A.M. and 12 degrees at 8 P.M. What was the difference in temperature at the two periods?

Who ever read thirty-seconds of a degree on a thermometer used as this suggests?

RULES.

IT

Is just as unpsychological to begin the teaching of arithmetic by a mass of inherited rules, as it is senseless to try to teach language by means of mere rules of speech.

TILLICH.

WHOEVER Would bring his pupils to intelligent computation should develop no rule, but should wait until the children themselves discover it. - FETZGA.

GIVE me leave to take notice of one thing I think a fault in the ordinary method of education, and that is, the charging of children's memories, upon all occasions, with rules and precepts, which they often do not understand, and constantly as soon forget as given. LOCKE.

United States money has been treated in this book before. The purpose of the previous pages on this subject is to acquaint the pupil with the common U. S. metal coins, that he may become familiar with change.

When dollars and cents are written by the pupil, he is using the decimal notation. When he adds and subtracts dollars and cents, he adds and subtracts decimals. For that reason, the subject of U. S. money may be taken up just before the pupil enters on work in decimals.

Besides the coins spoken of in a previous chapter, there are gold coins representing the values of $2.50, $5, $10, and $20.

Then there is paper money, founded on credit. It represents value, but in itself has no value.

This paper money is made up of paper promises to pay the amounts named, in gold or silver, on demand.

It includes bank bills, U. S. treasury notes, government bonds, etc.

These notes are used in the place of coin, and are preferred in many sections of the country, because they are light, and are more easily carried than either gold or silver. They represent the values $1, $2, $5, $10, $20, $50, $100, $500, $1000.

NOTE. It is interesting to know that in the eastern part of the U. S., paper money is almost exclusively used for amounts of $1 and above, while on the Pacific coast, gold and silver are used in nearly every transaction.

The standard of U. S. money is the gold dollar. Gold is used because in itself it has great worth and little bulk, and because it varies very little in value.

WRITING DOLLARS AND CENTS.

Dollars and cents are written together. Thus, two dollars and sixteen cents is written, $2.16.

The dollars are separated from the cents by a period. If the number of cents is less than ten, the tens' place is filled by a 0. Thus, we write twenty dollars and two cents, $20.02.

Mills, or tenths of a cent, are written to the right of the cents. Five dollars, six cents, four mills is written, $5.064.

Four hundred two dollars.

Two hundred dollars and forty cents.

Six hundred eight dollars and one cent.

ADDING DOLLARS AND CENTS.

In adding dollars and cents, write the numbers as for ordinary addition, taking care to write the cents