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6. Bought pieces of silver plate weighing 6 oz. 10oz. 25 oz. find their cost at £2 : 12 :3 per oz.

6 + 10 + 25 oz. = 41 oz.
£. 8.

d.
2 12 3

cost per oz. 10

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7. Given to an equal number of men, women, and children, in all 99 persons, sums of 2s. 6d., Is. 6d., 6d. respectively, how much was given altogether?

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Rule. Write the dividend and divisor in a line, with a curved line between them.

Divide the number of the highest denomination by the divisor; the quotient is the first term of the quotient required.

Change the remainder into a number of the next lower denomination, add it to the number of that denomination in the dividend, and divide the sum by the divisor.

Proceed in the same manner, till the whole dividend has been divided.

Note. If the divisor be not greater than 12, or composed of factors not greater than 12, the division may be carried on in the method of short division. If the divisor be greater than 12, and not composed of such factors, the division will be in the manner of long division.

EXAMPLES. 1. Divide £4063 : 9 : 101 by 9.

£.
9)4063 9 101

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2. Divide £768 : 11:31 by 28.

£. s. d.
$7)768

il 31
28
4)109 15 104 - 1)

-22 f. remainder.
Ans.

27 8 111

3

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4. Divide 1087 tons 10 cwt. Iqr. 15 lbs. by 196.

tons. cwt. qr. Ibs. 7)1087 10 1 15

196 = 4 X 7 X7. 7)155 7 0 22

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5. If 53 purses contain £4307 : 11:6, how much is in each, supposing all to contain the same?

£. d.
53)4307 11 6( 81 £.

424

s.

67 53

14
20

53)291(5s.

265

26
12

53)318(6u.

318

Ans. £81:5:6.

III. TO MULTIPLY A COMPOUND QUANTITY BY A VULGAR FRACTION.

Rule 1. Express the compound quantity as a fraction of some one denomination involved ; multiply by the multiplier, and express the result in positive terms.

Rule 2. Multiply by the numerator of the fraction, and divide by the denominator. If the multiplier be a mixed number, multiply by the integer and fraction separately, and add the products.

Note. The ist method is preferable, when denominator is large; the 2nd, when small.

EXAMPLE. Multiply £8 : 17 : 104 by 77.

First method

£8 : 17 : 104 X 7

143 68

X 160 24191

7 68 = £8: 17-S. X

8 9

1423 X 68 = £

160 X 9

71 = £67

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IV. TO MULTIPLY A COMPOUND QUANTITY BY A DECIMAL FRACTION.

Rule. Convert the compound quantity into a decimal of one of its denominations, multiply by the multiplier, and express the result in positive terms.

If the inultiplier be a recurring decimal, it must be reduced to a vulgar fraction, and the operation performed by the last case.

EXAMPLE Multiply 2 tons 3 cwt. 2 qrs. by 6.24375.

6.24375
4

2.175
3.500 cwt.
2,0

3121875
2.175 tons.

4370625

624375 1248750

2.000 qrs.

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V. TO DIVIDE A COMPOUND QUANTITY BY A VULGAR FRACTION.

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Rule. If the divisor be a mixed number, reduce it to an improper fraction. Invert the divisor, and multiply by the resulting fraction.

EXAMPLE
Divide 13 cwt. 3 qrs. 113 lbs. by 73.
2 23

2
2

2
13 cwt. 3 qrs. 11-lbs. 7-= 13 cwt. 3 qrs. 11- lbs. > x-.
3

5
3

23
57
3

417

3
13 cwt. 3—-qrs. {X-

=13—-cwt. X-
120
23

480 23
6657 X 3

6657 cwt.

cwt.
480 X 23

3680
2977
1 cwt.

3680 2977 2977

217
cwt.
qrs.

=3--

qrs. 3680 920

920 217 1519

139 qrs. =lbs.

=64 lbs. 920 230

230
2
2

139
.-. 13 cwt. 3 yrs. 11— lbs. •7-=1 cwt. 3 qrs. 6—- Ibs.

5
3

230

a

VI. TO DIVIDE A COMPOUND QUANTITY BY A DECIMAL FRACTION.

Rule. Convert the compound quantity into a decimal of one of its denominations; divide by the divisor, and express the result in positive terms.

If the divisor be a recurring decimal, it must be reduced fraction, and the division performed by the last case.

EXAMPLE. Divide £180 : 15 : 111 by 25.375.

4)1.0000 f. 12)11.2500 d.

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6.0 d.

63437 50750

126875 126875

Ans. £7:2:6.

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