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Or we may reason as follows. I divide 117 by 18, which gives 6, and 9 remainder. 9 whole ones are 90 tenths, and 5 are 95 tenths; this divided by 18 gives 5, which must be tenths, and 5 remainder. 5 tenths are 50 hundredths, and 4 are 54 hundredths; this divided by 18 gives 3, which must be 3 hundredths. The answer is 6.53 each, as before.
If you divide 7.75 barrels of flour equally among 13 men, how much will you give each of them?
It is evident that they cannot have so much as a barrel each. 7.757781788. Dividing this by 13, I obtain 100 596 and a small remainder, which is not worth noticing, since it is only a part of a thousandth of a barrel. .596. Or we may reason thus: 7 whole ones are 70 tenths, and are 77 tenths. This divided by 13 gives 5, which must be tenths, and 12 remainder. 12 tenths are 120 hundredths, and 5 are 125 hundredths. This divided by 13 gives 9, which must be hundredths, and 8 remainder. We may now reduce this to thousandths, by annexing a zero. 8 hundredths are 80 thousandths. This divided by 13 gives 6, which must be thousandths, and 2 remainder. Thousandths will be sufficiently exact in this instance, we may therefore
5 96 1000
omit the remainder. The answer is .596 + of a barrel each.
From the above examples it appears, that when only the dividend contains decimals, division is performed as in whole numbers, and in the result as many decimal places must be pointed off from the right, as there are in the dividend.
Note. If there be a remainder after all the figures have been brought down, the division may be carried further, by annexing zeros. In estimating the decimal places in the quotient, the zeros must be counted with the decimal places of the dividend.
At $6.75 a cord, how many cords of wood may be bought for $38?
In this example there are decimals in the divisor only. $6.75 is 675 cents or $75 of a dollar. The 38 dollars must also be reduced to cents or hundredths. This is done by annexing two zeros. Then as many times as 675 hundredths are contained in 3800 hundredths, so many cords may be bought.
The answer is 5 cords, or reducing the fraction to a decimal, by annexing zeros and continuing the division, 5.62+ cords.
If 3.423 yards of cloth cost $25, what is that per yard? 3.4233,42 = HH.
The question is, if 3433 of a yard cost $25, what is that a yard?
According to Art. XXIV., we must multiply 25 by 1000, that is, annex three zeros, and divide by 3423.
The answer is $71233, or reducing the fraction to cents. $7.30 per yard.
If 1.875 yard of cloth is sufficient to make a coat; how many coats may be made of 47.5 yards?
In this example the divisor is thousandths, and the dividend tenths. If two zeros be annexed to the dividend it will be reduced to thousandths.
1875 thousandths are contained in 47500 thousandths 256 times, or reducing the fraction to decimals, 25.33 + times, consequently, 25 coats, and of another coat may be made from it.
From the three last examples we derive the following rule: When the divisor only contains decimals, or when there are more decimal places in the divisor than in the dividend, annex as many zeros to the dividend as the places in the divisor exceed those in the dividend, and then proceed as in whole numbers. The answer will be whole numbers.
At $2.25 per gallon, how many gallons of wine may be bought for $15.375?
In this example the purpose is to find how many times $2.25 is contained in $15.375. There are more decimal places in the dividend than in the divisor. The first thing that suggests itself, is to reduce the divisor to the same denomination as the dividend, that is, to mills or thousandths. This is done by annexing a zero, thus, $2.250. The question is now, to find how many times 2250 mills are contained in 15375 mills. It is not important whether the poin' be taken away or not.
Instead of reducing the divisor to mills or thousandths, we may reduce the dividend to cents or hundredths, thus, $15.375 are 1537.5 cents. The question is now, to find how many times 225 cents are contained in 1537.5 cents. This is now the same as the case where there were decimals in the dividend only, the divisor being a whole number.
6.83 gals. Ans. as before.
If 3.15 bushels of oats will keep a horse 1 week, how many weeks will 37.5764 bushels keep him?
The question is, to find how many times 3.15 is contained in 37.5764. The dividend contains ten thousandths. The divisor is 31500 ten thousandths.
Instead of reducing the divisor to ten-thousandths, we may reduce the dividend to hundredths. 37.5764 are 3757.64 hundredths of a bushel. The decimal .64 in this, is a frac tion of an hundredth.
3.15 are 315 hundredths. Now the question is, to find how many times 315 hundredths are contained in 3757.64 hundredths.
11.929 weeks. Ans.
11.929 weeks. Ans. as before.
From the two last examples we derive the following rule for division: When the dividend contains more decimal places