28. How multiply decimals?

Multiply as in whole numbers, and from the right of the product, point off as many figures for decimals as there are decimal places in both factors.

REMARKS.3.-1. If the product has not as many figures as there are decimals in both factors, the deficiency must be supplied by prefixing ciphers. (Ex 4.)

2. To multiply a decimal by 10, 100, 1000, etc., remove the decimal point as many figures to the right as there are ciphers in the multiplier. For, each removal of the decimal point one place to the right, multiplies the number by 10.

4. What is the product of .004 multiplied by .03?

ANALYSIS.-The product of the significant figures 4×3=12. But there are five decimals in the given factors; therefore the product must have five decimals. Prefixing three ciphers to 12, it becomes .00012

OPERATION.

.004

.03

.00012 Ans.

21. Allowing 5.5 yards to a rod, how many yards are there in 20.25 rods?

22. If a man earns 1.25 dol. a day, how much will he earn in 19.5 days?

23. How many pounds of coffee in 10 sacks, allowing 37.5 pounds to a sack?

24. If a gallon of molasses is worth .54 dol., how much are 18.75 gallons worth?

25. What is the product of 1.005 multiplied by .008? 26. What is the product of one thousandth into seven hundredths?

27. What is the product of five ten-thousandths intc seven tenths?

DIVISION OF DECIMALS.

MENTAL EXERCISES.

1. At 2 tenths of a dime apiece, how many oranges can a lad buy for 8 tenths of a dime?

ANALYSIS.-2 tenths dime are contained in 8 tenths dime, 4 times. Therefore, etc. (P. 63, Q. 10.)

2. How many times 3 tenths in 6 tenths of a dollar? 3. How many times are 7 hundredths contained in 35 hundredths? .4 in .8? 150 in ?

25

4. If a man pays 6 tenths of a dollar for 2 tenths of a barrel of apples, what must he pay for 1 tenth of a barrel?

I

ANALYSIS.-The object is to divide 6 into 2 equal parts. (P. 63, Q. 10.) Since these fractions have a common denominator, one numerator may be divided by the other like whole numbers.

5. How many times are .08 contained in .64? 6. Divide .4 by .2; .6 by .3; .8 by .4.

7. Divide .08 by .02; .16 by .04.

SLATE EXERCISES.

1. How many times .2 in .6?

ANALYSIS. Since these decimals have a common denominator, they are like numbers; hence, one can be divided by the other as common fractions, and the quotient is a whole number. (Page 121, Q. 46.)

OPERATION.

.2).6

Ans. 3 times.

ANALYSIS.-Reducing the given decimals to a OPERATION. common denominator, we have .04 and .30. Now,

.04).30 Ans. 7.5

.04 is in .30, 7 times and .02 remainder. We put the 7 in units' place, because it is units. Annexing a cipher to the remainder, .04 is in .020, .5 times and o remainder. We set the 5 in tenths' place. Ars. 7.5 times.

3. How

.400).012 Ans. 0.03

many times .4 in .012? ANALYSIS.-Reducing these decimals to a com- OPERATION. mon denominator, we have .4.400 and .012. Now, as .400 is not contained in .012, we put a cipher in units' place. Annexing a cipher to the dividend, we find .400 is not contained in .0120; we therefore put a cipher in tenths' place. Annexing another cipher, .400 is in .01200, 3 hundredths time and o remainder. Ans. .03 times. 29. How are decimals divided?

Reduce the decimals to a common denominator, and divide the numerator of the dividend by that of the divisor, placing a decimal point on the right of the quotient.

Annex ciphers to the remainder, and divide as before. The figures on the left of the decimal point denote whole numbers; those on the right, decimals.

Or, divide as in whole numbers, and from the right of the quotient, point off as many decimals as the decimal places in the dividend exceed those in the divisor.

REMARKS.-1. If there are not figures enough in the quotient for the decimals required by the second method, prefix ciphers. 2. To divide a decimal by 10, 100, 1000, etc.,

Remove the decimal point in the dividend as many places to the left as there are ciphers in the divisor.

3. If there is a remainder after carrying the work as far as desired, the sign (+) is annexed to the quotient to show it is not exact. EXAMPLES FOR PRACTICE.

1. What is the quotient of .028 divided by 7? Ans. .004, 2. What is the quotient of .432 divided by .144? Ans. 3. 3. What is the quotient of 515 divided by 1.03? Ans. .505.

4. Divide 2.37 by 9.

Ans. 0.2633+; or, .2633}. 5. At .25 dol. a pound, how much honey can be bought for 2.75 dollars?

6. How many building-lots can be made from 12.75 acres of land, allowing .25 of an acre to a lot?

25. .00003.00004.

15. .0039÷.26. 20. 246.751-÷85.

26. A farmer sold 75 sheep for 187.5 dollars: what

was that apiece?

27. If you travel 40.75 miles in a day, how long will it take to travel 195.6 miles?

28. If 34.5 bushels of apples cost 17.25 dollars, what will bushel cost?

29. If 18.75 tons of hay cost 196.875 dollars, what will ton cost?

30. How many revolutions will a wheel 9.4 ft. in circumference make in going 5280 feet?

31. If 1 acre of land produces 25.6 bushels of corn, how many acres will be required to produce 4635 bushels?

32. How many times are five thousandths contained in 37 hundredths?

33. How many times are seventy-five ten-thousandths contained in eight thousandths.

34. How many times are seven millionths contained in three hundred-thousandths?

UNITED STATES MONEY.

1. What is Money?

Money is the standard of value, and is often called Currency.

2. What is United States Money?

United States Money is the national currency of the United States. It is also called Federal Money. 3. What are its denominations?

Eagles, dollars, dimes, cents, and mills.

66

I dime, d.

I dollar, $, or dol.

66

I eagle, E.

dol.

50 cts. dol.; 33 cts. dol. ; 25 cts.

=

20 cts. dol.; 121⁄2 cts.=§ dol.; 10 cts.

NOTES.-I. It will be observed that the denominations of U. S. money, like the orders of whole numbers, increase and decrease by the scale of 10. It is thence called Decimal Currency.

2. The sign of U. S. money is the character ($), called the dollar mark, placed before the sum to be expressed.

4. How is U. S. Money written?

Dollars are written as whole numbers, with the gn ($) prefixed to them.

Cents are written in the first two places on the right of the decimal point; because they are hundredths of a dollar. Thus 13 dollars 25 cents are written $13.25.

Mills are written in the third place on the right; because they are thousandths of a dollar; as $25.038.

REMARKS.- -1. Eagles are expressed by tens of dollars; dimes by tens of cents. Thus, 15 eagles are $150, and 6 dimes are 60 cents.