SUBTRACTION OF DECIMALS.

RULE.

Place the number, as in addition, with the least under the greatest; and in the difference, set the point directly under those in the example.

1 From 100.17, take 84 476, what is left?

answer 15.694

2 What is the difference between the sum of 841.46+ 109.62+34 691, and of 478.462+37.66+378.8?

answer 90,849

MULTIPLICATION OF DECIMALS

RULE.

Multiply as in integers, and point off as many places in the product, as are in both the factors.

decimal

Note I. If the decimal places be wanting in the product, fupply them with ciphers to the decimal point.

2. Multiplication in decimals may be contracted thus;

Set the units figure of the multiplier under fuch place of the multipicand, as is to be the loweft retained in the product; and place all the remaining figures of the multiplier in an inverted order in multiply ing begin with the figure in the multiplicand which stands over the multiplying figure, adding the increase which may arife by carrying one for the first five. and one more for every ten after and place the products fo, that the right hand figures stand under each other.

EXAMPLES.

facit 39146,63239 305

39146,6 32 2 Multiply 79,347 by 23,15 facit 1836,88305 S Multiply ,63478

by ,8264 ,524582192 4 Multiply 3,141592 by 52,7438 165,6995001296 5 Multiply ,385746 by ,00463 ,00178600398 6 Multiply ,002534 by ,03256 ,00008250704

7 Multiply 245,378263 by 72,4385, reserving 4 places of decimals in the product

facit 17774,8333 8 Multiply 674,4375 by 27.368, reserving only the inte. gers in the product.

9 Multiply 27,14986 by 92.41035, and retain 6 places of decimals in the product.

facit 2508,928065 10 Multiply 184,8207 by 13,57493, and retain 3 places of decimals in the product.

facit 2508,928

facit 18458

DIVISION OF DECIMALS.

RULE.

When the dividend has not as many decimal places as the divisor, or will not contain it, annex ciphers to supply the defect ; then divide as in integers ; and point off in the quotient, as many decimal places as the decimal places of the dividend exceed those in the divisor, Or,

Let

Let the divisor be conceived to stand under the containing left hand figures of the dividend, and the first figure of the quotient will possess the same place of integers or decimals, as that in the dividend which corresponds to the units place of the divisor.

When there are many figures in the divisor, the operation may be contracted, thus

find what place of integers, or decimals, the first figure of the quotient will possess ; and consider how many quotient figures will serve the present purpose ; then take the same number of the left hand of the divisor, and as many of the dividend as will contain - them (less than ten times) rejecting the rest ; then, instead of bringing figures down from the dividend, separate one from the right of the divisor, as often as necessary, till the whole be exhausted; remembering to carry from the right hand figures of the divisor, as in contracted multiplication.

When there are not so many figures in the divisor, divide as usual, till there be as many of the quotient figures found as the divisor is short of the intended quotient; then use the contraction.

EXAMPLES.. 1. Divide 2508,92806 by 92,41035 92,41035)2508,92806(27,1498 + facit,

18482070

Contracted, so as to have three decimal places in the quotient. 92,4103,5)2508,92806(27,149+facit.

1848207

8 Divide ,00178600398 by ,60463

9

385746

Divide 2508,928065051 by 92,41035, so as to have 4

Note. The quotient must consist of as many decimal places, as there are ciphers annexed.

If a compound fraction be given, reduce it first to a single one.

8 What is the equivalent decimal for

9 What is the decimal of?

facit 5

75

,1923+ 45614+ ,6043956+ ,07766+ answer,375

5.7 36

,04

10 What are the equivalent decimals for 1⁄2, ¿, 18, Z and 142 answer 55, 95, 375, 1875, 10546875

236

CASE 2.

To reduce any sum, or quantity, to the decimal of a given denomination;

RULE.

First, Divide the given sum, &c. in its lowest mentioned denomination, by the number of like parts in the proposed integer; the quotient will be the decimal required. Or,

Secondly, Write the given numbers orderly from the least to the greatest in a perpendicular column, and divide each of them by such a number as will reduce it to the next name, annexing the quotient to the succeeding number; the last quotient will be the required decimal.

EXAMPLES