9. How does the number of decimals in a product correspond to that of the factors ? Ans. The number is equal. 10. How does the number of decimals in a dividend correspond to that of the divisor and quotient ? Ans. It is equal. 11. If the divisor has more decimals than the dividend, what is necessary to be done? Ans. Add decimal zeros to the dividend until it has as many decimals as the divisor. 12. If the divisor and dividend have the same number of decimals, will there be any in the quotient ? Ans. No. 13. If it be necessary that there should be decimals in the quotient, what must be done? Ans. More decimal zeros must be added to the dividend. 14. Do zeros annexed to a decimal change its value ? Ans. No. 15. If zeros are prefixed to a decimal, and the decimal point removed to the left of the zeros, is the value changed ? Ans. Each decimal zero thus prefixed renders the value one-tenth, or divides it by ten. 16. In multiplying by more than one figure, where is the first figure of each line or partial product placed, and why? Ans. It is placed in the column of the same order as the multiplier ; that is, directly under it, because every consecutive order to the left is ten times the value of the preceding order. DENOMINATE NUMBERS. All arithmetical numbers may be considered Denominate, even abstract numbers, as every figure in each successive order, beginning at the right and going to the left, is ten times the value of the same figure in the previous order, and may be arranged in a table; thus, 10 units = 1 ten. In the United States currency, the orders have the same relation; thus, 10 mills (m.) = 1 cent (ct.). 10 dollars = 1 eagle. Dimes and eagles are coins, but are not regarded in computation; but only dollars ($), cents, and mills, the cents holding two places. There is generally a decimal point placed between dollars and cents; thus, $456.295, which is numerated “ four hundred and fifty-six dollars, twenty-nine cents and five mills. It may also be numerated without any change in its value, “ four hundred and fifty-six thousand, two hundred and ninety-five mills. ADDITION. As the relations of the orders in United States money is the same as in abstract numbers, hence their application is the same ; and in addition and subtraction like orders must be placed under each other, and in every other way the same methods are followed. PROBLEMS. $25.365 9.100 1. What is the sum of twenty-five dollars, thirty-six cents and five mills; twelve dollars, eighteen cents and four mills; nine dollars and ten cents; thirty dollars and five mills; fifteen dollars and three cents. $91.684 Ans., Ninety-one dollars, sixty-eight cents and four mills. 2. Add the following sums of money: Five dollars, thirty cents and four mills. $5.304 3.002 2.030 Seven dollars and three mills. 7.003 Twelve dollars and one cent 12.010 Nine dollars. 9.000 $38.349 (3.) (5.) Add 97.548 Add $386.946 Add 387,642 mills. 68.754 5372.875 548,753 97.632 64759.654 . 659,864 198.564 876943.687 3,217,634 $462.498 $947463.162 4,813,893 mills. REM. 1.—The sum of the last example may be numerated thus: Four millions eight hundred and thirteen thousand, eight hundred and ninety-three mills; or, thus : four thousand eight hundred and thirteen dollars, eighty-nine cents and three mills. REM. 2.-Mills are numerated the same as abstract numbers. SUBTRACTION. $287.304 1. From two hundred and eighty194.293 seven dollars, thirty cents and four $93.011 mills, take one hundred and ninety four dollars, twenty-nine cents and three mills. Remainder, Ninety-three dollars, one cent and one mill. (2.) (3.) (4.) $475648.364 $9,486,397.213 $21795.375 387654.875 6,397,423.875 10963.625 $87993.489 $3,088,973.338 $10831.750 (5.) (6.) (8.) (9.) 100000 100 100 100.00 100.00 99999 99 2.50 1 1 99 98.50 97.50 REM.-As in addition and subtraction, so also in multiplication, the process is the same as that of abstract integers and decimals ; hence there is no need of further esemplification. English money is reckoned in pounds, shillings, pence, and farthings; sometimes also in guineas; thus, TABLE. = 1 shilling (s.). 12 pence PROBLEMS. Reduce £1 to shillings, pence, and farthings. £1 £1 = 20 shillings. £1 = 240 pence. 12 £1 = 960 farthings. 240 pence. 4 960 farthings. As there are twenty shillings in one pound, there will always be twenty times as many shillings as pounds; and as there are twelve pence in every shilling, there will be twelve times as many pence as shillings; and four times as many farthings as pence. COR.—A higher denomination is reduced to a lower one by multiplication. Reduce 960 farthings to pence, shillings and pounds; thus, 4 ) 960 farthings. 1 pound. As four farthings make one penny, there will be one |