3. The boys charged 10¢ admission. For the first evening, the boys sold 32 tickets; for the second evening, 25 tickets; for the third, 27 tickets. What sum of money was received from the sale of tickets?

4. How much money did the boys have left from the sale of tick ets after paying expenses and buying a six-dollar radiopticon?

5. Gertrude and Ruth Deane made peanut candy, which they sold at 35¢ a box, and chocolate candy, which they sold at 40¢ a box. For each box of peanut candy, their expenses were: for 1 pound of sugar, $.115; for shelled peanuts, $.10; for butter, $.045. The profit on each box of peanut candy was how much?

6. For each box of chocolate candy, the girls used 11⁄2 lb. of brown sugar at $.10 a pound;cake of chocolate at $.28 a cake; a tablespoon of butter, $.045; cup of milk, $.02; and 2 teaspoons of vanilla, $.02. How much did the chocolate candy cost a box? How much profit was made on each box?

*7. The girls made 12 boxes of peanut candy and 18 boxes of chocolate candy. Find their total profit.

1. What number is used in building the table of units, tens, and hundreds? What number is used in building the table of United States money?

Any plan based upon the number ten is called a decimal1 plan.

1 The word decimal is from the Latin word decem, meaning ten. We find this Latin word also in December, which was at one time the tenth month of the year.

READING AND WRITING DECIMALS

2. What part of a dollar is 1 dime? 3 dimes? 7 dimes? 3. What part of a dollar is 1 cent? 11 cents?

4. What part of a dollar is 1 mill? 5 mills?

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Such fractions as 10, 1%, 10, 180, 100, 1000, 100 are decimal fractions written as common fractions.

The denominator of a decimal fraction must be 10, or a product of a number of tens. It may be 10; 10 × 10, or 100; 10 × 10 × 10, or 1000; 10 x 10 x 10 x 10, or 10,000; or the product of some other number of tens.

In writing United States money:

of a dollar is written $.10; 1 of a dollar is written $.30.

25

Too of a dollar is written $.01; of a dollar is written $.25.

10% of a dollar is written $.001; 10% of a dollar is written $.005.

Decimal parts of other quantities may be written in the same

manner:

of a mile may be written .10 miles, or .1 miles; of a mile may be written .30 miles, or .3 miles.

ʊ of a pound may be written .01 pounds; 25% of a pound,

.25 pounds.

100

To of a ton may be written .001 tons; 100 of a ton, .005

tons.

Fractions that have their denominators expressed are called common fractions.

1,4,1%, 10% are common fractions.

Fractions that have their denominators indicated by a decimal point are called decimal fractions or decimals.

.9, .02, .325 are decimals.

In writing decimals, one figure at the right of the decimal point expresses tenths, two figures express hundredths, and three express thousandths.

.9 is read nine tenths.

.09 is read nine hundredths.

.009 is read nine thousandths.

2.3 is read two and three tenths.

4.11 is read four and eleven hundredths.

In reading numbers, the word and is used only at the decimal point. The number 135.5 is read, one hundred thirty-five and five tenths.

5. .25, .37, .44.

10. 6.001, 4.002, 3.075. 15. 52.18, 154.225.

In writing decimals, use as many zeros as are necessary to give hundredths two places, thousandths three places.

ADDITION AND SUBTRACTION OF DECIMALS

66. Addition and Subtraction of Decimals

I

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(1) A railway train covers, during the first hour of its run, 45.25 miles; during the second hour, 54.5 miles; and during the third hour, 51.125 miles. What is the distance covered?

The distance covered equals the sum of 45.25 mi., 54.5 mi., and 51.125 mi. 45.25 mi.

(2) What is the difference in the record of the train for the first and third hours?

The difference in the records equals 51.125 mi. - 45.25 mi.

51.125 mi.

45.25 66
5.875 mi.

The difference in the records = 5.875 mi.

(3) What is the difference in the record of the train for the second and third hours?

The difference in the records equals 54.5 mi. — 51.125 mi.

Notice that in problem (3) the decimal places in the subtrahend exceed the number in the minuend and that ciphers are mentally supplied.

I. In the addition and subtraction of United States money, why are cents written under cents, and dollars under dollars?

2. In the addition and subtraction of other decimals, why are tenths written under tenths, hundredths under hundredths, and thousandths under thousandths?

In the addition and subtraction of decimals, all numbers should be written with their decimal points in the same vertical line.

II. Three machines are to be loaded on a car. The first weighs 1.75 tons; the second, .375 tons; and the third, 2.4 tons. What is their total weight?

12. Four loads of hay are to be put into a barn. The first load weighs 1.125 tons; the second, 1.75 tons; the third, 1.8 tons; the fourth, 1.9 tons. Find the weight of the four loads.

13. A wagon that, unloaded, weighs .25 tons weighs, when loaded with coal, 1.375 tons. What is the weight of its load?